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The resulting flowfield is quite complex, and accurate predictions of the flow and heat transfer have been difficult to obtain, particularly in the near field of the injected jet. The flowfield is characterized by a spectrum of vortical structures including the dominant kidney vortex, the horse-shoe vortex, the wake vortices and the shear layer vortices. These anisotropic and unsteady structures are not well represented by empirical or ad-hoc turbulence models, and lead to inaccurate predictions in the near field of the jet. In this paper, a variety of modeling approaches have been reviewed, and the limitations of these approaches are identified. Recent emergence of Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) tools allow the resolution of the coherent structure dynamics, and it is shown in this paper, that such approaches provide improved predictions over that obtained with turbulence models.}, year = {2001} } @BOOK{Adam75, AUTHOR = {Adams, R.}, TITLE = {Sobolev Spaces}, PUBLISHER = {Academic Press}, YEAR = {1975}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {New York, London} } @ARTICLE{AdFo77, AUTHOR = {Adams, R. and Fournier, J.}, TITLE = {Cone conditions and properties of {S}obolev spaces}, YEAR = {1977}, JOURNAL = {J. Math. Anal. App.}, VOLUME = {61}, NUMBER = {}, PAGES = {713-734} } @INCOLLECTION{AdLe99, AUTHOR = {Adams, N.A. and Leonard, A.}, TITLE = {Deconvolution of subgrid scales for the simulation of shock-turbulence interaction}, BOOKTITLE = {Direct and Large Eddys Simulation III}, PUBLISHER = {Kluwer}, YEAR = {1999}, EDITOR = {P. Voke, N.D. Sandham and L. 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Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {12}, YEAR = {1959}, PAGES = {623--727}, ISSN = {0010-3640}, MRCLASS = {35.43}, MRNUMBER = {0125307 (23 \#A2610)}, MRREVIEWER = {E. Magenes}, } @article {MR3652175, AUTHOR = {Akbas, M. and Kaya, S. and Rebholz, L. G.}, TITLE = {On the stability at all times of linearly extrapolated {BDF}2 timestepping for multiphysics incompressible flow problems}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {33}, YEAR = {2017}, NUMBER = {4}, PAGES = {999--1017}, ISSN = {0749-159X}, MRCLASS = {65M20 (65L06 65L20 65M60 76D05)}, MRNUMBER = {3652175}, MRREVIEWER = {Alexander Ostermann}, DOI = {10.1002/num.22061}, URL = {https://doi.org/10.1002/num.22061}, } @ARTICLE{ABHM06, AUTHOR = {Akervik, E. and Brandt, L. and Henningson, D. S. and Hoepffner, J. and Marxen, O. and Schlatter, P.}, TITLE = {Steady solutions of the Navier-Stokes equations by selective frequency damping}, YEAR = {2006}, JOURNAL = {Physics of Fluids}, VOLUME = {}, NUMBER = {18}, PAGES = {68-102} } @article {MR2091397, AUTHOR = {Akrivis, Georgios and Smyrlis, Yiorgos-Sokratis}, TITLE = {Implicit-explicit {BDF} methods for the {K}uramoto-{S}ivashinsky equation}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {51}, YEAR = {2004}, NUMBER = {2-3}, PAGES = {151--169}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {65M06}, MRNUMBER = {2091397 (2005h:65126)}, MRREVIEWER = {Andrei I. Tolstykh}, DOI = {10.1016/j.apnum.2004.03.002}, URL = {http://dx.doi.org/10.1016/j.apnum.2004.03.002}, } @article {MR2026710, AUTHOR = {Akrivis, Georgios and Karakatsani, Fotini}, TITLE = {Modified implicit-explicit {BDF} methods for nonlinear parabolic equations}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {43}, YEAR = {2003}, NUMBER = {3}, PAGES = {467--483}, ISSN = {0006-3835}, MRCLASS = {65M20 (65L06)}, MRNUMBER = {2026710 (2004m:65139)}, MRREVIEWER = {Kathleen R. Fowler}, DOI = {10.1023/B:BITN.0000007057.13132.b3}, URL = {http://dx.doi.org/10.1023/B:BITN.0000007057.13132.b3}, } @article {MR1701828, AUTHOR = {Akrivis, Georgios and Crouzeix, Michel and Makridakis, Charalambos}, TITLE = {Implicit-explicit multistep methods for quasilinear parabolic equations}, JOURNAL = {Numer. 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Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {67}, YEAR = {1998}, NUMBER = {222}, PAGES = {457--477}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {65M60 (34G20 35K55 65M12)}, MRNUMBER = {1458216 (98g:65088)}, MRREVIEWER = {Bruno Scheurer}, DOI = {10.1090/S0025-5718-98-00930-2}, URL = {http://dx.doi.org/10.1090/S0025-5718-98-00930-2}, } @ARTICLE{Alek03, AUTHOR = {Alekseev, G.V.}, TITLE = {Control problems for the steady-state equations of magnetohydrodynamics of a viscous incompressible fluid}, YEAR = {2003}, JOURNAL = {J. Appl. Mech. Tech. Phys.}, VOLUME = {44}, NUMBER = {6}, PAGES = {890-898} } @ARTICLE{Alek04, AUTHOR = {Alekseev, G.V.}, TITLE = {Solvability of control problems for stationary equations of magnetohydrodynamics of a viscous fluid}, YEAR = {2004}, JOURNAL = {Siberian Math. J.}, VOLUME = {45}, NUMBER = {2}, PAGES = {197-213} } @article {MR3257642, AUTHOR = {Alexanderian, Alen and Petra, Noemi and Stadler, Georg and Ghattas, Omar}, TITLE = {A-optimal design of experiments for infinite-dimensional {B}ayesian linear inverse problems with regularized {$\ell_0$}-sparsification}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {36}, YEAR = {2014}, NUMBER = {5}, PAGES = {A2122--A2148}, ISSN = {1064-8275}, MRCLASS = {62K05 (35R30 62F15 65C60)}, MRNUMBER = {3257642}, DOI = {10.1137/130933381}, URL = {http://dx.doi.org/10.1137/130933381}, } @ARTICLE{Alfv42, AUTHOR = {Alfv\'{e}n, H.}, TITLE = {Existence of electromagnetic-hydrodynamic waves}, YEAR = {1942}, JOURNAL = {Nature}, VOLUME = {150}, NUMBER = {}, PAGES = {405} } @article {MR3249674, AUTHOR = {Allaire, Douglas and Willcox, Karen}, TITLE = {A mathematical and computational framework for multifidelity design and analysis with computer models}, JOURNAL = {Int. J. Uncertain. Quantif.}, FJOURNAL = {International Journal for Uncertainty Quantification}, VOLUME = {4}, YEAR = {2014}, NUMBER = {1}, PAGES = {1--20}, ISSN = {2152-5080}, MRCLASS = {Database Expansion Item}, MRNUMBER = {3249674}, DOI = {10.1615/Int.J.UncertaintyQuantification.2013004121}, URL = {http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2013004121}, } @inbook{doi:10.2514/6.2006-5274, author = {Juan Alonso and Seonghyeon Hahn and Frank Ham and Marcus Herrmann and Gianluca Iaccarino and Georgi Kalitzin and Patrick LeGresley and Ken Mattsson and Gorazd Medic and Parviz Moin and Heinz Pitsch and Jorg Schluter and Magnus Svard and Edwin van der Weide and Donghyun You and Xiaohua Wu}, title = {CHIMPS: A High-Performance Scalable Module for Multi-Physics Simulations}, booktitle = {42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference \& Exhibit}, chapter = {}, pages = {}, doi = {10.2514/6.2006-5274}, URL = {https://arc.aiaa.org/doi/abs/10.2514/6.2006-5274}, eprint = {https://arc.aiaa.org/doi/pdf/10.2514/6.2006-5274} } @article {MR2486839, AUTHOR = {Amara, Mohamed and Capatina, Daniela and Lizaik, L.}, TITLE = {Coupling of {D}arcy-{F}orchheimer and compressible {N}avier-{S}tokes equations with heat transfer}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {31}, YEAR = {2008/09}, NUMBER = {2}, PAGES = {1470--1499}, ISSN = {1064-8275}, MRCLASS = {65M60 (76S05 80A20)}, MRNUMBER = {2486839}, DOI = {10.1137/070709517}, URL = {https://doi.org/10.1137/070709517}, } @ARTICLE{AmAl05, AUTHOR = {Ambrosino, G. and Albanese, R.}, TITLE = {Magnetic control of plasma current, position, and shape in tokamaks: A survey of modeling and control approaches}, YEAR = {2005}, JOURNAL = {Control Syst. Mag.}, VOLUME = {25}, NUMBER = {5}, PAGES = {76-92} } @article{AmezKalWil11, Annote = {doi: 10.1175/2010MWR3530.1}, Author = {Amezcua, Javier and Kalnay, Eugenia and Williams, Paul D.}, Booktitle = {Monthly Weather Review}, Da = {2011/02/01}, Date = {2010/10/08}, Date-Added = {2012-11-10 00:22:21 +0000}, Date-Modified = {2012-11-10 00:22:48 +0000}, Doi = {10.1175/2010MWR3530.1}, Isbn = {0027-0644}, Journal = {Mon. Wea. Rev.}, FJournal = {Monthly Weather Review}, M3 = {doi: 10.1175/2010MWR3530.1}, Month = {2012/11/09}, Number = {2}, Pages = {608--619}, Publisher = {American Meteorological Society}, Title = {The Effects of the {RAW} Filter on the Climatology and Forecast Skill of the {SPEEDY} Model}, Ty = {JOUR}, Url = {http://dx.doi.org/10.1175/2010MWR3530.1}, Volume = {139}, Year = {2011}, Year1 = {2010}, Bdsk-Url-1 = {http://dx.doi.org/10.1175/2010MWR3530.1} } @article {AmezWill14, author = {Amezcua, Javier and Williams, Paul D.}, title = {The composite-tendency {Robert--Asselin--Williams (RAW)} filter in semi-implicit integrations}, journal={Q. J. R. Meteorol. Soc}, fjournal = {Quarterly Journal of the Royal Meteorological Society}, publisher = {John Wiley & Sons, Ltd}, issn = {1477-870X}, url = {http://dx.doi.org/10.1002/qj.2391}, keywords = {semi-implicit methods, leap-frog, Robert–Asselin, numerical integration}, year = {2015}, doi={doi:10.1002/qj.2391} } @ARTICLE{AmGi94, AUTHOR = {Amrouche, C. and Girault, V.}, TITLE = {Decomposition of vector spaces and application to the {S}tokes problem in arbitrary dimension}, YEAR = {1994}, JOURNAL = {Czechoslovak Math. J.}, VOLUME = {44(119)}, NUMBER = {1}, PAGES = {109-140} } @article {MR1309165, AUTHOR = {Amrouche, C. and Girault, V. and Giroire, J.}, TITLE = {Weighted {S}obolev spaces for {L}aplace's equation in {$\bold R^n$}}, JOURNAL = {J. Math. Pures Appl. (9)}, FJOURNAL = {Journal de Math\'ematiques Pures et Appliqu\'ees. Neuvi\`eme S\'erie}, VOLUME = {73}, YEAR = {1994}, NUMBER = {6}, PAGES = {579--606}, ISSN = {0021-7824}, CODEN = {JMPAAM}, MRCLASS = {46E35 (35J05)}, MRNUMBER = {1309165 (96h:46038)}, } @inproceedings {MR1844267, AUTHOR = {Amrouche, Cherif and Ne{\v{c}}asov{\'a}, {\v{S}}{\'a}rka}, TITLE = {Laplace equation in the half-space with a nonhomogeneous {D}irichlet boundary condition}, BOOKTITLE = {Proceedings of {P}artial {D}ifferential {E}quations and {A}pplications ({O}lomouc, 1999)}, JOURNAL = {Math. Bohem.}, FJOURNAL = {Academy of Sciences of the Czech Republic. Mathematical Institute. Mathematica Bohemica}, VOLUME = {126}, YEAR = {2001}, PAGES = {265--274}, ISSN = {0862-7959}, MRCLASS = {35J05 (35A05 35B65 35J25)}, MRNUMBER = {1844267 (2002e:35057)}, } @ARTICLE{AL77, AUTHOR = {Andr{\'{e}}, J.C. and Lesieur, M.}, TITLE = {Influence of helicity on the evolution of isotropic turbulence at high {R}eynolds number}, YEAR = {1977}, JOURNAL = {J. Fluid Mech.}, FJOURNAL = {Journal of Fluid Mechanics}, VOLUME = {81}, NUMBER = {}, PAGES = {187-207} } @ARTICLE{AP06, AUTHOR = {Andrieu, V. and Praly, L.}, TITLE = {On the existence of a {K}azantzis-{K}ravaris/{L}uenberger observer}, YEAR = {2006}, JOURNAL = {SIAM J. Control Optim.}, VOLUME = {45}, NUMBER = {2}, PAGES = {432--456} } @ARTICLE{Anit90, AUTHOR = {Ani{\c t}a, S.}, TITLE = {Optimal control of a nonlinear population dynamics with diffusion}, YEAR = {1990}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {152}, NUMBER = {1}, PAGES = {176-208} } @ARTICLE{Anit00, AUTHOR = {Ani{\c t}a, S.}, TITLE = {A fractional step scheme for the optimal control of a nonlinear population dynamics with diffusion}, YEAR = {2000}, JOURNAL = {An. {\c S}tiin{\c t}. Univ. Al. I. Cuza Ia{\c s}i Mat.}, VOLUME = {46}, NUMBER = {1}, PAGES = {157-168} } @article {MR2150767, AUTHOR = {Anitescu, Mihai and Pahlevani, Faranak and Layton, William J.}, TITLE = {Implicit for local effects and explicit for nonlocal effects is unconditionally stable}, JOURNAL = {Electron. Trans. Numer. Anal.}, FJOURNAL = {Electronic Transactions on Numerical Analysis}, VOLUME = {18}, YEAR = {2004}, PAGES = {174--187 (electronic)}, ISSN = {1068-9613}, MRCLASS = {65L05 (65M20)}, MRNUMBER = {2150767 (2006g:65095)}, MRREVIEWER = {Kevin Burrage}, } @article{10.1137/050631161, title = {Sensitivities in Large Eddy Simulation and Improved Estimates of Turbulent Flow Functionals}, publisher = {SIAM}, year = {2007}, doi = {DOI:10.1137/050631161}, issn = {10648275}, eissn = {10957197}, coden = {SJOCE3}, volume = {29}, number = {4}, pages = {1650-1667}, author = {Mihai Anitescu and William J. Layton}, keywords = {large eddy simulations; sensitivity; turbulence; 76D05; 35Q30; 90C31; }, url = {http://dx.doi.org/doi/10.1137/050631161}, } @ARTICLE{Aoyagi95, AUTHOR = {Aoyagi, A.}, TITLE = {Nonlinear leapfrog instability for {Fornberg's} pattern}, YEAR = {1995}, JOURNAL = {J. Comput. Phys.}, FJOURNAL ={Journal of Computational Physics}, VOLUME = {120}, NUMBER = {2}, PAGES = {316--322} } @book {MR0344384, AUTHOR = {Apostol, Tom M.}, TITLE = {Mathematical analysis}, EDITION = {Second}, PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.}, YEAR = {1974}, PAGES = {xvii+492}, MRCLASS = {26-01 (28-01)}, MRNUMBER = {MR0344384 (49 \#9123)}, } @ARTICLE{Apre98, AUTHOR = {Apreutesei, N.}, TITLE = {An optimal control problem of {L}otka-{V}olterra system with diffusion}, YEAR = {1998}, JOURNAL = {Bul. Inst. Politeh. Ia{\c s}i. Sec{\c t}. I. Mat. Mec. Teor. Fiz.}, VOLUME = {44(48)}, NUMBER = {1-2}, PAGES = {31-41} } @article {MR2344200, AUTHOR = {Arbogast, Todd and Brunson, Dana S.}, TITLE = {A computational method for approximating a {D}arcy-{S}tokes system governing a vuggy porous medium}, JOURNAL = {Comput. Geosci.}, FJOURNAL = {Computational Geosciences}, VOLUME = {11}, YEAR = {2007}, NUMBER = {3}, PAGES = {207--218}, ISSN = {1420-0597}, MRCLASS = {76S05 (65N30 76D07 76M10)}, MRNUMBER = {2344200}, MRREVIEWER = {Benito M. Chen-Charpentier}, DOI = {10.1007/s10596-007-9043-0}, URL = {https://doi.org/10.1007/s10596-007-9043-0}, } @article {MR1393572, AUTHOR = {Armero, F. and Simo, J. C.}, TITLE = {Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible {MHD} and {N}avier-{S}tokes equations}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {131}, YEAR = {1996}, NUMBER = {1-2}, PAGES = {41--90}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {76M10 (65M60 76W05)}, MRNUMBER = {1393572 (97g:76050)}, MRREVIEWER = {Michael Fr{\"o}hner}, DOI = {10.1016/0045-7825(95)00931-0}, URL = {http://dx.doi.org/10.1016/0045-7825(95)00931-0}, } @book {MR2042131, AUTHOR = {Arn\u{a}utu, Viorel and Neittaanm\"{a}ki, Pekka}, TITLE = {Optimal control from theory to computer programs}, SERIES = {Solid Mechanics and its Applications}, VOLUME = {111}, PUBLISHER = {Kluwer Academic Publishers Group, Dordrecht}, YEAR = {2003}, PAGES = {x+324}, ISBN = {1-4020-1771-5}, MRCLASS = {49-02 (49-04 49J20 49K20)}, MRNUMBER = {2042131}, MRREVIEWER = {William W. Hager}, DOI = {10.1007/978-94-017-2488-3}, URL = {https://doi.org/10.1007/978-94-017-2488-3}, } @BOOK{AR02, AUTHOR = {Archimedes, T. L. Heath (Translator)}, TITLE = {The Works of Archimedes}, PUBLISHER = {Dover}, YEAR = {2002}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @article {AsRuWe95, AUTHOR = {Ascher, Uri M. and Ruuth, Steven J. and Wetton, Brian T. R.}, TITLE = {Implicit-explicit methods for time-dependent partial differential equations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {32}, YEAR = {1995}, NUMBER = {3}, PAGES = {797--823}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65Mxx (65J15)}, MRNUMBER = {1335656 (96j:65076)}, MRREVIEWER = {K. B{\"o}hmer}, DOI = {10.1137/0732037}, URL = {http://dx.doi.org/10.1137/0732037}, } @article {ARW95, AUTHOR = {Ascher, Uri M. and Ruuth, Steven J. and Wetton, Brian T. R.}, TITLE = {Implicit-explicit methods for time-dependent partial differential equations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {32}, YEAR = {1995}, NUMBER = {3}, PAGES = {797--823}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65Mxx (65J15)}, MRNUMBER = {MR1335656 (96j:65076)}, MRREVIEWER = {K. B{\"o}hmer}, DOI = {10.1137/0732037}, URL = {http://dx.doi.org/10.1137/0732037}, } @book {MR1638643, AUTHOR = {Ascher, Uri M. and Petzold, Linda R.}, TITLE = {Computer methods for ordinary differential equations and differential-algebraic equations}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA}, YEAR = {1998}, PAGES = {xviii+314}, ISBN = {0-89871-412-5}, MRCLASS = {65Lxx (34A09 34A45 65-01)}, MRNUMBER = {1638643}, MRREVIEWER = {Michael Hanke}, DOI = {10.1137/1.9781611971392}, URL = {https://doi.org/10.1137/1.9781611971392}, } @article{Asselin_72, Annote = {doi: 10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2}, Author = {Asselin, Richard}, Booktitle = {Monthly Weather Review}, Da = {1972/06/01}, Date = {1972/06/01}, Date-Added = {2012-11-09 23:34:21 +0000}, Date-Modified = {2012-11-09 23:35:11 +0000}, Doi = {10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2}, Isbn = {0027-0644}, FJournal = {Monthly Weather Review}, Journal = {Mon. Wea. Rev.}, M3 = {doi: 10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2}, Month = {2012/11/09}, Number = {6}, Pages = {487--490}, Publisher = {American Meteorological Society}, Read = {1}, Title = {Frequency Filter for Time Integrations}, Ty = {JOUR}, Url = {http://dx.doi.org/10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2}, Volume = {100}, Year = {1972}, Year1 = {1972}, Bdsk-Url-1 = {http://dx.doi.org/10.1175/1520-0493(1972)100%3C0487:FFFTI%3E2.3.CO;2}} @BOOK{Atki89, AUTHOR = {Atkinson, K.}, TITLE = {An Introduction to Numerical Analysis, 2nd Edition }, PUBLISHER = {John Wiley \& Sons Canada}, YEAR = {1989}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @article {MR1427468, AUTHOR = {Axelsson, O. and Layton, W.}, TITLE = {A two-level discretization of nonlinear boundary value problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {33}, YEAR = {1996}, NUMBER = {6}, PAGES = {2359--2374}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65N30 (65J15)}, MRNUMBER = {1427468 (98c:65181)}, MRREVIEWER = {A. V. Dzhishkariani}, DOI = {10.1137/S0036142993247104}, URL = {http://dx.doi.org/10.1137/S0036142993247104}, } @article{10.1115/1.1485294, author = {Azzi, A. and Lakehal, D. }, title = "{Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models }", journal = {Journal of Turbomachinery}, volume = {124}, number = {3}, pages = {472-484}, year = {2002}, month = {07}, abstract = "{The paper presents recent trends in modeling jets in crossflow with relevance to film cooling of turbine blades. The aim is to compare two classes of turbulence models with respect to their predictive performance in reproducing near-wall flow physics and heat transfer. The study focuses on anisotropic eddy-viscosity/diffusivity models and explicit algebraic stress models, up to cubic fragments of strain and vorticity tensors. The first class of models are direct numerical simulation (DNS) based two-layer approaches transcending the conventional k−ε model by means of a nonisotropic representation of the turbulent transport coefficients; this is employed in connection with a near-wall one-equation model resolving the semi-viscous sublayer. The aspects of this new strategy are based on known channel-flow and boundary layer DNS statistics. The other class of models are quadratic and cubic explicit algebraic stress formulations rigorously derived from second-moment closures. The stress-strain relations are solved in the context of a two-layer strategy resolving the near-wall region by means of a nonlinear one-equation model; the outer core flow is treated by use of the two-equation model. The models are tested for the film cooling of a flat plate by a row of streamwise injected jets. Comparison of the calculated and measured wall-temperature distributions shows that only the anisotropic eddy-viscosity/diffusivity model can correctly predict the spanwise spreading of the temperature field and reduce the strength of the secondary vortices. The wall-cooling effectiveness was found to essentially depend on these two particular flow features. The non-linear algebraic stress models were of a mixed quality in film-cooling calculations. }", issn = {0889-504X}, doi = {10.1115/1.1485294}, url = {https://doi.org/10.1115/1.1485294}, eprint = {https://asmedigitalcollection.asme.org/turbomachinery/article-pdf/124/3/472/5605290/472\_1.pdf}, } @ARTICLE{Babuska_Tempone_Zouraris_04, AUTHOR = {Babu\v{s}ka, I.M. and Tempone, R. and Zouraris, G.E.}, TITLE = {Galerkin finite element approximations of stochastic elliptic partial differential equations}, YEAR = {2004}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {42}, NUMBER = {2}, PAGES = {800-825} } @article {MR2121215, AUTHOR = {Babu{\v{s}}ka, Ivo and Tempone, Ra{\'u}l and Zouraris, Georgios E.}, TITLE = {Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {194}, YEAR = {2005}, NUMBER = {12-16}, PAGES = {1251--1294}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {65N30 (60H15 60H35)}, MRNUMBER = {MR2121215 (2005j:65134)}, } @techreport{babusk_nobile_temp_05, Author = {Babu{\v{s}}ka, I.M. and Tempone, R. and Nobile, F.}, Institution = {MOX, Dipartimento di Matematica}, Title = {A stochastic collocation method for elliptic partial differential equations with random input data}, Year = {2005}} @article {MR2318799, AUTHOR = {Babu{\v{s}}ka, Ivo and Nobile, Fabio and Tempone, Ra{\'u}l}, TITLE = {A stochastic collocation method for elliptic partial differential equations with random input data}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {45}, YEAR = {2007}, NUMBER = {3}, PAGES = {1005--1034 (electronic) }, ISSN = {0036-1429}, MRCLASS = {65N35 (65C30)}, MRNUMBER = {MR2318799 (2008e:65372)}, MRREVIEWER = {Renato G. C. Spigler}, } @techreport{B76, Author = {G. Baker}, Institution = {Harvard University}, Title = {Galerkin Approximations for the {Navier-Stokes} Equations}, Year = {1976}} @Unpublished{Bakerxxx, author = {G. Baker}, title = {Galerkin Approximations for the {Navier-Stokes} Equations}, note = {Harvard University}, OPTkey = {}, month = {August}, year = {1976}, OPTannote = {} } @BOOK{B76xxxxx, AUTHOR = {Baker, B.}, TITLE = {Galerkin Approximations for the {N}avier-{S}tokes Equations}, PUBLISHER = {Harvard University}, YEAR = {1976}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @article {MR669634, AUTHOR = {Baker, Garth A. and Dougalis, Vassilios A. and Karakashian, Ohannes A.}, TITLE = {On a higher order accurate fully discrete {G}alerkin approximation to the {N}avier-{S}tokes equations}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {39}, YEAR = {1982}, NUMBER = {160}, PAGES = {339--375}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {65M60 (65N30 76D05)}, MRNUMBER = {669634 (84h:65096)}, DOI = {10.2307/2007319}, URL = {http://dx.doi.org/10.2307/2007319}, } @article {MR3031839, AUTHOR = {Bal, Guillaume and Langmore, Ian and Marzouk, Youssef}, TITLE = {Bayesian inverse problems with {M}onte {C}arlo forward models}, JOURNAL = {Inverse Probl. Imaging}, FJOURNAL = {Inverse Problems and Imaging}, VOLUME = {7}, YEAR = {2013}, NUMBER = {1}, PAGES = {81--105}, ISSN = {1930-8337}, MRCLASS = {60J22 (45Q05 62F15 65C05)}, MRNUMBER = {3031839}, DOI = {10.3934/ipi.2013.7.81}, URL = {http://dx.doi.org/10.3934/ipi.2013.7.81}, } @ARTICLE{Ball77, AUTHOR = {Ball, J.M.}, TITLE = {Remarks on blow-up and nonexistence theorems for nonlinear evolution equations}, YEAR = {1977}, JOURNAL = {Quart. J. Math. Oxford}, VOLUME = {2}, NUMBER = {28}, PAGES = {473-486} } @article {MR1664239, AUTHOR = {Balsara, D. and Pouquet, A.}, TITLE = {The formation of large-scale structures in supersonic magnetohydrodynamic flows}, JOURNAL = {Phys. Plasmas}, FJOURNAL = {Physics of Plasmas}, VOLUME = {6}, YEAR = {1999}, NUMBER = {1}, PAGES = {89--99}, ISSN = {1070-664X}, CODEN = {PHPAEN}, MRCLASS = {76W05 (85A30)}, MRNUMBER = {1664239 (99i:76147)}, DOI = {10.1063/1.873263}, URL = {http://dx.doi.org/10.1063/1.873263}, } @BOOK{BaKu89, AUTHOR = {Banks, H.T. and Kunisch, K.}, TITLE = {Estimation Techniques for Distributed Parameter Systems}, PUBLISHER = {Birkh\"auser}, YEAR = {1989}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {Boston} } @article {MR2305825, AUTHOR = {Barbato, David and Berselli, Luigi C. and Grisanti, Carlo R.}, TITLE = {Analytical and numerical results for the rational large eddy simulation model}, JOURNAL = {J. Math. Fluid Mech.}, FJOURNAL = {Journal of Mathematical Fluid Mechanics}, VOLUME = {9}, YEAR = {2007}, NUMBER = {1}, PAGES = {44--74}, ISSN = {1422-6928}, MRCLASS = {76F65 (35Q35 76D03)}, MRNUMBER = {2305825 (2009b:76080)}, DOI = {10.1007/s00021-006-0191-0}, URL = {http://dx.doi.org/10.1007/s00021-006-0191-0}, } @article {MR2102747, AUTHOR = {Barbu, Viorel and Da Prato, Giuseppe and Debussche, Arnaud}, TITLE = {Essential {$m$}-dissipativity of {K}olmogorov operators corresponding to periodic 2{D}-{N}avier {S}tokes equations}, JOURNAL = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.}, FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni}, VOLUME = {15}, YEAR = {2004}, NUMBER = {1}, PAGES = {29--38}, ISSN = {1120-6330}, MRCLASS = {35R60 (35Q30 37L40 60H15 76D05 76M35)}, MRNUMBER = {2102747}, MRREVIEWER = {Ana Bela Cruzeiro}, } @article {MR2352934, AUTHOR = {Barbu, Viorel and Da Prato, Giuseppe}, TITLE = {Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations}, JOURNAL = {Appl. Math. Optim.}, FJOURNAL = {Applied Mathematics and Optimization. An International Journal with Applications to Stochastics}, VOLUME = {56}, YEAR = {2007}, NUMBER = {2}, PAGES = {145--168}, ISSN = {0095-4616}, CODEN = {AMOMBN}, MRCLASS = {76M35 (35Q35 35R60 37A25 60H15 76D03 76W05)}, MRNUMBER = {2352934 (2008i:76157)}, MRREVIEWER = {Gheorghe Procopiuc}, DOI = {10.1007/s00245-007-0882-2}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1007/s00245-007-0882-2}, } @book{1213.76001, author="Barbu, Viorel", title="{Stabilization of Navier-Stokes flows}", language="English", publisher="{London: Springer}", year="2011", doi={10.1007/978-0-85729-043-4}, abstract="{The purpose of the paper is to analyse the stabilization of Navier-Stokes flows. One of its main results is that the equilibrium solutions of Navier-Stokes equations are exponentially stabilizable by finite-dimensional feedback controllers with support in the interior of the domain or on the boundary. The author also discusses the stochastic stabilization and robustness of stabilizable feedbacks. This analysis provides a pattern for the design of efficient stabilizable feedback controllers in problems of practical interest. The book is organized as follows. After some preliminaries, a few stabilization techniques for nonlinear parabolic-like equations in Hilbert spaces are presented. In Chapter 3 the feedback stabilization of stationary solutions of Navier-Stokes equations are discussed. The next two chapters deal with the stochastic stabilization of Navier-Stokes equations and with the robust stabilization of Navier-Stokes equations via the $H^\infty$-control theory, respectively.}", reviewer="{Ruxandra Stavre (Bucure\c{s}ti)}", keywords="{internal stabilization; boundary stabilization; stochastic stabilization; robust stabilizable feedback}", classmath="{76-02 (Research monographs (fluid mechanics)) 76D55 (Flow control and optimization) 76D03 (Existence, uniqueness, and regularity theory) 35Q30 (Stokes and Navier-Stokes equations) }", } @book {BarbuStabilization2011, AUTHOR = {Barbu, Viorel}, TITLE = {Stabilization of {N}avier-{S}tokes flows}, SERIES = {Communications and Control Engineering Series}, PUBLISHER = {Springer, London}, YEAR = {2011}, PAGES = {xii+276}, ISBN = {978-0-85729-042-7; 978-0-85729-043-4}, MRCLASS = {93-02 (35Q30 76D05 93C20 93D15)}, MRNUMBER = {3186318}, DOI = {10.1007/978-0-85729-043-4}, URL = {http://dx.doi.org/10.1007/978-0-85729-043-4}, } Barb76 @book {MR0390843, AUTHOR = {Barbu, Viorel}, TITLE = {Nonlinear semigroups and differential equations in {B}anach spaces}, NOTE = {Revised and enlarged translation of the Romanian ed.}, PUBLISHER = {Bucuresti: Editura Academiei; Leyden, The Netherlands: Noordhoff International Publishing}, YEAR = {1976}, PAGES = {352}, MRCLASS = {47HXX (34G05 47D05)}, MRNUMBER = {0390843 (52 \#11666)}, } %MR1195128 @book{Barb93, AUTHOR = {Barbu, Viorel}, TITLE = {Analysis and control of nonlinear infinite-dimensional systems}, SERIES = {Mathematics in Science and Engineering}, VOLUME = {190}, PUBLISHER = {Academic Press Inc.}, ADDRESS = {Boston, MA}, YEAR = {1993}, PAGES = {x+476}, ISBN = {0-12-078145-X}, MRCLASS = {49-02 (47N70 49J27 49J40 49K20 49K27 93C20)}, MRNUMBER = {MR1195128 (93j:49002)}, MRREVIEWER = {Asen L. Dontchev}, } @book {MR1636579, AUTHOR = {Barbu, Viorel}, TITLE = {Partial differential equations and boundary value problems}, SERIES = {Mathematics and its Applications}, VOLUME = {441}, NOTE = {Translated and revised from the 1993 Romanian original by the author}, PUBLISHER = {Kluwer Academic Publishers}, ADDRESS = {Dordrecht}, YEAR = {1998}, PAGES = {xii+277}, ISBN = {0-7923-5056-1}, MRCLASS = {35-01}, MRNUMBER = {1636579 (2000e:35002)}, MRREVIEWER = {L. Recke}, } @book {MR2582280, AUTHOR = {Barbu, Viorel}, TITLE = {Nonlinear differential equations of monotone types in {B}anach spaces}, SERIES = {Springer Monographs in Mathematics}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2010}, PAGES = {x+272}, ISBN = {978-1-4419-5541-8}, MRCLASS = {34-02 (34G20 34G25 35A16 47J35 47N20)}, MRNUMBER = {2582280 (2011d:34001)}, MRREVIEWER = {Jean Mawhin}, DOI = {10.1007/978-1-4419-5542-5}, URL = {http://dx.doi.org/10.1007/978-1-4419-5542-5}, } @BOOK{Barb01, AUTHOR = {Barbu, Viorel}, TITLE = {Convexity and Optimization in Banach Spaces}, PUBLISHER = {Kluwer Academic Publishers}, YEAR = {2001}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @book {MR860772, AUTHOR = {Barbu, V. and Precupanu, Th.}, TITLE = {Convexity and optimization in {B}anach spaces}, SERIES = {Mathematics and its Applications (East European Series)}, VOLUME = {10}, EDITION = {Romanian}, EDITION = {Second}, PUBLISHER = {D. Reidel Publishing Co., Dordrecht; Editura Academiei Republicii Socialiste Rom\^{a}nia, Bucharest}, YEAR = {1986}, PAGES = {xviii+397}, ISBN = {90-277-1761-3}, MRCLASS = {49D45 (46-02 49A22 90C48)}, MRNUMBER = {860772}, } @ARTICLE{BarbuKu96, AUTHOR = {Barbu, V. and Kunisch, K.}, TITLE = {Identification of Nonlinear Elliptic Equations}, YEAR = {1996}, JOURNAL = {Appl. Math. Optim}, VOLUME = {33}, NUMBER = {}, PAGES = {139-167} } @ARTICLE{Barb98, AUTHOR = {Barbu, Viorel}, TITLE = {Optimal control of {N}avier-{S}tokes equations with periodic inputs}, YEAR = {1998}, JOURNAL = {Nonlinear Analysis, Theory, Methods \& Applications}, VOLUME = {31}, NUMBER = {}, PAGES = {15-31} } MR1813822 - BS01 @article {BS01, AUTHOR = {Barbu, V. and Sritharan, S. S.}, TITLE = {Flow invariance preserving feedback controllers for the {N}avier-{S}tokes equation}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {255}, YEAR = {2001}, NUMBER = {1}, PAGES = {281--307}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {93C20 (35B37 35Q30 76D03 93B52)}, MRNUMBER = {MR1813822 (2002c:93086)}, MRREVIEWER = {Enrique Fern{\'a}ndez Cara}, } AUTHOR = {Barbu, V. and Sritharan, S.S.}, TITLE = {Flow Invariance Preserving Feedback Controllers for the {N}avier-{S}tokes Equation}, YEAR = {2001}, JOURNAL = {J. Math. Anal. Appl.}, VOLUME = {255}, NUMBER = {1}, PAGES = {281-307} } @ARTICLE{barb09a, AUTHOR = {Barbu, Viorel}, TITLE = {The Stabilization by noise of the linearized {Navier-Stokes} equation}, YEAR = {2009}, JOURNAL = {}, VOLUME = {}, NUMBER = {}, PAGES = {preprint} } @article {MR1959739, AUTHOR = {Barbu, Viorel and Hav{\^a}rneanu, Teodor and Popa, C{\u{a}}t{\u{a}}lin and Sritharan, S. S.}, TITLE = {Exact controllability for the magnetohydrodynamic equations}, JOURNAL = {Comm. Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {56}, YEAR = {2003}, NUMBER = {6}, PAGES = {732--783}, ISSN = {0010-3640}, CODEN = {CPAMA}, MRCLASS = {93B05 (35Q35 76D55 76W05 93C20)}, MRNUMBER = {1959739 (2004b:93012)}, MRREVIEWER = {Mary Ann Horn}, DOI = {10.1002/cpa.10072}, URL = {http://dx.doi.org/10.1002/cpa.10072}, } @article {MR1478658, AUTHOR = {Barbu, Viorel}, TITLE = {Optimal control of linear periodic resonant systems in {H}ilbert spaces}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {35}, YEAR = {1997}, NUMBER = {6}, PAGES = {2137--2156}, ISSN = {0363-0129}, CODEN = {SJCODE}, MRCLASS = {49J20}, MRNUMBER = {1478658 (98j:49004)}, MRREVIEWER = {Nicolae H. Pavel}, DOI = {10.1137/S036301299529478X}, URL = {http://dx.doi.org/10.1137/S036301299529478X}, } @phdthesis{Bar83, Author = {Bardina, J.}, Date-Added = {}, Date-Modified = {}, School = {Stanford University}, Title = {Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows}, Year = {1983}} @article{Barleon1991401, title = "{MHD} flow in liquid-metal-cooled blankets", journal={Fusion Eng. Des.}, fjournal={Fusion Engineering and Design}, volume = "14", pages = "401 - 412", year = "1991", note = "", issn = "0920-3796", doi = "10.1016/0920-3796(91)90021-H", url = "http://www.sciencedirect.com/science/article/pii/092037969190021H", author = "L. Barleon and V. Casal and L. Lenhart" } @ARTICLE{BaBl04, AUTHOR = {Barrett, J. and Blowey, J.}, TITLE = {Finite element approximations of a nonlinear cross-diffusion population model}, YEAR = {2004}, JOURNAL = {Numer. Math.}, VOLUME = {98}, NUMBER = {}, PAGES = {195-221} } @article {MR2328834, AUTHOR = {Barrow, John D. and Maartens, Roy and Tsagas, Christos G.}, TITLE = {Cosmology with inhomogeneous magnetic fields}, JOURNAL = {Phys. Rep.}, FJOURNAL = {Physics Reports. A Review Section of Physics Letters}, VOLUME = {449}, YEAR = {2007}, NUMBER = {6}, PAGES = {131--171}, ISSN = {0370-1573}, CODEN = {PRPLCM}, MRCLASS = {83F05}, MRNUMBER = {2328834 (2008e:83115)}, MRREVIEWER = {C. Gauthier}, DOI = {10.1016/j.physrep.2007.04.006}, URL = {http://dx.doi.org/10.1016/j.physrep.2007.04.006}, } @BOOK{Ba96, AUTHOR = {Batchelor, G.K.}, TITLE = {The Life and Legacy of G. I. Taylor}, PUBLISHER = {Cambridge Univ. Press}, YEAR = {1996}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @BOOK{Ba02, AUTHOR = {Batchelor, G.K.}, TITLE = {An introduction to fluid dynamics}, PUBLISHER = {Cambridge Univ. Press}, YEAR = {2002}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @book{BearCheng2010, author = {Bear, Jacob and Cheng, Alexander}, year = {2010}, month = {01}, pages = {}, title = {Modeling Groundwater Flow and Contaminant Transport}, volume = {23}, journal = {Springer, Dordrecht}, doi = {10.1007/978-1-4020-6682-5} } @book{bear1979hydraulics, title={Hydraulics of Groundwater}, author={Bear, Jacob}, isbn={0070041709 9780070041707}, series={Dover Books on Engineering}, year={1979}, publisher={McGraw-Hill Book Co.} } @article{Beausoleil-Morrison2002, author = {Beausoleil-Morrison, Ian}, year = {2002}, month = {10}, pages = {857-871}, title = {The adaptive coupling of computational fluid dynamics with whole-building thermal simulation}, volume = {34}, journal = {Energy and Buildings}, doi = {10.1016/S0378-7788(02)00061-0} } @article{beavers_joseph_1967, title={Boundary conditions at a naturally permeable wall}, volume={30}, DOI={10.1017/S0022112067001375}, number={1}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press}, author={Beavers, Gordon S. and Joseph, Daniel D.}, year={1967}, pages={197-€“207} } @article{FLM:381918, title={Boundary conditions at a naturally permeable wall}, volume={30}, DOI={10.1017/S0022112067001375}, number={1}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press}, author={Beavers, Gordon S. and Joseph, Daniel D.}, year={1967}, pages={197-207} } @ARTICLE{Berg96, AUTHOR = {Berger, M.A.}, TITLE = {Inverse Cascades in a periodic domain}, YEAR = {1996}, JOURNAL = {Astrophysical Letters and Communications}, VOLUME = {34}, NUMBER = {}, PAGES = {225-230} } @ARTICLE{Berg97, AUTHOR = {Berger, M.A.}, TITLE = {Magnetic helicity in a periodic domain}, YEAR = {1997}, JOURNAL = {J. Geophys. Res.}, VOLUME = {102}, NUMBER = {}, PAGES = {2637--2644} } @ARTICLE{BKLL00, AUTHOR = {Berger, T. and Kim, J. and Lee, C. and Lim, J.}, TITLE = {Turbulent boundary layer control utilizing {L}orentz force}, YEAR = {2000}, JOURNAL = {Phys. Fluids}, VOLUME = {12}, NUMBER = {}, PAGES = {631-649} } @book {MR0482275, AUTHOR = {Bergh, J. and L{\"o}fstr{\"o}m, J.}, TITLE = {Interpolation spaces. {A}n introduction}, NOTE = {Grundlehren der Mathematischen Wissenschaften, No. 223}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1976}, PAGES = {x+207}, MRCLASS = {46M35}, MRNUMBER = {MR0482275 (58 \#2349)}, } @article {MR2076053, AUTHOR = {Bernardi, C. and Chac\'{o}n Rebollo, T. and G\'{o}mez M\'{a}rmol, M. and Lewandowski, R. and Murat, F.}, TITLE = {A model for two coupled turbulent fluids. {III}. {N}umerical approximation by finite elements}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {98}, YEAR = {2004}, NUMBER = {1}, PAGES = {33--66}, ISSN = {0029-599X}, MRCLASS = {76F99 (65N12 65N30 76M10)}, MRNUMBER = {2076053}, MRREVIEWER = {Xiaoming Wang}, DOI = {10.1007/s00211-003-0490-9}, URL = {https://doi.org/10.1007/s00211-003-0490-9}, } @article {MR1974191, AUTHOR = {Bernardi, C. and Chac\'{o}n Rebollo, T. and Lewandowski, R. and Murat, F.}, TITLE = {A model for two coupled turbulent fluids. {II}. {N}umerical analysis of a spectral discretization}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {40}, YEAR = {2002}, NUMBER = {6}, PAGES = {2368--2394 (2003)}, ISSN = {0036-1429}, MRCLASS = {76F99 (65N35 76D99 76M22)}, MRNUMBER = {1974191}, MRREVIEWER = {Xiaoming Wang}, DOI = {10.1137/S0036142901385829}, URL = {https://doi.org/10.1137/S0036142901385829}, } @incollection {MR1935990, AUTHOR = {Bernardi, C. and Chac\'{o}n Rebollo, T. and Lewandowski, R. and Murat, F.}, TITLE = {A model for two coupled turbulent fluids. {I}. {A}nalysis of the system}, BOOKTITLE = {Nonlinear partial differential equations and their applications. {C}oll\`ege de {F}rance {S}eminar, {V}ol. {XIV} ({P}aris, 1997/1998)}, SERIES = {Stud. Math. Appl.}, VOLUME = {31}, PAGES = {69--102}, PUBLISHER = {North-Holland, Amsterdam}, YEAR = {2002}, MRCLASS = {76F99 (35Q35 76D99 86A05)}, MRNUMBER = {1935990}, MRREVIEWER = {Xiaoming Wang}, DOI = {10.1016/S0168-2024(02)80006-6}, URL = {https://doi.org/10.1016/S0168-2024(02)80006-6}, } @article {MR1674378, AUTHOR = {Berroukeche, Mostefa and Maschke, Erich K. and Saramito, Bernard}, TITLE = {Convergence of an unconditionally stable semi-implicit scheme for linear incompressible {MHD} equations}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {328}, YEAR = {1999}, NUMBER = {1}, PAGES = {81--86}, ISSN = {0764-4442}, CODEN = {CASMEI}, MRCLASS = {76M20 (76W05)}, MRNUMBER = {1674378 (99k:76097)}, DOI = {10.1016/S0764-4442(99)80016-0}, URL = {http://dx.doi.org/10.1016/S0764-4442(99)80016-0}, } @article {MR2192847, AUTHOR = {Berselli, Luigi C.}, TITLE = {On the large eddy simulation of the {T}aylor-{G}reen vortex}, JOURNAL = {J. Math. Fluid Mech.}, FJOURNAL = {Journal of Mathematical Fluid Mechanics}, VOLUME = {7}, YEAR = {2005}, NUMBER = {suppl. 2}, PAGES = {S164--S191}, ISSN = {1422-6928}, MRCLASS = {76F65 (65M70 76D05 76D17)}, MRNUMBER = {2192847 (2006j:76072)}, MRREVIEWER = {Bernard J. Geurts}, DOI = {10.1007/s00021-005-0152-z}, URL = {http://dx.doi.org/10.1007/s00021-005-0152-z}, } MR2185509 @book {BIL06, AUTHOR = {Berselli, L.C. and Iliescu, T. and Layton, W.J.}, TITLE = {Mathematics of large eddy simulation of turbulent flows}, SERIES = {Scientific Computation}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2006}, PAGES = {xviii+348}, ISBN = {978-3-540-26316-6; 3-540-26316-0}, MRCLASS = {76F65 (35Q30 76D05 76F05)}, MRNUMBER = {MR2185509 (2006h:76071)}, MRREVIEWER = {Bertrand Michaux}, } @techreport{BJG_tr, Author = {Berselli, L.C. and John, V. and Grisanti}, Institution = {}, Title = {}, Year = {}} @ARTICLE{BJG, AUTHOR = {Berselli, L.C. and Grisanti, C.R. and John, V.}, TITLE = {On commutator errors in the divergence of the space averaged {N}avier-{S}tokes equations}, YEAR = {}, JOURNAL = {}, VOLUME = {}, NUMBER = {}, PAGES = {} } MR2333730 @article {BGJ, AUTHOR = {Berselli, L.C. and Grisanti, C.R. and John, V.}, TITLE = {Analysis of commutation errors for functions with low regularity}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {206}, YEAR = {2007}, NUMBER = {2}, PAGES = {1027--1045}, ISSN = {0377-0427}, CODEN = {JCAMDI}, MRCLASS = {76F65 (35Q30 76D05 76M25)}, MRNUMBER = {MR2333730 (2009e:76094)}, MRREVIEWER = {Richard Pasquetti}, } MR2248564 @article {BJ06, AUTHOR = {Berselli, L.C. and John, V.}, TITLE = {Asymptotic behaviour of commutation errors and the divergence of the {R}eynolds stress tensor near the wall in the turbulent channel flow}, JOURNAL = {Math. Methods Appl. Sci.}, FJOURNAL = {Mathematical Methods in the Applied Sciences}, VOLUME = {29}, YEAR = {2006}, NUMBER = {14}, PAGES = {1709--1719}, ISSN = {0170-4214}, CODEN = {MMSCDB}, MRCLASS = {76F65 (35B40 35Q30)}, MRNUMBER = {MR2248564 (2008a:76071)}, MRREVIEWER = {Serge Prudhomme}, } @techreport{BC09, Author = {Berselli, L.C. and Cordoba, D.}, Institution = {}, Title = {On the regularity of the solution to the 3D NSE: A remark on the role of helicity}, Year = {2009}} @article {MR3944203, AUTHOR = {Berselli, Luigi C. and Fagioli, Simone and Spirito, Stefano}, TITLE = {Suitable weak solutions of the {N}avier-{S}tokes equations constructed by a space-time numerical discretization}, JOURNAL = {J. Math. Pures Appl. (9)}, FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`eme S\'{e}rie}, VOLUME = {125}, YEAR = {2019}, PAGES = {189--208}, ISSN = {0021-7824}, MRCLASS = {35Q30 (35D30 76D03 76D05)}, MRNUMBER = {3944203}, MRREVIEWER = {Michael J. Carley}, DOI = {10.1016/j.matpur.2018.09.004}, URL = {https://doi.org/10.1016/j.matpur.2018.09.004}, } @article {MR3516170, AUTHOR = {Bertagna, L. and Quaini, A. and Veneziani, A.}, TITLE = {Deconvolution-based nonlinear filtering for incompressible flows at moderately large {R}eynolds numbers}, JOURNAL = {Internat. J. Numer. Methods Fluids}, FJOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {81}, YEAR = {2016}, NUMBER = {8}, PAGES = {463--488}, ISSN = {0271-2091}, MRCLASS = {76D05 (76Fxx)}, MRNUMBER = {3516170}, MRREVIEWER = {Roger Lewandowski}, DOI = {10.1002/fld.4192}, URL = {https://doi.org/10.1002/fld.4192}, } MR1640759 @book {BB98, AUTHOR = {Bertero, M. and Boccacci, P.}, TITLE = {Introduction to inverse problems in imaging}, PUBLISHER = {Institute of Physics Publishing}, ADDRESS = {Bristol}, YEAR = {1998}, PAGES = {xii+351}, ISBN = {0-7503-0439-1; 0-7503-0435-9}, MRCLASS = {78A45 (35R30 44A12 65R30 68U10 92C55)}, MRNUMBER = {MR1640759 (99k:78027)}, MRREVIEWER = {Vladimir A. Sharafutdinov}, } 10.1063/1.1706426 @ article{Betchov61, title = {Semi-Isotropic Turbulence and Helicoidal Flows}, publisher = {AIP}, year = {1961}, doi = {DOI:10.1063/1.1706426}, issn = {00319171}, coden = {PFLDAS}, volume = {4}, number = {7}, pages = {925-926}, author = {Betchov, R.}, url = {http://dx.doi.org/doi/10.1063/1.1706426}, } @ARTICLE{tomAIAA, AUTHOR = {Bewley, T. and Trenchea, C.}, TITLE = {Noncooperative optimization of controls for time periodic {Navier-Stokes} systems with multiple solutions}, YEAR = {}, JOURNAL = {AIAA}, VOLUME = {2002-2754}, NUMBER = {}, PAGES = {} } @ARTICLE{BDM08, AUTHOR = {Bhattacharya, Amitabh and Das, Arup and Moser, Robert D.}, TITLE = {A filtered-wall formulation for large-eddy simulation of wall bounded turbulence}, YEAR = {2008}, JOURNAL = {Phys. 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An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {30}, YEAR = {2014}, NUMBER = {1}, PAGES = {015004, 32}, ISSN = {0266-5611}, MRCLASS = {62F15 (65C05 86A22)}, MRNUMBER = {3151683}, DOI = {10.1088/0266-5611/30/1/015004}, URL = {http://dx.doi.org/10.1088/0266-5611/30/1/015004}, } 1145.76300 @book{Biskamp03, author={Biskamp, D.}, title={Magnetohydrodynamic turbulence}, YEAR = {2003}, publisher={Cambridge University Press}, } @book {MR1250152, AUTHOR = {Biskamp, Dieter}, TITLE = {Nonlinear magnetohydrodynamics}, SERIES = {Cambridge Monographs on Plasma Physics}, VOLUME = {1}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1993}, PAGES = {xiv+378}, ISBN = {0-521-40206-9}, MRCLASS = {76-02 (76E25 76F99 76W05 76Y05 85A30)}, MRNUMBER = {1250152 (95d:76002)}, MRREVIEWER = {Alexander Lifschitz}, DOI = {10.1017/CBO9780511599965}, URL = {http://dx.doi.org/10.1017/CBO9780511599965}, } @book {Biskamp_MRP_2005, AUTHOR = {Biskamp, Dieter}, TITLE = {Magnetic Reconnection in Plasmas}, SERIES = {Cambridge Monographs on Plasma Physics}, VOLUME = {3}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2005}, PAGES = {404}, ISBN = {0521020360}, MRCLASS = {}, MRNUMBER = {}, MRREVIEWER = {}, DOI = {}, URL = {}, } @ARTICLE{Bleck74, AUTHOR = {Bleck, Rainer}, TITLE = {Short-Range Prediction in Isentropic Coordinates with Filtered and Unfiltered Numerical Models}, YEAR = {1974}, JOURNAL = {Mon. 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W}, TITLE = {Numerical methods in astrophysics}, SERIES = {Series in Astronomy and Astrophysics}, PUBLISHER = {Taylor \& Francis}, ADDRESS = {New York}, YEAR = {2007}, PAGES = {x+329}, ISBN = {978-0-7503-0883-0; 0-7503-0883-4}, MRCLASS = {85-08 (76W05 76X05 85-02)}, MRNUMBER = {2285316 (2007m:85001)}, } @incollection {MR2001876, AUTHOR = {Boffi, Daniele and Gastaldi, Lucia}, TITLE = {A finite element approach for the immersed boundary method}, NOTE = {In honour of Klaus-J\"{u}rgen Bathe}, JOURNAL = {Comput. \& Structures}, FJOURNAL = {Computers \& Structures. An International Journal}, VOLUME = {81}, YEAR = {2003}, NUMBER = {8-11}, PAGES = {491--501}, ISSN = {0045-7949}, MRCLASS = {76M10 (65M60 74F10 76D03 92C35)}, MRNUMBER = {2001876}, MRREVIEWER = {Alessandro Veneziani}, DOI = {10.1016/S0045-7949(02)00404-2}, URL = {https://doi.org/10.1016/S0045-7949(02)00404-2}, } @misc{kellberg2004deployable, title={Deployable spacecraft mount for electric propulsion}, author={Kellberg, C.}, url={http://www.google.com/patents/US20040164205}, year={2004}, month=aug # "~26", publisher={Google Patents}, note={US Patent App. 10/371,838} } @ARTICLE{BI06, AUTHOR = {Borggaard, J. and Iliescu, T.}, TITLE = {Approximate deconvolution boundary conditions for large eddy simulation}, YEAR = {2006}, JOURNAL = {Applied Math. Letters}, VOLUME = {19}, NUMBER = {}, PAGES = {735-740} } @ARTICLE{BG05, AUTHOR = {Borz{\`i}, A. and Griesse, R.}, TITLE = {Experiences with a space-time multigrid method for the optimal control of a chemical turbulence model}, YEAR = {2005}, JOURNAL = {Int. J. Numer. Meth. Fluids}, VOLUME = {47}, NUMBER = {}, PAGES = {879-885} } @ARTICLE{BG05, AUTHOR = {Bos, F. van der and Geurts, B.J.}, TITLE = {Commutator error in the filtering approach to {LES}}, YEAR = {2005}, JOURNAL = {Phys. Fluids}, VOLUME = {17}, NUMBER = {}, PAGES = {035108} } MR2136436 @article {BoGe05, AUTHOR = {Bos, F. van der and Geurts, B.J.}, TITLE = {Commutator errors in the filtering approach to large-eddy simulation}, JOURNAL = {Phys. Fluids}, FJOURNAL = {Physics of Fluids}, VOLUME = {17}, YEAR = {2005}, NUMBER = {3}, PAGES = {035108, 20}, ISSN = {1070-6631}, CODEN = {PHFLE6}, MRCLASS = {76F65}, MRNUMBER = {MR2136436 (2006a:76060)}, MRREVIEWER = {John Volker}, } @article{BoudierGicquel2007, author = {Boudier, G. and L.Y.M., Gicquel and Poinsot, Thierry and Bissi\`{e}res, D. and B\'{e}rat, Claude}, year = {2007}, month = {01}, pages = {3075-3082}, title = {Comparison of {LES}, {RANS} and experiments in an aeronautical gas turbine combustion chamber}, volume = {31}, journal = {Proceedings of the Combustion Institute}, doi = {10.1016/j.proci.2006.07.067} } @article {MR1996061, AUTHOR = {Bourlioux, Anne and Layton, Anita T. and Minion, Michael L.}, TITLE = {High-order multi-implicit spectral deferred correction methods for problems of reactive flow}, JOURNAL = {J. Comput. 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G. and Takhirov, A. and Trenchea, C.}, TITLE = {Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering}, JOURNAL = {Internat. J. Numer. Methods Fluids}, FJOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {70}, YEAR = {2012}, NUMBER = {7}, PAGES = {805--828}, ISSN = {0271-2091}, CODEN = {IJNFDW}, MRCLASS = {76D05 (76F65 76M10)}, MRNUMBER = {2983747}, DOI = {10.1002/fld.2732}, URL = {http://dx.doi.org/10.1002/fld.2732}, } @article {MR1624716, AUTHOR = {Boyd, John P.}, TITLE = {Two comments on filtering (artificial viscosity) for {C}hebyshev and {L}egendre spectral and spectral element methods: preserving boundary conditions and interpretation of the filter as a diffusion}, JOURNAL = {J. Comput. 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Ridgway}, TITLE = {The mathematical theory of finite element methods}, SERIES = {Texts in Applied Mathematics}, VOLUME = {15}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1994}, PAGES = {xii+294}, ISBN = {0-387-94193-2}, MRCLASS = {65-01 (46N40 65L60 65M60 65N30 73V05 76M10)}, MRNUMBER = {1278258 (95f:65001)}, MRREVIEWER = {J. T. Oden}, } @article {MR2286189, AUTHOR = {Bresch, Didier and Koko, Jonas}, TITLE = {Operator-splitting and {L}agrange multiplier domain decomposition methods for numerical simulation of two coupled {N}avier-{S}tokes fluids}, JOURNAL = {Int. J. Appl. Math. Comput. Sci.}, FJOURNAL = {International Journal of Applied Mathematics and Computer Science}, VOLUME = {16}, YEAR = {2006}, NUMBER = {4}, PAGES = {419--429}, ISSN = {1641-876X}, MRCLASS = {76M10 (65M55 76D05)}, MRNUMBER = {2286189 (2007h:76075)}, } @book {Brez73, AUTHOR = {Br{\'e}zis, H.}, TITLE = {Op\'erateurs maximaux monotones et semi-groupes de contractions dans les espaces de {H}ilbert}, NOTE = {North-Holland Mathematics Studies, No. 5. 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Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {36}, YEAR = {1980/81}, NUMBER = {1}, PAGES = {1--25}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65J15 (58E07 65N30)}, MRNUMBER = {595803 (83f:65089a)}, MRREVIEWER = {Erich Bohl}, DOI = {10.1007/BF01395985}, URL = {http://dx.doi.org/10.1007/BF01395985}, } @article {MR615889, AUTHOR = {Brezzi, F. and Rappaz, J. and Raviart, P.-A.}, TITLE = {Finite-dimensional approximation of nonlinear problems. {II}. {L}imit points}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {37}, YEAR = {1981}, NUMBER = {1}, PAGES = {1--28}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65J15 (58E07 65N30)}, MRNUMBER = {615889 (83f:65089b)}, MRREVIEWER = {Erich Bohl}, DOI = {10.1007/BF01396184}, URL = {http://dx.doi.org/10.1007/BF01396184}, } @article {MR634749, AUTHOR = {Brezzi, F. and Rappaz, J. and Raviart, P.-A.}, TITLE = {Finite-dimensional approximation of nonlinear problems. {III}. {S}imple bifurcation points}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {38}, YEAR = {1981/82}, NUMBER = {1}, PAGES = {1--30}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65J15 (58E07 65N30)}, MRNUMBER = {634749 (83f:65090)}, DOI = {10.1007/BF01395805}, URL = {http://dx.doi.org/10.1007/BF01395805}, } @ARTICLE{BFLLM73, AUTHOR = {Brissaud, A. and Frisch, U. and Leorat, J. and Lesieur, M. and Mazure, A.}, TITLE = {Helicity cascades in fully developed isotropic turbulence}, YEAR = {1973}, JOURNAL = {Physics of Fluids}, VOLUME = {16}, NUMBER = {8}, PAGES = {} } @article {Brouwer1912, AUTHOR = {Brouwer, L. E. J.}, TITLE = {\"{U}ber die {E}rweiterung des {D}efinitionsbereichs einer stetigen {F}unktion}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {79}, YEAR = {1918}, NUMBER = {3}, PAGES = {209--211}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {Contributed Item}, MRNUMBER = {MR1511921}, } @article{BruFili2007, year={2007}, issn={0091-150X}, journal={Pharmaceutical Chemistry Journal}, volume={41}, number={9}, doi={10.1007/s11094-007-0099-x}, title={Principles of magnetohydrodynamic thermochemotherapy of malignant tumors (A review)}, url={http://dx.doi.org/10.1007/s11094-007-0099-x}, publisher={Springer US}, author={Brusentsov, N.A. and Brusentsova, T.N. and Filinova, E.Yu.}, pages={455-460}, language={English} } @article {MR3283906, AUTHOR = {Bui-Thanh, Tan and Ghattas, Omar}, TITLE = {An analysis of infinite dimensional {B}ayesian inverse shape acoustic scattering and its numerical approximation}, JOURNAL = {SIAM/ASA J. Uncertain. Quantif.}, FJOURNAL = {SIAM/ASA Journal on Uncertainty Quantification}, VOLUME = {2}, YEAR = {2014}, NUMBER = {1}, PAGES = {203--222}, ISSN = {2166-2525}, MRCLASS = {65N21 (49J50 49K20 49K40 49N45 49N60 62F15 62G99)}, MRNUMBER = {3283906}, DOI = {10.1137/120894877}, URL = {http://dx.doi.org/10.1137/120894877}, } @techreport{2019-midpointFSI, author = {Bukac, Martina and Trenchea, Catalin}, Institution = {University of Pittsburgh}, title = "Unconditionally stable partitioned second-order variable step method for fluid-structure interaction", year = "2019", month = "", note = "", } @techreport{MartinaBukacCatalinTrenchea2019, Author = {Bukac, Martina and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {BOundary Update via Resolvent for fluid-structure interaction}, Year = {2018}} @techreport{BLMTT14, Author = {Bukac, Martina and Layton, William and Moraiti, Marina and Tran, Hoang and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Analysis of partitioned methods for Biot system}, Year = {2014}} @article {NUM:NUM21968, author = {Bukac, Martina and Layton, William and Moraiti, Marina and Tran, Hoang and Trenchea, Catalin}, title = {Analysis of partitioned methods for the {Biot} System}, journal = {Numerical Methods for Partial Differential Equations}, issn = {1098-2426}, url = {http://dx.doi.org/10.1002/num.21968}, doi = {10.1002/num.21968}, pages = {n/a--n/a}, keywords = {Biot system, partitioned methods, poroelasticity}, year = {2015}, } @article {MR3553935, AUTHOR = {Buka\v{c}, Martina and Muha, Boris}, TITLE = {Stability and convergence analysis of the extensions of the kinematically coupled scheme for the fluid-structure interaction}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {54}, YEAR = {2016}, NUMBER = {5}, PAGES = {3032--3061}, ISSN = {0036-1429}, MRCLASS = {65M60 (65M12 65M15 74F10 74H15 74S05 76M10)}, MRNUMBER = {3553935}, MRREVIEWER = {Rafael F. Santos}, DOI = {10.1137/16M1055396}, URL = {https://doi.org/10.1137/16M1055396}, } @article {MR3343599, AUTHOR = {Buka\v{c}, Martina and Yotov, Ivan and Zunino, Paolo}, TITLE = {An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {31}, YEAR = {2015}, NUMBER = {4}, PAGES = {1054--1100}, ISSN = {0749-159X}, MRCLASS = {65M60 (74F10 76D05)}, MRNUMBER = {3343599}, MRREVIEWER = {Fr\'ed\'eric Charles Lebon}, URL = {https://doi.org/10.1002/num.21936}, } @article{10.1115/1.2464142, author = {Bunker, Ronald S.}, title = "{Gas Turbine Heat Transfer: Ten Remaining Hot Gas Path Challenges}", journal = {Journal of Turbomachinery}, volume = {129}, number = {2}, pages = {193-201}, year = {2006}, month = {07}, abstract = "{The advancement of turbine cooling has allowed engine design to exceed normal material temperature limits, but it has introduced complexities that have accentuated the thermal issues greatly. Cooled component design has consistently trended in the direction of higher heat loads, higher through-wall thermal gradients, and higher in-plane thermal gradients. The present discussion seeks to identify ten major thermal issues, or opportunities, that remain for the turbine hot gas path (HGP) today. These thermal challenges are commonly known in their broadest forms, but some tend to be little discussed in a direct manner relevant to gas turbines. These include uniformity of internal cooling, ultimate film cooling, microcooling, reduced incident heat flux, secondary flows as prime cooling, contoured gas paths, thermal stress reduction, controlled cooling, low emission combustor-turbine systems, and regenerative cooling. Evolutionary or revolutionary advancements concerning these issues will ultimately be required in realizable engineering forms for gas turbines to breakthrough to new levels of performance. Herein lies the challenge to researchers and designers. It is the intention of this summary to provide a concise review of these issues, and some of the recent solution directions, as an initial guide and stimulation to further research.}", issn = {0889-504X}, doi = {10.1115/1.2464142}, url = {https://doi.org/10.1115/1.2464142}, eprint = {https://asmedigitalcollection.asme.org/turbomachinery/article-pdf/129/2/193/5842430/193\_1.pdf}, } @BOOK{Burl95, AUTHOR = {Burlaga, L.F.}, TITLE = {Interplanetary Magnetohydrodynamics}, PUBLISHER = {Oxford Univ. Press}, YEAR = {1995}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {London, U. K.} } @article {MR2367927, AUTHOR = {Burman, Erik and Fern{\'a}ndez, Miguel A.}, TITLE = {Stabilized explicit coupling for fluid-structure interaction using {N}itsche's method}, JOURNAL = {C. R. Math. Acad. Sci. Paris}, FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, VOLUME = {345}, YEAR = {2007}, NUMBER = {8}, PAGES = {467--472}, ISSN = {1631-073X}, MRCLASS = {76M25 (65M06 74F10 74S30)}, MRNUMBER = {2367927 (2008k:76093)}, DOI = {10.1016/j.crma.2007.09.010}, URL = {http://dx.doi.org/10.1016/j.crma.2007.09.010}, } @article {MR2498525, AUTHOR = {Burman, Erik and Fern{\'a}ndez, Miguel A.}, TITLE = {Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {198}, YEAR = {2009}, NUMBER = {5-8}, PAGES = {766--784}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {74F10 (76D10)}, MRNUMBER = {2498525 (2010b:74029)}, DOI = {10.1016/j.cma.2008.10.012}, URL = {http://dx.doi.org/10.1016/j.cma.2008.10.012}, } @article{doi:10.1002/nme.4607, author = {Burman, Erik and Fern\'{a}ndez, Miguel A.}, title = {Explicit strategies for incompressible fluid-structure interaction problems: Nitsche type mortaring versus {Robin-Robin} coupling}, journal = {International Journal for Numerical Methods in Engineering}, volume = {97}, number = {10}, pages = {739-758}, keywords = {fluid-structure interaction, incompressible flow, finite element methods, Nitsche's method, time-discretization, loosely coupled schemes, Robin-Robin coupling}, doi = {10.1002/nme.4607}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4607}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.4607}, abstract = {SUMMARY We discuss explicit coupling schemes for fluid-structure interaction problems where the added mass effect is important. In this paper, we show the close relation between coupling schemes by using Nitsche's method and a Robin–Robin type coupling. In the latter case, the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators. Recalling the explicit method proposed in Comput. Methods Appl. Mech. Engrg. 198(5-8):766–784, 2009, we make the observation that this scheme is stable under a hyperbolic type CFL condition, but that optimal accuracy imposes a parabolic type CFL conditions because of the splitting error. Two strategies to enhance the accuracy of the coupling scheme under the hyperbolic CFL-condition are suggested, one using extrapolation and defect-correction and one using a penalty-free non-symmetric Nitsche method. Finally, we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions. 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The studies of such a multiscale problem often use multiple computer models, while each of computer models is applied to a small range of spatial and time scales. Accurate solution normally requires exchanging information between a macroscopic model and a microscopic model that can be done by coupling the two models. With the approach, it is possible to obtain an informative solution with the current computer memory and speed. This paper used a few examples of fluid flow and heat and mass transfer in engineered spaces to conclude that a coupled macroscopic and microscopic model is likely to have a solution and the solution is unique. A stable solution for the coupled model can be obtained if some criteria are met. The information transfer between the macroscopic and microscopic models is mostly two ways. A one-way assumption can be accepted when the impact from small scale on large scale is not very significant." } @article {MR3097033, AUTHOR = {Chen, Wenbin and Gunzburger, Max and Sun, Dong and Wang, Xiaoming}, TITLE = {Efficient and long-time accurate second-order methods for the {S}tokes-{D}arcy system}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {51}, YEAR = {2013}, NUMBER = {5}, PAGES = {2563--2584}, ISSN = {0036-1429}, MRCLASS = {65M60 (35Q35 65M12 65M15 76D07 76S05)}, MRNUMBER = {3097033}, MRREVIEWER = {Jos{\'e} R. Fern{\'a}ndez}, DOI = {10.1137/120897705}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1137/120897705}, } @article {MR3934674, AUTHOR = {Cheng, Qing and Shen, Jie and Yang, Xiaofeng}, TITLE = {Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the {SAV} approach}, JOURNAL = {J. Sci. 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Fluids}, FJOURNAL = {Physics of Fluids}, VOLUME = {14}, YEAR = {2002}, NUMBER = {12}, PAGES = {4344--4351}, ISSN = {1070-6631}, CODEN = {PHFLE6}, MRCLASS = {76F65}, MRNUMBER = {MR1938234}, } @BOOK{DF77, AUTHOR = {Daugherty, R.L. and Franzini, J.B.}, TITLE = {Fluid Mechanics with Engineering Applications}, PUBLISHER = {McGraw-Hill}, YEAR = {1977}, SERIES = {}, VOLUME = {}, EDITION = {7$^{th}$}, ADDRESS = {New York} } @BOOK{DL84, AUTHOR = {Dautray R., and Lions, J.-L. and Sneddon, I. N. (Translator)}, TITLE = {Mathematical Analysis and Numerical Methods for Science and Technology: Physical Origins and Classical Methods}, PUBLISHER = {Springer-Verlag}, YEAR = {1984}, SERIES = {}, VOLUME = {1}, EDITION = {}, ADDRESS = {New York} } @book {MR1156075, AUTHOR = {Dautray, Robert and Lions, Jacques-Louis}, TITLE = {Mathematical analysis and numerical methods for science and technology. {V}ol. 5}, NOTE = {Evolution problems. I, With the collaboration of Michel Artola, Michel Cessenat and H{\'e}l{\`e}ne Lanchon, Translated from the French by Alan Craig}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1992}, PAGES = {xiv+709}, ISBN = {3-540-50205-X; 3-540-66101-8}, MRCLASS = {00A05 (35-01 47-01)}, MRNUMBER = {1156075 (92k:00006)}, } @ARTICLE{DPSBJ92, AUTHOR = {Davidenko, J. and Pertsov, A. and Salomonsz, R. and Baxter, W. and Jalife, J.}, TITLE = {Stationary and drifting spiral waves of excitation in isolated cardiac-muscle}, YEAR = {1992}, JOURNAL = {Nature}, VOLUME = {355}, NUMBER = {6358}, PAGES = {349-351} } MR1825486 @book {Davi01, AUTHOR = {Davidson, P. A.}, TITLE = {An introduction to magnetohydrodynamics}, SERIES = {Cambridge Texts in Applied Mathematics}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2001}, PAGES = {xviii+431}, ISBN = {0-521-79487-0}, MRCLASS = {76W05 (76-01)}, MRNUMBER = {MR1825486 (2002c:76103)}, MRREVIEWER = {Manuel N{\'u}{\~n}ez Jim{\'e}nez}, } @book {MR0380189, AUTHOR = {Davis, Philip J.}, TITLE = {Interpolation and approximation}, NOTE = {Republication, with minor corrections, of the 1963 original, with a new preface and bibliography}, PUBLISHER = {Dover Publications Inc.}, ADDRESS = {New York}, YEAR = {1975}, PAGES = {xv+393}, MRCLASS = {41-02 (42-02)}, MRNUMBER = {MR0380189 (52 \#1089)}, } @ARTICLE{DaPh09, AUTHOR = {Davis, L. and Pahlevani, F.}, TITLE = {Semi-€implicit schemes for transient {Navier-Stokes} equations and eddy viscosity models}, YEAR = {2009}, JOURNAL = {Numer. Meth. Part. D. E.}, FJOURNAL ={Numerical Methods for Partial Differential Equations}, VOLUME = {25}, NUMBER = {1}, PAGES = {212--231} } @ARTICLE{Deb_Babuska_Oden_01, AUTHOR = {Deb, M.K. and Babu\v{s}ka, I.M. and Oden, J.T.}, TITLE = {Solution of stochastic partial differential equations using {G}alerkin finite element techniques}, YEAR = {2001}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, VOLUME = {190}, NUMBER = {48}, PAGES = {6359-6372} } @ARTICLE{DeTa06, AUTHOR = {Dentz, M. and Tartakovsky, D.M. and Abarca, E. and Guadagnini, A. and Sanchez-Vila, X. and Carrera, J.}, TITLE = {Variable-density flow in porous media}, YEAR = {2006}, JOURNAL = {J. Fluid Mech.}, VOLUME = {561}, NUMBER = {}, PAGES = {209-235} } @article{DeCar1986, Annote = {doi: 10.1175/1520-0493(1986)114<0880:SDPOTA>2.0.CO;2}, Author = {D{\'e}qu{\'e}, Michel and Cariolle, Daniel}, Booktitle = {Monthly Weather Review}, Da = {1986/05/01}, Date = {1986/05/01}, Date-Added = {2012-11-15 18:46:55 +0000}, Date-Modified = {2012-11-15 18:46:55 +0000}, Doi = {10.1175/1520-0493(1986)114<0880:SDPOTA>2.0.CO;2}, Isbn = {0027-0644}, FJournal = {Monthly Weather Review}, Journal = {Mon. Wea. Rev.}, M3 = {doi: 10.1175/1520-0493(1986)114<0880:SDPOTA>2.0.CO;2}, Month = {2012/11/15}, Number = {5}, Pages = {880--884}, Publisher = {American Meteorological Society}, Title = {Some Destabilizing Properties of the {A}sselin Time Filter}, Ty = {JOUR}, Url = {http://dx.doi.org/10.1175/1520-0493(1986)114<0880:SDPOTA>2.0.CO;2}, Volume = {114}, Year = {1986}, Year1 = {1986}, Bdsk-Url-1 = {http://dx.doi.org/10.1175/1520-0493(1986)114%3C0880:SDPOTA%3E2.0.CO;2}} @incollection {MR2862440, AUTHOR = {Deriaz, Erwan and Despres, Bruno and Faccanoni, Gloria and Gostaf, Kirill Pichon and Imbert-G{\'e}rard, Lise-Marie and Sadaka, Georges and Sart, Remy}, TITLE = {Magnetic equations with {${\bf FreeFem}{+}{+}$}: the {G}rad-{S}hafranov equation \& the current hole}, BOOKTITLE = {C{EMRACS}'10 research achievements: numerical modeling of fusion}, SERIES = {ESAIM Proc.}, VOLUME = {32}, PAGES = {76--94}, PUBLISHER = {EDP Sci., Les Ulis}, YEAR = {2011}, MRCLASS = {65M60 (65Y15 76M10 76W05)}, MRNUMBER = {2862440}, DOI = {10.1051/proc/2011013}, URL = {http://dx.doi.org/10.1051/proc/2011013}, } @book {MR1230384, AUTHOR = {DiBenedetto, E.}, TITLE = {Degenerate parabolic equations}, SERIES = {Universitext}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1993}, PAGES = {xvi+387}, ISBN = {0-387-94020-0}, MRCLASS = {35K65 (35-02)}, MRNUMBER = {MR1230384 (94h:35130)}, MRREVIEWER = {Ya Zhe Chen}, } @article {MR3689928, AUTHOR = {Diele, Fasma and Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Numerical analysis of a first-order in time implicit-symplectic scheme for predator--prey systems}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {74}, YEAR = {2017}, NUMBER = {5}, PAGES = {948--961}, ISSN = {0898-1221}, MRCLASS = {Prelim}, MRNUMBER = {3689928}, DOI = {10.1016/j.camwa.2017.04.030}, URL = {http://dx.doi.org/10.1016/j.camwa.2017.04.030}, } @techreport{DiGaTr18, Author = {Diele, Fasma and Garvie, Marcus R. and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Analysis of a second-order in time implicit-symplectic scheme for predator-prey systems}, Year = {2018}} @unpublished{DieleMarangiTrenchea2014, author = "Diele, Fasma and Marangi, Carmela and Trenchea, Catalin", title = "Positive Symplectic Integrators for Predator-Prey Dynamics", year = "2014", month = "", note = "Preprint", } @article {MR2231860, AUTHOR = {Diening, L. and Prohl, A. and Ru{\v{z}}i{\v{c}}ka, Michael}, TITLE = {Semi-implicit {E}uler scheme for generalized {N}ewtonian fluids}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {44}, YEAR = {2006}, NUMBER = {3}, PAGES = {1172--1190 (electronic)}, ISSN = {0036-1429}, MRCLASS = {65M06 (35Q35 76A05 76M25)}, MRNUMBER = {MR2231860 (2007f:65033)}, MRREVIEWER = {Komali S. Sastri}, } @BOOK{Dieu60, AUTHOR = {Dieudonn\'{e}, J.}, TITLE = {Foundations of Modern Analysis}, PUBLISHER = {Academic Press}, YEAR = {1960}, SERIES = {Pure Appl. Math.}, VOLUME = {}, EDITION = {}, ADDRESS = {New York} } @phdthesis{DiscacciatiPHD2004, title = {Domain decomposition methods for the coupling of surface and groundwater flows}, author = {Discacciati, Marco}, institution = {IACS}, School = {\'{E}cole Polytechnique F\'{e}d\'{e}rale de Lausanne}, address = {Lausanne}, pages = {165}, year = {2004}, abstract = {The purpose of this thesis is to investigate, from both the mathematical and numerical viewpoint, the coupling of surface and porous media flows, with particular concern on environmental applications. Domain decomposition methods are applied to set up effective iterative algorithms for the numerical solution of the global problem. To this aim, we reformulate the coupled problem in terms of an interface (Steklov-Poincaré) equation and we investigate the properties of the Steklov-Poincaré operators in order to characterize optimal preconditioners that, at the discrete level, yield convergence in a number of iterations independent of the mesh size h. We consider a new approach to the classical Robin-Robin method and we reinterpret it as an alternating direction iterative algorithm. This allows us to characterize robust preconditioners for the linear Stokes/Darcy problem which improve the behaviour of the classical Dirichlet- Neumann and Neumann-Neumann ones. Several numerical tests are presented to assess the convergence properties of the proposed algorithms. Finally, the nonlinear Navier-Stokes/Darcy coupling is investigated and a general nonlinear domain decomposition strategy is proposed for the solution of the interface problem, extending the usual Newton or fixed-point based algorithms.}, } @article {MR1936102, AUTHOR = {Discacciati, Marco and Miglio, Edie and Quarteroni, Alfio}, TITLE = {Mathematical and numerical models for coupling surface and groundwater flows}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {43}, YEAR = {2002}, NUMBER = {1-2}, PAGES = {57--74}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {76M10 (65M55 65M60 76D05 76S05)}, MRNUMBER = {1936102 (2003h:76087)}, MRREVIEWER = {Ma{\l}gorzata Peszy{\'n}ska}, DOI = {10.1016/S0168-9274(02)00125-3}, URL = {http://dx.doi.org/10.1016/S0168-9274(02)00125-3}, } @article {MR2553940, AUTHOR = {Discacciati, Marco and Quarteroni, Alfio}, TITLE = {Navier-{S}tokes/{D}arcy coupling: modeling, analysis, and numerical approximation}, JOURNAL = {Rev. Mat. Complut.}, FJOURNAL = {Revista Matem\'atica Complutense}, VOLUME = {22}, YEAR = {2009}, NUMBER = {2}, PAGES = {315--426}, ISSN = {1139-1138}, ISBN = {978-84-95215-09-3}, MRCLASS = {76S05 (65M55 65M60 76D05 76Z05)}, MRNUMBER = {2553940}, MRREVIEWER = {Alessandro Veneziani}, DOI = {10.5209/rev_REMA.2009.v22.n2.16263}, URL = {https://doi.org/10.5209/rev_REMA.2009.v22.n2.16263}, } @ARTICLE{DG01a, AUTHOR = {Ditlevsen, P. and Giuliani, P.}, TITLE = {Cascades in helical turbulence}, YEAR = {2001}, JOURNAL = {Phys. Rev. E}, FJOURNAL = {Physical Review E}, VOLUME = {63}, NUMBER = {}, PAGES = {036304/1-4} } @ARTICLE{DG01b, AUTHOR = {Ditlevsen, P. and Giuliani, P.}, TITLE = {Dissipation in helical turbulence}, YEAR = {2001}, JOURNAL = {Physics of Fluids}, VOLUME = {13}, NUMBER = {}, PAGES = {} } @article{dobrowolny1980a, adsurl = {http://adsabs.harvard.edu/abs/1980PhRvL..45..144D}, author = {Dobrowolny, M. and Mangeney, A. and Veltri, P.}, doi = {10.1103/PhysRevLett.45.144}, format = {print}, journal = {Phys. Rev. Lett.}, keywords = {Incompressible flow, Magnetohydrodynamic waves, Plasma turbulence, Solar wind, Wave polarization}, pages = {144--147}, title = {Fully developed anisotropic hydromagnetic turbulence in interplanetary space}, volume = {45}, year = {1980} } @ARTICLE{DF02, AUTHOR = {Doering, C. and Foias, C.}, TITLE = {Energy dissipation in body-forced turbulence}, YEAR = {2002}, JOURNAL = {J. Fluid Mech.}, VOLUME = {467}, NUMBER = {}, PAGES = {289-306} } MR1325465 @book {DG95, AUTHOR = {Doering, Charles R. and Gibbon, J. D.}, TITLE = {Applied analysis of the {N}avier-{S}tokes equations}, SERIES = {Cambridge Texts in Applied Mathematics}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1995}, PAGES = {xiv+217}, ISBN = {0-521-44557-4; 0-521-44568-X}, MRCLASS = {76D05 (35Q30 76F05 76F20)}, MRNUMBER = {1325465 (96a:76024)}, MRREVIEWER = {Alain Miranville}, DOI = {10.1017/CBO9780511608803}, URL = {http://dx.doi.org/10.1017/CBO9780511608803}, } @incollection {MR0273830, AUTHOR = {Douglas, Jr., Jim and Dupont, Todd}, TITLE = {Alternating-direction {G}alerkin methods on rectangles}, BOOKTITLE = {Numerical {S}olution of {P}artial {D}ifferential {E}quations, {II} ({SYNSPADE} 1970) ({P}roc. {S}ympos., {U}niv. of {M}aryland, {C}ollege {P}ark, {M}d., 1970)}, PAGES = {133--214}, PUBLISHER = {Academic Press, New York}, YEAR = {1971}, MRCLASS = {65.65}, MRNUMBER = {0273830 (42 \#8706)}, } @INCOLLECTION{Do05, AUTHOR = {Domaradzki, J. A.}, TITLE = {Modeling challenges and approaches in LES for physically complex flows}, BOOKTITLE = {Large-Eddy Simulation of Complex Flows, proceedings of Euromech Colloquium 469}, PUBLISHER = {Technical University Dresden}, YEAR = {2005}, EDITOR = {}, SERIES = {}, VOLUME = {}, EDITION = {}, PAGES = {84}, ADDRESS = {Germany, Oct. 6-8} } @ARTICLE{DoHaVe00, AUTHOR = {Dontchev, A.L. and Hager, W.W. and Veliov, V.M.}, TITLE = {Second-order {R}unge-{K}utta approximations in control constrained optimal control}, YEAR = {2000}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {38}, NUMBER = {1}, PAGES = {202-226} } @article {GGGE:GGGE53, author = {Dormy, Emmanuel and Valet, Jean-Pierre and Courtillot, Vincent}, title = {Numerical models of the geodynamo and observational constraints}, journal = {Geochemistry, Geophysics, Geosystems}, volume = {1}, number = {10}, issn = {1525-2027}, url = {http://dx.doi.org/10.1029/2000GC000062}, doi = {10.1029/2000GC000062}, pages = {n/a--n/a}, keywords = {Geodynamo, Earth core, geomagnetic field, magnetic records}, year = {2000}, } @book {MR2407755, TITLE = {Mathematical aspects of natural dynamos}, SERIES = {Fluid Mechanics of Astrophysics and Geophysics}, VOLUME = {13}, EDITOR = {Dormy, Emmanuel and Soward, Andrew M.}, PUBLISHER = {Grenoble Sciences. Universite Joseph Fourier, Grenoble}, YEAR = {2007}, PAGES = {xxii+482}, ISBN = {978-1-58488-954-0; 1-58488-954-3}, MRCLASS = {76-02 (76E20 76E25 76U05 76W05 85A30 86-02 86A25)}, MRNUMBER = {2407755 (2009g:76001)}, MRREVIEWER = {John Adam}, DOI = {10.1201/9781420055269}, URL = {http://dx.doi.org/10.1201/9781420055269}, } @article {MR2360172, AUTHOR = {Dormy, Emmanuel and N{\'u}{\~n}ez, Manuel}, TITLE = {Introduction [{S}pecial issue: {M}agnetohydrodynamics in astrophysics and geophysics]}, JOURNAL = {Geophys. Astrophys. Fluid Dyn.}, FJOURNAL = {Geophysical and Astrophysical Fluid Dynamics}, VOLUME = {101}, YEAR = {2007}, NUMBER = {3-4}, PAGES = {169}, ISSN = {0309-1929}, MRCLASS = {76-06 (76W05)}, MRNUMBER = {2360172}, DOI = {10.1080/03091920701523287}, URL = {http://dx.doi.org/10.1080/03091920701523287}, } @ARTICLE{DH99, AUTHOR = {Drenner, R.W. and Hambright, K.D.}, TITLE = {Biomanipulation of fish assemblages as a lake restoration technique}, YEAR = {1999}, JOURNAL = {Arch. Hydrobiol.}, VOLUME = {146}, NUMBER = {2}, PAGES = {129-165} } @ARTICLE{max92, AUTHOR = {Du,Q. and Gunzburger, M. and Peterson, J.}, TITLE = {Analysis and approximation of the Ginzburg-Landau model of superconductivity}, YEAR = {1992}, JOURNAL = {SIAM Review}, VOLUME = {34}, NUMBER = {}, PAGES = {54-81} } @ARTICLE{Du94, AUTHOR = {Du, Q.}, TITLE = {Global existence and uniqueness of solutions of the time-dependent {G}inzburg-{L}andau model of superconductivity}, YEAR = {1994}, JOURNAL = {Applicable Analysis}, VOLUME = {53}, NUMBER = {}, PAGES = {1-17} } MR1361269 @article {DGH95, AUTHOR = {Du, Q. and Gunzburger, M.D. and Hou, L.S.}, TITLE = {Analysis and finite element approximation of optimal control problems for a {L}adyzhenskaya model for stationary, incompressible, viscous flows}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {61}, YEAR = {1995}, NUMBER = {3}, PAGES = {323--343}, ISSN = {0377-0427}, CODEN = {JCAMDI}, MRCLASS = {49K20 (49M25 49N60 65M60 76D05 76M10)}, MRNUMBER = {MR1361269 (96h:49048)}, } @article{DUCHAINE20091129, title = "Development and assessment of a coupled strategy for conjugate heat transfer with Large Eddy Simulation: Application to a cooled turbine blade", journal = "International Journal of Heat and Fluid Flow", volume = "30", number = "6", pages = "1129 - 1141", year = "2009", issn = "0142-727X", doi = "https://doi.org/10.1016/j.ijheatfluidflow.2009.07.004", url = "http://www.sciencedirect.com/science/article/pii/S0142727X09001180", author = "F. Duchaine and A. Corpron and L. Pons and V. Moureau and F. Nicoud and T. Poinsot", keywords = "Conjugate heat transfer, Large Eddy Simulation, Code coupling, Stability analysis", abstract = "Although Large Eddy Simulation (LES) is identified today as the most promising method for turbulent flow problems, few applications of LES coupled to heat transfer solvers in solids have been published. This paper describes a coupling strategy of a LES solver and a heat transfer code within solids on parallel architectures. The numerical methods used in both solvers are briefly recalled before discussing the coupling strategy in terms of physical quantities to exchange (fluxes and temperatures), stability and parallel efficiency. The stability study is performed using an amplification matrix analysis on a one-dimensional case and allows the determination and optimization of coupling parameters. The coupled tool is then applied to a cooled turbine blade model where results demonstrate both the efficiency of the parallel implementation and the quality of the results. Coupled and non-coupled simulations are compared to experimental results and discussed in terms of cooling efficiency and flow structures." } @phdthesis{Du_04, Author = {Dunca, A.}, Date-Added = {}, Date-Modified = {}, School = {University of Pittsburgh}, Title = {Space averaged {N}avier {S}tokes equations in the presence of walls}, Year = {2004}} %DuncaEps06, @article {MR2213398, AUTHOR = {Dunca, A. and Epshteyn, Y.}, TITLE = {On the {S}tolz-{A}dams deconvolution model for the large-eddy simulation of turbulent flows}, JOURNAL = {SIAM J. Math. Anal.}, FJOURNAL = {SIAM Journal on Mathematical Analysis}, VOLUME = {37}, YEAR = {2006}, NUMBER = {6}, PAGES = {1890--1902 (electronic)}, ISSN = {0036-1410}, MRCLASS = {76F65 (76D03 76D05)}, MRNUMBER = {2213398 (2006k:76066)}, MRREVIEWER = {Bertrand Michaux}, DOI = {10.1137/S0036141003436302}, URL = {http://dx.doi.org/10.1137/S0036141003436302}, } @techreport{Dunca02, Author = {Dunca, A.}, Institution = {Argonne National Lab, report number ANL/MCS-P1101-1003}, Title = {Investigation of a shape optimization algorithm for turbulent flows}, Year = {2002, http://www-fp.mcs.anl.gov/division/publications/}} @techreport{DJL, Author = {Dunca, A. and John, V. and Layton, W.}, Institution = {}, Title = {}, Year = {}} %DJL04 @incollection {MR2085847, AUTHOR = {Dunca, A. and John, V. and Layton, W. J.}, TITLE = {The commutation error of the space averaged {N}avier-{S}tokes equations on a bounded domain}, BOOKTITLE = {Contributions to current challenges in mathematical fluid mechanics}, SERIES = {Adv. Math. Fluid Mech.}, PAGES = {53--78}, PUBLISHER = {Birkh\"auser}, ADDRESS = {Basel}, YEAR = {2004}, MRCLASS = {76F65 (35Q30 76D05)}, MRNUMBER = {MR2085847 (2005j:76052)}, MRREVIEWER = {Luigi Carlo Berselli}, } @INCOLLECTION{DJLS01, AUTHOR = {Dunca, A. and John, V. and Layton, W. and Sahin, N.}, TITLE = {Numerical analysis of large eddy simulation}, BOOKTITLE = {{DNS/LES} progress and challenges}, PUBLISHER = {Greyden Press}, YEAR = {2001}, EDITOR = {Liu, C. and Sakeland, L. and Beutner, T.}, SERIES = {}, VOLUME = {}, EDITION = {}, PAGES = {359-364}, ADDRESS = {Columbus} } @article{10.1115/1.1397776, author = {Dunn, Michael G. }, title = "{Convective Heat Transfer and Aerodynamics in Axial Flow Turbines}", journal = {Journal of Turbomachinery}, volume = {123}, number = {4}, pages = {637-686}, year = {2001}, month = {02}, abstract = "{The primary focus of this paper is convective heat transfer in axial flow turbines. Research activity involving heat transfer generally separates into two related areas: predictions and measurements. The problems associated with predicting heat transfer are coupled with turbine aerodynamics because proper prediction of vane and blade surface-pressure distribution is essential for predicting the corresponding heat transfer distribution. The experimental community has advanced to the point where time-averaged and time-resolved three-dimensional heat transfer data for the vanes and blades are obtained routinely by those operating full-stage rotating turbines. However, there are relatively few CFD codes capable of generating three-dimensional predictions of the heat transfer distribution, and where these codes have been applied the results suggest that additional work is required. This paper outlines the progression of work done by the heat transfer community over the last several decades as both the measurements and the predictions have improved to current levels. To frame the problem properly, the paper reviews the influence of turbine aerodynamics on heat transfer predictions. This includes a discussion of time-resolved surface-pressure measurements with predictions and the data involved in forcing function measurements. The ability of existing two-dimensional and three-dimensional Navier–Stokes codes to predict the proper trends of the time-averaged and unsteady pressure field for full-stage rotating turbines is demonstrated. Most of the codes do a reasonably good job of predicting the surface-pressure data at vane and blade midspan, but not as well near the hub or the tip region for the blade. In addition, the ability of the codes to predict surface-pressure distribution is significantly better than the corresponding heat transfer distributions. Heat transfer codes are validated against measurements of one type or another. Sometimes the measurements are performed using full rotating rigs, and other times a much simpler geometry is used. In either case, it is important to review the measurement techniques currently used. Heat transfer predictions for engine turbines are very difficult because the boundary conditions are not well known. The conditions at the exit of the combustor are generally not well known and a section of this paper discusses that problem. The majority of the discussion is devoted to external heat transfer with and without cooling, turbulence effects, and internal cooling. As the design community increases the thrust-to-weight ratio and the turbine inlet temperature, there remain many turbine-related heat transfer issues. Included are film cooling modeling, definition of combustor exit conditions, understanding of blade tip distress, definition of hot streak migration, component fatigue, loss mechanisms in the low turbine, and many others. Several suggestions are given herein for research and development areas for which there is potentially high payoff to the industry with relatively small risk.}", issn = {0889-504X}, doi = {10.1115/1.1397776}, url = {https://doi.org/10.1115/1.1397776}, eprint = {https://asmedigitalcollection.asme.org/turbomachinery/article-pdf/123/4/637/5842876/637\_1.pdf}, } Doi = {10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2}, Url = {http://dx.doi.org/10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2}, @article{Durran1991, Annote = {doi: 10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2}, Author = {Durran, Dale R. }, Booktitle = {Monthly Weather Review}, Da = {1991/03/01}, Date = {1991/03/01}, Date-Added = {2012-11-17 00:56:38 +0000}, Date-Modified = {2012-11-17 00:56:38 +0000}, Isbn = {0027-0644}, FJournal = {Monthly Weather Review}, Journal = {Mon. Wea. Rev.}, FJournal = {Monthly Weather Review}, M3 = {doi: 10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2}, Month = {2012/11/16}, Number = {3}, Pages = {702--720}, Publisher = {American Meteorological Society}, Title = {The Third-Order {Adams-Bashforth} Method: {An} Attractive Alternative to Leapfrog Time Differencing}, Ty = {JOUR}, Volume = {119}, Year = {1991}, Year1 = {1991}, doi="10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2", url="http://dx.doi.org/10.1175/1520-0493(1991)119<0702:TTOABM>2.0.CO;2" } @book {MR2723959, AUTHOR = {Durran, Dale R.}, TITLE = {Numerical methods for fluid dynamics}, SERIES = {Texts in Applied Mathematics}, VOLUME = {32}, EDITION = {Second}, NOTE = {With applications to geophysics}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2010}, PAGES = {xvi+516}, ISBN = {978-1-4419-6411-3}, MRCLASS = {76-02 (65-02 76Mxx 86-08 86A10)}, MRNUMBER = {2723959 (2011i:76001)}, DOI = {10.1007/978-1-4419-6412-0}, URL = {http://dx.doi.org/10.1007/978-1-4419-6412-0}, } @book {DurranBOOK, AUTHOR = {Durran, Dale R.}, TITLE = {Numerical methods for fluid dynamics}, SERIES = {Texts in Applied Mathematics}, VOLUME = {32}, EDITION = {Second}, NOTE = {With applications to geophysics}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2010}, PAGES = {xvi+516}, ISBN = {978-1-4419-6411-3}, MRCLASS = {76-02 (65-02 76Mxx 86-08 86A10)}, MRNUMBER = {2723959 (2011i:76001)}, DOI = {10.1007/978-1-4419-6412-0}, URL = {http://dx.doi.org/10.1007/978-1-4419-6412-0}, } @ARTICLE{DB12, author = {Durran, Dale R. and Blossey, Peter N.}, title = "{Implicit-Explicit Multistep Methods for Fast-Wave-Slow-Wave Problems}", journal={Mon. Wea. Rev.}, FJOURNAL = {Monthly Weather Review}, year = 2012, volume = 140, number = 4, pages = {1307--1325}, doi = {10.1175/MWR-D-11-00088.1}, url="http://dx.doi.org/10.1175/MWR-D-11-00088.1" } @article {MR1765736, AUTHOR = {Dutt, Alok and Greengard, Leslie and Rokhlin, Vladimir}, TITLE = {Spectral deferred correction methods for ordinary differential equations}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {40}, YEAR = {2000}, NUMBER = {2}, PAGES = {241--266}, ISSN = {0006-3835}, MRCLASS = {65L05 (65F20 65L20)}, MRNUMBER = {1765736 (2001e:65104)}, MRREVIEWER = {Ekkehard Wagenf{\"u}hrer}, DOI = {10.1023/A:1022338906936}, URL = {http://dx.doi.org/10.1023/A:1022338906936}, } @Article{B509983H, author ="Earl, David J. and Deem, Michael W.", title ="Parallel tempering: Theory{,} applications{,} and new perspectives", journal ="Phys. Chem. Chem. Phys.", year ="2005", volume ="7", issue ="23", pages ="3910-3916", publisher ="The Royal Society of Chemistry", doi ="10.1039/B509983H", url ="http://dx.doi.org/10.1039/B509983H", abstract ="We review the history of the parallel tempering simulation method. From its origins in data analysis{,} the parallel tempering method has become a standard workhorse of physicochemical simulations. We discuss the theory behind the method and its various generalizations. We mention a selected set of the many applications that have become possible with the introduction of parallel tempering{,} and we suggest several promising avenues for future research."} @article{0037.28802, title = {The Hydromagnetic Equations}, author = {Els\"asser, Walter M.}, journal = {Phys. Rev.}, volume = {79}, issue = {1}, pages = {183--183}, numpages = {0}, year = {1950}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRev.79.183}, url = {http://link.aps.org/doi/10.1103/PhysRev.79.183} } @article {MR2104427, AUTHOR = {Emmrich, Etienne}, TITLE = {Error of the two-step {BDF} for the incompressible {N}avier-{S}tokes problem}, JOURNAL = {M2AN Math. Model. Numer. Anal.}, FJOURNAL = {M2AN. Mathematical Modelling and Numerical Analysis}, VOLUME = {38}, YEAR = {2004}, NUMBER = {5}, PAGES = {757--764}, ISSN = {0764-583X}, MRCLASS = {76M10 (35Q30 65M15 76D05)}, MRNUMBER = {2104427 (2005g:76076)}, MRREVIEWER = {Jean-Luc Guermond}, DOI = {10.1051/m2an:2004037}, URL = {http://dx.doi.org/10.1051/m2an:2004037}, } @article {MR2641310, AUTHOR = {Emmrich, E.}, TITLE = {Two-step {BDF} time discretisation of nonlinear evolution problems governed by monotone operators with strongly continuous perturbations}, JOURNAL = {Comput. Methods Appl. Math.}, FJOURNAL = {Computational Methods in Applied Mathematics}, VOLUME = {9}, YEAR = {2009}, NUMBER = {1}, PAGES = {37--62}, ISSN = {1609-4840}, MRCLASS = {65J08 (34G20 35K15 47J25 47N20 65L06)}, MRNUMBER = {2641310 (2011c:65095)}, MRREVIEWER = {Lucas J{\'o}dar}, } @article {MR0371242, AUTHOR = {Ene, Horia I. and S\'anchez-Palencia, Enrique}, TITLE = {\'{E}quations et ph\'enom\`{e}nes de surface pour l'\'{e}coulement dans un mod\`{e}le de milieu poreux}, JOURNAL = {J. M\'ecanique}, FJOURNAL = {Journal de M\'ecanique Th\'eorique et Appliqu\'ee. Journal of Theoretical and Applied Mechanics}, VOLUME = {14}, YEAR = {1975}, PAGES = {73--108}, ISSN = {0750-7240}, MRCLASS = {76.35}, MRNUMBER = {0371242}, MRREVIEWER = {Colin Rogers}, } MR1408680 @book {EnHaNe96, AUTHOR = {Engl, H.W. and Hanke, M. and Neubauer, A.}, TITLE = {Regularization of inverse problems}, SERIES = {Mathematics and its Applications}, VOLUME = {375}, PUBLISHER = {Kluwer Academic Publishers Group}, ADDRESS = {Dordrecht}, YEAR = {1996}, PAGES = {viii+321}, ISBN = {0-7923-4157-0}, MRCLASS = {65J20 (35R30 47A50 47H17)}, MRNUMBER = {MR1408680 (97k:65145)}, MRREVIEWER = {Ulrich Tautenhahn}, } @techreport{EpKu07, Author = {Epshteyn, Y. and Kurganov, A.}, Institution = {University of Pittsburgh}, Title = {New Discontinuous {G}alerkin Methods for the {K}eller-{S}egel Chemotaxis Model}}, Year = {2007}} @article{ERRERA2017587, title = "A coupling approach to modeling heat transfer during a full transient flight cycle", journal = "International Journal of Heat and Mass Transfer", volume = "110", pages = "587 - 605", year = "2017", issn = "0017-9310", doi = "https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.048", url = "http://www.sciencedirect.com/science/article/pii/S0017931016331222", author = "M.-P. Errera and M. Lazareff and J.-D. Garaud and T. Soubri\'{e} and C. Douta and T. Federici", keywords = "Fluid-structure interaction, Conjugate heat transfer, Thermal coupling, Transient, Numerical stability, Flight cycle", abstract = "The purpose of the present study is to describe novel numerical coupling schemes to analyze the transient temperature field in a solid via a conjugate heat transfer procedure. Emphasis is put on the interfacial treatment based on two complementary treatments: Dirichlet-Robin and Neumann-Robin transmission conditions. The numerical methods are first presented on the basis of a stability analysis in an aerothermal model problem. Stability conditions are expressed and the mathematical expression of the most relevant coupling parameters are provided for the first time. Furthermore, an overview of all the coefficients that can be used in a transient thermally-coupled procedure are given and a unified approach for steady and unsteady ramps is proposed. Then, these interfacial schemes are applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate. A comparative study with realistic operating conditions is carried out, at low and large Biot numbers. It is shown that certain choices of coupling coefficients, even if physically reasonable, may result in non-converging algorithms. This confirms that a model problem provides insight to the behavior of complicated heat transfer cases and constitutes an invaluable aid for generating efficient interfacial schemes. Indeed, the numerical computations demonstrate the efficiency of the numerical schemes based on the main theoretical results. The trends predicted by the model problem are recovered and excellent convergence properties are observed in all cases." } @article {MR2485439, AUTHOR = {Ervin, Vincent J. and Jenkins, Eleanor White and Sun, Shuyu}, TITLE = {Coupled generalized nonlinear {S}tokes flow with flow through a porous medium}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {47}, YEAR = {2009}, NUMBER = {2}, PAGES = {929--952}, ISSN = {0036-1429}, MRCLASS = {65N30 (76S05)}, MRNUMBER = {2485439}, MRREVIEWER = {Martin Vohral\'\i k}, DOI = {10.1137/070708354}, URL = {https://doi.org/10.1137/070708354}, } MR2344062 @article {ErLaNe06, AUTHOR = {Ervin, Vincent J. and Layton, William J. and Neda, Monika}, TITLE = {Numerical analysis of a higher order time relaxation model of fluids}, JOURNAL = {Int. J. Numer. Anal. Model.}, FJOURNAL = {International Journal of Numerical Analysis and Modeling}, VOLUME = {4}, YEAR = {2007}, NUMBER = {3-4}, PAGES = {648--670}, ISSN = {1705-5105}, MRCLASS = {76F02 (35Q35 76L05 76M10 76N99)}, MRNUMBER = {MR2344062 (2008j:76035)}, } @techreport{ELN10, Author = {Ervin, Vincent J. and Layton, W.J. and Neda, M.}, Institution = {University of Pittsburgh}, Title = {Numerical Analysis of Filter Based Stabilization for Evolution Equations}, Year = {2010}} @article {ErLaNe10, AUTHOR = {Ervin, Vincent J. and Layton, William J. and Neda, Monika}, TITLE = {Numerical {A}nalysis of {F}ilter-{B}ased {S}tabilization for {E}volution {E}quations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {50}, YEAR = {2012}, NUMBER = {5}, PAGES = {2307--2335}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {Preliminary Data}, MRNUMBER = {3022220}, DOI = {10.1137/100782048}, URL = {http://dx.doi.org/10.1137/100782048}, } @Article{axioms4040518, AUTHOR = {Ervin, Vincent J. and Kubacki, Michaela and Layton, William and Moraiti, Marina and Si, Zhiyong and Trenchea, Catalin}, TITLE = {On Limiting Behavior of Contaminant Transport Models in Coupled Surface and Groundwater Flows}, JOURNAL = {Axioms}, VOLUME = {4}, YEAR = {2015}, NUMBER = {4}, PAGES = {518--529}, URL = {http://www.mdpi.com/2075-1680/4/4/518}, ISSN = {2075-1680}, ABSTRACT = {There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutionary system including contaminant transport and analyze its quasi-static limits.}, DOI = {10.3390/axioms4040518} } @article {MR3898069, AUTHOR = {Ervin, Vincent J. and Kubacki, Michaela and Layton, William and Moraiti, Marina and Si, Zhiyong and Trenchea, Catalin}, TITLE = {Partitioned penalty methods for the transport equation in the evolutionary {S}tokes-{D}arcy-transport problem}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {35}, YEAR = {2019}, NUMBER = {1}, PAGES = {349--374}, ISSN = {0749-159X}, MRCLASS = {65M60 (35Q35 65M12 65M15 76D07 76M10 76S05)}, MRNUMBER = {3898069}, DOI = {10.1002/num.22303}, URL = {https://doi.org/10.1002/num.22303}, } MR1625845 @book {Evan98, AUTHOR = {Evans, L.C.}, TITLE = {Partial differential equations}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {19}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {1998}, PAGES = {xviii+662}, ISBN = {0-8218-0772-2}, MRCLASS = {35-01}, MRNUMBER = {MR1625845 (99e:35001)}, MRREVIEWER = {Luigi Rodino}, } @article{Evans_Tremaine_1999, doi = {10.1086/301057}, url = {https://doi.org/10.1086%2F301057}, year = 1999, month = {oct}, publisher = {{IOP} Publishing}, volume = {118}, number = {4}, pages = {1888--1899}, author = {N. Wyn Evans and Scott Tremaine}, title = {Linear Multistep Methods for Integrating Reversible Differential Equations}, journal = {The Astronomical Journal}, abstract = {This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here we report on a subset of these methods—the zero-growth methods—that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps—one of which is explicit. Variable time steps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps per radian are required for stability.} } @book {MR0495013, AUTHOR = {Fairweather, G.}, TITLE = {Finite element {G}alerkin methods for differential equations}, NOTE = {Lecture Notes in Pure and Applied Mathematics, Vol. 34}, PUBLISHER = {Marcel Dekker Inc.}, ADDRESS = {New York}, YEAR = {1978}, PAGES = {ix+263}, ISBN = {0-8247-6673-3}, MRCLASS = {65N30 (65-02 65L10)}, MRNUMBER = {MR0495013 (58 \#13781)}, MRREVIEWER = {Reinhard Scholz}, } @article {MR0296602, AUTHOR = {Fefferman, C.}, TITLE = {The multiplier problem for the ball}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {94}, YEAR = {1971}, PAGES = {330--336}, ISSN = {0003-486X}, MRCLASS = {42A18 (42A92 47B99)}, MRNUMBER = {MR0296602 (45 \#5661)}, MRREVIEWER = {R. Larsen}, } @book {MR2286737, AUTHOR = {Fierros Palacios, Angel}, TITLE = {The {H}amilton-type principle in fluid dynamics}, NOTE = {Fundamentals and applications to magnetohydrodynamics, thermodynamics, and astrophysics}, PUBLISHER = {Springer, Vienna}, YEAR = {2006}, PAGES = {xxvi+404}, ISBN = {978-3-211-24964-2; 3-211-24964-8}, MRCLASS = {76M30 (76W05 85A30)}, MRNUMBER = {2286737 (2009a:76143)}, } @article {MR708454, AUTHOR = {Fink, James P. and Rheinboldt, Werner C.}, TITLE = {On the discretization error of parametrized nonlinear equations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {20}, YEAR = {1983}, NUMBER = {4}, PAGES = {732--746}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15 (47H17)}, MRNUMBER = {708454 (85i:65072)}, MRREVIEWER = {H. Schwetlick}, DOI = {10.1137/0720049}, URL = {http://dx.doi.org/10.1137/0720049}, } @article {MR701832, AUTHOR = {Fink, J. P. and Rheinboldt, W. C.}, TITLE = {On the error behavior of the reduced basis technique for nonlinear finite element approximations}, JOURNAL = {Z. Angew. Math. Mech.}, FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten}, VOLUME = {63}, YEAR = {1983}, NUMBER = {1}, PAGES = {21--28}, ISSN = {0044-2267}, CODEN = {ZAMMAX}, MRCLASS = {73K25 (58E07 65N30)}, MRNUMBER = {701832 (85e:73047)}, MRREVIEWER = {Szczepan Borkowski}, DOI = {10.1002/zamm.19830630105}, URL = {http://dx.doi.org/10.1002/zamm.19830630105}, } @article {MR769244, AUTHOR = {Fink, James P. and Rheinboldt, Werner C.}, TITLE = {Solution manifolds and submanifolds of parametrized equations and their discretization errors}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {45}, YEAR = {1984}, NUMBER = {3}, PAGES = {323--343}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {58E07 (47H17 65J15)}, MRNUMBER = {769244 (86d:58018)}, MRREVIEWER = {J. Dane{\v{s}}}, DOI = {10.1007/BF01391412}, URL = {http://dx.doi.org/10.1007/BF01391412}, } @article {MR765693, AUTHOR = {Fink, J. P. and Rheinboldt, W. C.}, TITLE = {The role of the tangent mapping in analyzing bifurcation behaviour}, JOURNAL = {Z. Angew. Math. Mech.}, FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten}, VOLUME = {64}, YEAR = {1984}, NUMBER = {9}, PAGES = {407--412}, ISSN = {0044-2267}, CODEN = {ZAMMAX}, MRCLASS = {58E07 (47H17 65J15)}, MRNUMBER = {765693 (86d:58019)}, MRREVIEWER = {J. Dane{\v{s}}}, DOI = {10.1002/zamm.19840640908}, URL = {http://dx.doi.org/10.1002/zamm.19840640908}, } @article {MR795950, AUTHOR = {Fink, James P. and Rheinboldt, Werner C.}, TITLE = {Local error estimates for parametrized nonlinear equations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {22}, YEAR = {1985}, NUMBER = {4}, PAGES = {729--735}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15 (65H10)}, MRNUMBER = {795950 (87a:65106)}, MRREVIEWER = {G. J. Miel}, DOI = {10.1137/0722044}, URL = {http://dx.doi.org/10.1137/0722044}, } @article {MR849277, AUTHOR = {Fink, James P. and Rheinboldt, Werner C.}, TITLE = {Folds on the solution manifold of a parametrized equation}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {23}, YEAR = {1986}, NUMBER = {4}, PAGES = {693--706}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {58C27 (58C40 58E07 65J15)}, MRNUMBER = {849277 (87i:58021)}, MRREVIEWER = {J{\"u}rgen Scheurle}, DOI = {10.1137/0723045}, URL = {http://dx.doi.org/10.1137/0723045}, } @article {MR888753, AUTHOR = {Fink, James P. and Rheinboldt, Werner C.}, TITLE = {A geometric framework for the numerical study of singular points}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {24}, YEAR = {1987}, NUMBER = {3}, PAGES = {618--633}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65J15 (58C27 58E07)}, MRNUMBER = {888753 (88h:65118)}, MRREVIEWER = {J{\"u}rgen Scheurle}, DOI = {10.1137/0724042}, URL = {http://dx.doi.org/10.1137/0724042}, } @article {MR1817374, AUTHOR = {Fischer, Paul and Mullen, Julia}, TITLE = {Filter-based stabilization of spectral element methods}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {332}, YEAR = {2001}, NUMBER = {3}, PAGES = {265--270}, ISSN = {0764-4442}, CODEN = {CASMEI}, MRCLASS = {65M60}, MRNUMBER = {1817374 (2001m:65129)}, DOI = {10.1016/S0764-4442(00)01763-8}, URL = {http://dx.doi.org/10.1016/S0764-4442(00)01763-8}, } @ARTICLE{Fist97, AUTHOR = {Fister, R.}, TITLE = {Optimal control of harvesting in a predator-prey parabolic system}, YEAR = {1997}, JOURNAL = {Houston J. Math.}, VOLUME = {23}, NUMBER = {2}, PAGES = {341-355} } @ARTICLE{FM03, AUTHOR = {Fister, K.R. and Mc{C}arthy, C. M.}, TITLE = {Optimal control of a chemotaxis system}, YEAR = {2003}, JOURNAL = {Quart. Appl. Math.}, VOLUME = {61}, NUMBER = {2}, PAGES = {193-211} } @ARTICLE{FisMcc07, AUTHOR = {Fister, K.R. and Mc{C}arthy, C. M.}, TITLE = {Identification of a chemotactic sensitivity in a coupled system}, YEAR = {2007}, JOURNAL = {}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{F75, AUTHOR = {Fix, G.J.}, TITLE = {Finite element methods for ocean circulation problems}, YEAR = {1975}, JOURNAL = {SIAM J. Applied Math.}, VOLUME = {29}, NUMBER = {}, PAGES = {371-387} } MR1467006 @incollection {F97, AUTHOR = {Foias, C.}, TITLE = {What do the {N}avier-{S}tokes equations tell us about turbulence?}, BOOKTITLE = {Harmonic analysis and nonlinear differential equations ({R}iverside, {CA}, 1995)}, SERIES = {Contemp. Math.}, VOLUME = {208}, PAGES = {151--180}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1997}, MRCLASS = {76Fxx (35Q30 76D05)}, MRNUMBER = {MR1467006 (99e:76055)}, MRREVIEWER = {Alain Miranville}, } @article {MR0435626, AUTHOR = {Foia{\c{s}}, C. and Temam, R.}, TITLE = {Structure of the set of stationary solutions of the {N}avier-{S}tokes equations}, JOURNAL = {Comm. Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {30}, YEAR = {1977}, NUMBER = {2}, PAGES = {149--164}, ISSN = {0010-3640}, MRCLASS = {35Q10}, MRNUMBER = {0435626 (55 \#8584)}, MRREVIEWER = {D. E. Edmunds}, } @incollection {MR0447841, AUTHOR = {Foia{\c{s}}, C. and Temam, R.}, TITLE = {A generic property of the set of stationary solutions of {N}avier {S}tokes equations}, BOOKTITLE = {Turbulence and {N}avier-{S}tokes equations ({P}roc. {C}onf., {U}niv. {P}aris-{S}ud, {O}rsay, 1975)}, PAGES = {24--28. Lecture Notes in Math., Vol. 565}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1976}, MRCLASS = {35Q10 (58D15)}, MRNUMBER = {0447841 (56 \#6151)}, MRREVIEWER = {J. S. Joel}, } @techreport{FHN04, Author = {Foias, C. and Hoang, L.T. and Nicolaenko, B.}, Institution = {}, Title = {On the helicity in the 3D {Navier-Stokes} equations, {I} and {II}}, Year = {2004}} @article {MR903787, AUTHOR = {Foias, C. and Manley, O. and Temam, R.}, TITLE = {Attractors for the {B}\'enard problem: existence and physical bounds on their fractal dimension}, JOURNAL = {Nonlinear Anal.}, FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods}, VOLUME = {11}, YEAR = {1987}, NUMBER = {8}, PAGES = {939--967}, ISSN = {0362-546X}, CODEN = {NOANDD}, MRCLASS = {35Q10 (35B99 58F12)}, MRNUMBER = {903787 (89f:35166)}, MRREVIEWER = {C. Bardos}, DOI = {10.1016/0362-546X(87)90061-7}, URL = {http://dx.doi.org/10.1016/0362-546X(87)90061-7}, } @ARTICLE{Fran_Schwab_Todor_04, AUTHOR = {Frauenfelder, P. and Schwab, C. and Todor, R.A.}, TITLE = {Finite elements for elliptic problems with stochastic coefficients}, YEAR = {2005}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, VOLUME = {194}, NUMBER = {2-5}, PAGES = {205-228} } @ARTICLE{FHT01, AUTHOR = {Foias, C. and Holm, D.D. and Titi, E. S.}, TITLE = {The {N}avier-{S}tokes-alpha model of fluid turbulence}, YEAR = {2001}, JOURNAL = {Physica D}, VOLUME = {152-153}, NUMBER = {}, PAGES = {505-519} } MR1878243-FHT02 @article {FHT02, AUTHOR = {Foias, C. and Holm, D.D. and Titi, E.S.}, TITLE = {The three dimensional viscous {C}amassa-{H}olm equations, and their relation to the {N}avier-{S}tokes equations and turbulence theory}, JOURNAL = {J. Dynam. Differential Equations}, FJOURNAL = {Journal of Dynamics and Differential Equations}, VOLUME = {14}, YEAR = {2002}, NUMBER = {1}, PAGES = {1--35}, ISSN = {1040-7294}, CODEN = {JDDEEH}, MRCLASS = {76F02 (35Q30 35Q35 37L30 37N10 76D99 76F20)}, MRNUMBER = {MR1878243 (2002k:76070)}, MRREVIEWER = {Hongjun Gao}, } AUTHOR = {Foias, C. and Holm, D. and Titi, E. S.}, TITLE = {The three dimensional viscous {C}amassa-{H}olm equations, and their relation to the {N}avier-{S}tokes equations and turbulence theory}, YEAR = {2002}, JOURNAL = {Journal of Dynamics and Differential Equations}, VOLUME = {14}, NUMBER = {}, PAGES = {1-35} } @incollection {MR2549136, AUTHOR = {Font, J. A.}, TITLE = {General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics}, BOOKTITLE = {Hyperbolic problems: theory, numerics, applications}, PAGES = {3--17}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2008}, MRCLASS = {83C55 (35L65 35Q75 76W05)}, MRNUMBER = {2549136}, DOI = {10.1007/978-3-540-75712-2_1}, URL = {http://dx.doi.org/10.1007/978-3-540-75712-2_1}, } @article {MR0395249, AUTHOR = {Fornberg, B.}, TITLE = {On the instability of leap-frog and {C}rank-{N}icolson approximations of a nonlinear partial differential equation}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {27}, YEAR = {1973}, PAGES = {45--57}, ISSN = {0025-5718}, MRCLASS = {65M10}, MRNUMBER = {0395249 (52 \#16046)}, MRREVIEWER = {D. Schultz}, } @incollection {MR2856654, AUTHOR = {Frangos, M. and Marzouk, Y. and Willcox, K. and van Bloemen Waanders, B.}, TITLE = {Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems}, BOOKTITLE = {Large-scale inverse problems and quantification of uncertainty}, SERIES = {Wiley Ser. Comput. Stat.}, PAGES = {123--149}, PUBLISHER = {Wiley, Chichester}, YEAR = {2011}, MRCLASS = {62F15 (60G35 65C60)}, MRNUMBER = {2856654}, } @techreport{FHV96, Author = {Frank, J. and Hundsdorfer, W. and Verwer, J.}, Institution = {Centrum Wiskunde and Informatica (CWI)}, Title = {Stability of {Implicit-Explicit} linear multistep methods}, Year = {1996}} @article {MR1485815, AUTHOR = {Frank, J. and Hundsdorfer, W. and Verwer, J. G.}, TITLE = {On the stability of implicit-explicit linear multistep methods}, NOTE = {Special issue on time integration (Amsterdam, 1996)}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {25}, YEAR = {1997}, NUMBER = {2-3}, PAGES = {193--205}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {65L20 (65L06)}, MRNUMBER = {1485815 (98m:65126)}, MRREVIEWER = {H. Brunner}, DOI = {10.1016/S0168-9274(97)00059-7}, URL = {http://dx.doi.org/10.1016/S0168-9274(97)00059-7}, } @article {MR1158174, AUTHOR = {Friedman, Avner and Reitich, Fernando}, TITLE = {Parameter identification in reaction-diffusion models}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {8}, YEAR = {1992}, NUMBER = {2}, PAGES = {187--192}, ISSN = {0266-5611}, CODEN = {INPEEY}, MRCLASS = {35R30 (35K57)}, MRNUMBER = {MR1158174 (92j:35186)}, URL = {http://stacks.iop.org/0266-5611/8/187}, } @article{FrPoLeMa75, author={Frisch, U. and Pouquet, A. and Leorat, J. and Mazure, A.}, title={Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence}, journal={J. Fluid Mech.}, volume={68}, pages={769-778}, year={1975}} MR1428905 @book {Fris95, AUTHOR = {Frisch, U.}, TITLE = {Turbulence}, NOTE = {The legacy of A. N. Kolmogorov}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1995}, PAGES = {xiv+296}, ISBN = {0-521-45103-5}, MRCLASS = {76-02 (35Q30 76D05 76Fxx 76M35)}, MRNUMBER = {MR1428905 (98e:76002)}, MRREVIEWER = {Philip J. Holmes}, } @ARTICLE{FuTa97, AUTHOR = {Fureby, C. and Tabor, G.}, TITLE = {Mathematical and physical constraints on large-eddy simulations}, YEAR = {1997}, JOURNAL = {Theor. Comput. Fluid Dyn.}, VOLUME = {9}, NUMBER = {2}, PAGES = {85-102} } @BOOK{FuIm96, AUTHOR = {Fursikov, A.V. and Imanuvilov, O.Yu.}, TITLE = {Controllability of {E}volutions {E}quations}, PUBLISHER = {Seoul National University}, YEAR = {1996}, SERIES = {Lecture Notes Series, Vol. 34}, VOLUME = {}, EDITION = {}, ADDRESS = {Korea} } MR1726442 @book {Furs00, AUTHOR = {Fursikov, A.V.}, TITLE = {Optimal control of distributed systems. {T}heory and applications}, SERIES = {Translations of Mathematical Monographs}, VOLUME = {187}, NOTE = {Translated from the 1999 Russian original by Tamara Rozhkovskaya}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {2000}, PAGES = {xiv+305}, ISBN = {0-8218-1382-X}, MRCLASS = {49-02 (35B37 35Q30 49J20 49K20 76D55 93C20)}, MRNUMBER = {MR1726442 (2000m:49001)}, MRREVIEWER = {Irena Lasiecka}, } @ARTICLE{FI99, AUTHOR = {Fursikov, A. V. and Imanuvilov, O. Yu.}, TITLE = {Exact controllability of the {N}avier-{S}tokes and {B}oussinesq equations}, YEAR = {1999}, JOURNAL = {Uspekhi Mat. Nauk.}, VOLUME = {54}, NUMBER = {3}, PAGES = {93-146} } @ARTICLE{GL61, AUTHOR = {Gailitis, A. and Lielausis, O.}, TITLE = {On a possibility to reduce the hydrodynamical resistance of a plate in an electrolyte }, YEAR = {1961}, JOURNAL = {Applied Magnetohydrodynamics (in Russian). Reports of the Physics Institute}, VOLUME = {12}, NUMBER = {}, PAGES = {143-146} } @book {MR0637067, AUTHOR = {Gaines, Robert E. and Mawhin, Jean L.}, TITLE = {Coincidence degree, and nonlinear differential equations}, SERIES = {Lecture Notes in Mathematics, Vol. 568}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1977}, PAGES = {i+262}, ISBN = {3-540-08067-8}, MRCLASS = {47H15 (34B15 34K10 55C20)}, MRNUMBER = {MR0637067 (58 \#30551)}, MRREVIEWER = {R. Kannan}, } @article {MR2642821, AUTHOR = {Galbally, D. and Fidkowski, K. and Willcox, K. and Ghattas, O.}, TITLE = {Non-linear model reduction for uncertainty quantification in large-scale inverse problems}, JOURNAL = {Internat. J. Numer. Methods Engrg.}, FJOURNAL = {International Journal for Numerical Methods in Engineering}, VOLUME = {81}, YEAR = {2010}, NUMBER = {12}, PAGES = {1581--1608}, ISSN = {0029-5981}, CODEN = {IJNMBH}, MRCLASS = {65C60}, MRNUMBER = {2642821 (2011a:65024)}, MRREVIEWER = {Peter A. Lachenbruch}, DOI = {10.1002/nme.2746}, URL = {http://dx.doi.org/10.1002/nme.2746}, } @BOOK{Ga00, AUTHOR = {Galdi, G.P.}, TITLE = {Lectures in Mathematical Fluid Dynamics}, PUBLISHER = {Birkhauser-Verlag}, YEAR = {2000}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @BOOK{Ga94, AUTHOR = {Galdi, G.P.}, TITLE = {An introduction to the {M}athematical {T}heory of the {N}avier-{S}tokes equations}, PUBLISHER = {Springer}, YEAR = {1994}, SERIES = {}, VOLUME = {I}, EDITION = {}, ADDRESS = {Berlin} } GL00_MR1753115 @article {MR1753115, AUTHOR = {Galdi, G.P. and Layton, W.J.}, TITLE = {Approximation of the larger eddies in fluid motions. {II}. {A} model for space-filtered flow}, JOURNAL = {Math. Models Methods Appl. Sci.}, FJOURNAL = {Mathematical Models \& Methods in Applied Sciences}, VOLUME = {10}, YEAR = {2000}, NUMBER = {3}, PAGES = {343--350}, ISSN = {0218-2025}, MRCLASS = {76F65 (76M25)}, MRNUMBER = {MR1753115 (2001h:76074)}, } @article{galtier-2000, author = {Galtier,S. and Nazarenko,S. V. and Newell,A. C. and Pouquet,A.}, title = {A weak turbulence theory for incompressible magnetohydrodynamics}, fjournal = {Journal of Plasma Physics}, journal = {J. Plasma Phys.}, volume = {63}, issue = {05}, month = {6}, year = {2000}, issn = {1469-7807}, pages = {447--488}, numpages = {42}, doi = {null}, URL = {http://journals.cambridge.org/article_S0022377899008284}, } @article {MR3180857, AUTHOR = {Galvin, Keith J. and Rebholz, Leo G. and Trenchea, Catalin}, TITLE = {Efficient, {U}nconditionally {S}table, and {O}ptimally {A}ccurate {FE} {A}lgorithms for {A}pproximate {D}econvolution {M}odels}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {52}, YEAR = {2014}, NUMBER = {2}, PAGES = {678--707}, ISSN = {0036-1429}, MRCLASS = {65M60 (45K05 76D05 76F65)}, MRNUMBER = {3180857}, DOI = {10.1137/120887412}, URL = {http://dx.doi.org/10.1137/120887412}, } @article{Ganesan2007, author = {Ganesan, V.}, year = {2007}, month = {04}, pages = {}, title = {Non-Reacting and Reacting Flow Analysis in an Aero-Engine Gas Turbine Combustor Using CFD}, journal = {SAE Technical Papers}, doi = {10.4271/2007-01-0916} } @article{GARG2002109, title = "Heat transfer research on gas turbine airfoils at {NASA GRC}", journal = "International Journal of Heat and Fluid Flow", volume = "23", number = "2", pages = "109 - 136", year = "2002", issn = "0142-727X", doi = "https://doi.org/10.1016/S0142-727X(01)00144-8", url = "http://www.sciencedirect.com/science/article/pii/S0142727X01001448", author = "Vijay K. Garg", keywords = "Gas turbine heat transfer, Film cooling, Internal cooling channel, Blade tip, Rough blade", abstract = "The turbine gas path is a very complex flow field due to a variety of flow and heat transfer phenomena encountered in turbine passages. This manuscript provides an overview of the current work in this field at the NASA Glenn Research Center (GRC). Based on the author's preference, however, more emphasis is on the computational work. There is much more experimental work in progress at GRC than that reported here. Specifically, the external flow and heat transfer characteristics are described over smooth and rough turbine blades for a range of parameter values. For smooth blades, the effect of film-cooling holes as well as internal cooling channels with ribs and bleed holes is considered. Studies on the blade tip region, susceptible to burnout and oxidation due to high thermal loading, are also described. Wherever possible, predictions of heat transfer coefficient on the real blade surface, obtained using in-house-developed codes, are compared with the available experimental data. Suggestions for further work are outlined." } @book {MR2542010, AUTHOR = {Garnier, E. and Adams, N. and Sagaut, P.}, TITLE = {Large eddy simulation for compressible flows}, SERIES = {Scientific Computation}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2009}, PAGES = {x+276}, ISBN = {978-90-481-2818-1}, MRCLASS = {76F65 (65-02 65M99 76-02)}, MRNUMBER = {2542010 (2010g:76074)}, DOI = {10.1007/978-90-481-2819-8}, URL = {http://dx.doi.org/10.1007/978-90-481-2819-8}, } @ARTICLE{GT05a, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Spatiotemporal dynamics of two generic predator-prey models}, YEAR = {2010}, JOURNAL = {Journal of Biological Dynamics}, VOLUME = {}, NUMBER = {4:6}, PAGES = {559-570} } @ARTICLE{GT05b, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Finite Element Approximation of Spatially Extended Predator-Prey Interactions with the {H}olling Type {I}{I} Functional Response}, YEAR = {2007}, JOURNAL = {Numer. Math.}, VOLUME = {107}, NUMBER = {4}, PAGES = {641-667} } @ARTICLE{GT05c, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Optimal Control of a Nutrient--Phytoplankton--Zooplankton--Fish System}, YEAR = {2007}, JOURNAL = {SIAM J. Control Optim.} , VOLUME = {46}, NUMBER = {}, PAGES = {775-791} } @ARTICLE{GT05d, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Numerical Analysis of a Nutrient--Plankton Optimal Control Problem}, YEAR = {}, JOURNAL = {In preparation}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{GaTr07a, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Global existence for {G}ierer-{M}einhardt reaction-diffusion systems for pattern formation}, YEAR = {}, JOURNAL = {In preparation}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{GaTr07b, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Parameter identification for reaction-diffusion equations modeling pattern formation }, YEAR = {June 29 - July 1, 2007}, JOURNAL = {SIAM Conference on Control and Its Applications, San Francisco, California}, VOLUME = {}, NUMBER = {}, PAGES = {} } %2009%Inverse Problems @ARTICLE{GaTr09a, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {Identification of {S}pace-{T}ime {D}istributed {P}arameters in the {G}ierer--{M}einhardt {R}eaction-{D}iffusion {S}ystem}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {74}, YEAR = {2014}, NUMBER = {1}, PAGES = {147--166}, ISSN = {0036-1399}, MRCLASS = {Preliminary Data}, MRNUMBER = {3164563}, DOI = {10.1137/120885784}, URL = {http://dx.doi.org/10.1137/120885784}, } @ARTICLE{GaTr11, AUTHOR = {Garvie, Marcus R. and Trenchea, Catalin}, TITLE = {A three level finite element approximation of a pattern formation model in developmental biology}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {127}, YEAR = {2014}, NUMBER = {3}, PAGES = {397--422}, ISSN = {0029-599X}, MRCLASS = {65M60 (35-XX 92-XX)}, MRNUMBER = {3216814}, DOI = {10.1007/s00211-013-0591-z}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1007/s00211-013-0591-z}, } @ARTICLE{GaMaTr09, AUTHOR = {Garvie, Marcus R. and Maini, Philip and Trenchea, Catalin}, TITLE = {An efficient and robust numerical algorithm for estimating parameters in {Turing} systems}, YEAR = {2010}, JOURNAL = {J. Comp. Phys.}, VOLUME = {229}, NUMBER = {19}, PAGES = {7058-7071} } @book {MR2061539, AUTHOR = {Gautschi, Walter}, TITLE = {Orthogonal polynomials: computation and approximation}, SERIES = {Numerical Mathematics and Scientific Computation}, NOTE = {Oxford Science Publications}, PUBLISHER = {Oxford University Press}, ADDRESS = {New York}, YEAR = {2004}, PAGES = {x+301}, ISBN = {0-19-850672-4}, MRCLASS = {42-02 (33C45 33F05 42C05)}, MRNUMBER = {MR2061539 (2005e:42001)}, MRREVIEWER = {Leonid B. Golinski{\u\i}}, } @ARTICLE{GB81, AUTHOR = {Gauthier, J.P. and Bornard, G.}, TITLE = {Observability for any $u(t)$ of a class of nonlinear systems}, YEAR = {1981}, JOURNAL = {IEEE Transactions on Automatic Control}, VOLUME = {AC-26}, NUMBER = {4}, PAGES = {922-926} } @ARTICLE{GK94, AUTHOR = {Gauthier, J.P. and Kupka, I.}, TITLE = {Observability and observers for nonlinear systems}, YEAR = {1994}, JOURNAL = {SIAM J. Control and Optimization}, VOLUME = {32}, NUMBER = {4}, PAGES = {975-994} } @BOOK{GK01, AUTHOR = {Gauthier, J.P. and Kupka, I.}, TITLE = {Deterministic observation theory and applications}, PUBLISHER = {Cambridge University Press}, YEAR = {2001}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {Cambridge} } @book {MR0315898, AUTHOR = {Gear, C. William}, TITLE = {Numerical initial value problems in ordinary differential equations}, PUBLISHER = {Prentice-Hall, Inc., Englewood Cliffs, N.J.}, YEAR = {1971}, PAGES = {xvii+253}, MRCLASS = {65L05}, MRNUMBER = {0315898}, MRREVIEWER = {T. E. Hull}, } @ARTICLE{GLFSM03, AUTHOR = {Gentleman, W. and Leising, A. and Frost, B. and Strom, S. and Murray, J.}, TITLE = {Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics}, YEAR = {2003}, JOURNAL = {Deep-Sea Res. Pt. II}, VOLUME = {50}, NUMBER = {}, PAGES = {2847-2875} } @book {MR2289481, AUTHOR = {Gerbeau, Jean-Fr{\'e}d{\'e}ric and Le Bris, Claude and Leli{\`e}vre, Tony}, TITLE = {Mathematical methods for the magnetohydrodynamics of liquid metals}, SERIES = {Numerical Mathematics and Scientific Computation}, PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = {2006}, PAGES = {xiv+310}, ISBN = {978-0-19-856665-6; 0-19-856665-4}, MRCLASS = {76W05 (35Q35 65M60 65N30 76D03 76M10)}, MRNUMBER = {2289481 (2008i:76205)}, MRREVIEWER = {A. J. Meir}, DOI = {10.1093/acprof:oso/9780198566656.001.0001}, URL = {http://dx.doi.org/10.1093/acprof:oso/9780198566656.001.0001}, } Ger86-MR845232 @article {MR845232, AUTHOR = {Germano, M.}, TITLE = {Differential filters of elliptic type}, JOURNAL = {Phys. Fluids}, FJOURNAL = {The Physics of Fluids}, VOLUME = {29}, YEAR = {1986}, NUMBER = {6}, PAGES = {1757--1758}, ISSN = {0031-9171}, CODEN = {PFLDAS}, MRCLASS = {76F05}, MRNUMBER = {MR845232 (87h:76075b)}, } Ger86b - MR845231 @article {MR845231, AUTHOR = {Germano, M.}, TITLE = {Differential filters for the large eddy numerical simulation of turbulent flows}, JOURNAL = {Phys. Fluids}, FJOURNAL = {The Physics of Fluids}, VOLUME = {29}, YEAR = {1986}, NUMBER = {6}, PAGES = {1755--1757}, ISSN = {0031-9171}, CODEN = {PFLDAS}, MRCLASS = {76F05}, MRNUMBER = {MR845231 (87h:76075a)}, } @ARTICLE{Geu97, AUTHOR = {Geurts, B. J.}, TITLE = {Inverse modeling for large eddy simulation}, YEAR = {1997}, JOURNAL = {Phys. Fluids}, VOLUME = {9}, NUMBER = {}, PAGES = {3585} } @BOOK{G03, AUTHOR = {Geurts, B.J.}, TITLE = {Elements of direct and large eddy simulation}, PUBLISHER = {Edwards Publishing}, YEAR = {2003}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } GH03 - MR1971789 @article {MR1971789, AUTHOR = {Geurts, B.J. and Holm, D.D.}, TITLE = {Regularization modeling for large-eddy simulation}, JOURNAL = {Phys. Fluids}, FJOURNAL = {Physics of Fluids}, VOLUME = {15}, YEAR = {2003}, NUMBER = {1}, PAGES = {L13--L16}, ISSN = {1070-6631}, CODEN = {PHFLE6}, MRCLASS = {76F65}, MRNUMBER = {MR1971789 (2004b:76088)}, } @ARTICLE{GH05, AUTHOR = {Geurts, B.J. and Holm, D.D.}, TITLE = {Leray and {LANS}-alpha modeling of turbulent mixing}, YEAR = {2006}, JOURNAL = {J. of Turbulence}, VOLUME = {7}, NUMBER = {10}, PAGES = {1-33} } MR2211986 @article {GeHo06, AUTHOR = {Geurts, B.J. and Holm, D.D.}, TITLE = {Commutator errors in large-eddy simulation}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and General}, VOLUME = {39}, YEAR = {2006}, NUMBER = {9}, PAGES = {2213--2229}, ISSN = {0305-4470}, CODEN = {JPHAC5}, MRCLASS = {76F65}, MRNUMBER = {MR2211986 (2006k:76067)}, MRREVIEWER = {Bertrand Michaux}, } @ARTICLE{GhDh98, AUTHOR = {Ghanem, R. and Dham, S.}, TITLE = {Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media}, YEAR = {1998}, JOURNAL = {Transport in Porous Media}, VOLUME = {32}, NUMBER = {}, PAGES = {239-262} } @article{GHC, author = {Gibson,J. 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Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {333}, YEAR = {2007}, NUMBER = {1}, PAGES = {295--310}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {49K20 (35Q30 49J20 76D05 76D55 76W05)}, MRNUMBER = {MR2323492 (2008f:49035)}, MRREVIEWER = {Ruxandra Stavre}, } @ARTICLE{GLSTW09, AUTHOR = {Gunzburger, M. and Lee, E. and Saka, Y. and Trenchea, C. and Wang, X.}, TITLE = {Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence}, YEAR = {2010}, JOURNAL = {J. Sci. Comput.}, VOLUME = {45}, NUMBER = {1-3}, PAGES = {294-332} } @ARTICLE{GuTrWe12, AUTHOR = {Gunzburger, M. and Trenchea, C. and Webster, C.}, TITLE = {A generalized stochastic collocation approach to constrained optimization for random data identification problems}, YEAR = {2014}, JOURNAL = {Preprint}, VOLUME = {}, NUMBER = {}, PAGES = {} } @techreport{GuTrWe11, Author = {Gunzburger, M. and Trenchea, C. and Webster, C.}, Institution = {University of Pittsburgh}, Title = {A generalized methodology for the solution of stochastic identification problems constrained by partial differential equations with random input data}, Year = {2011}} @techreport{GuTrWe15, Author = {Gunzburger, M. and Trenchea, C. and Webster, C.}, Institution = {University of Pittsburgh}, Title = {Error estimates for a stochastic collocation approach to identification and control problems for random elliptic PDEs}, Year = {2015}} @article{GunLab12, author = {Gunzburger, M. and Labovsky, A.}, title = {High Accuracy Method for Turbulent Flow Problems}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {22}, number = {06}, pages = {1250005}, year = {2012}, doi = {10.1142/S0218202512500054}, URL = {http://www.worldscientific.com/doi/abs/10.1142/S0218202512500054}, eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218202512500054} } @article{10.1137/100801731, title = {Error Estimates of Stochastic Optimal {Neumann} Boundary Control Problems}, publisher = {SIAM}, JOURNAL = {SIAM J. Numer. Anal.}, year = {2011}, doi = {DOI:10.1137/100801731}, issn = {00361429}, eissn = {10957170}, coden = {SJNAAM}, volume = {49}, number = {4}, pages = {1532-1552}, author = {Max D. Gunzburger and Hyung-Chun Lee and Jangwoon Lee}, keywords = {stochastic optimal control; finite element method; Karhunen-Lo\8Fve expansion; }, url = {http://dx.doi.org/doi/10.1137/100801731}, } @techreport{GuzelTrenchea2017, Author = {Guzel, Ahmet and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {The {Williams} step increases the stability and accuracy of the {hoRA} time filter}, Year = {2017}} @article {MR3807176, AUTHOR = {Guzel, Ahmet and Trenchea, Catalin}, TITLE = {The {W}illiams step increases the stability and accuracy of the ho{RA} time filter}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {131}, YEAR = {2018}, PAGES = {158--173}, ISSN = {0168-9274}, MRCLASS = {Prelim}, MRNUMBER = {3807176}, DOI = {10.1016/j.apnum.2018.05.003}, URL = {https://doi-org.pitt.idm.oclc.org/10.1016/j.apnum.2018.05.003}, } @article {MR3803857, AUTHOR = {Guzel, Ahmet and Layton, William}, TITLE = {Time filters increase accuracy of the fully implicit method}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {58}, YEAR = {2018}, NUMBER = {2}, PAGES = {301--315}, ISSN = {0006-3835}, MRCLASS = {65L04 (65L05)}, MRNUMBER = {3803857}, DOI = {10.1007/s10543-018-0695-z}, URL = {https://doi-org.pitt.idm.oclc.org/10.1007/s10543-018-0695-z}, } @book {Eldad2014, AUTHOR = {Haber, Eldad}, TITLE = {Computational Methods in Geophysical Electromagnetics}, SERIES = {Mathematics in Industry}, VOLUME = {}, NOTE = {}, PUBLISHER = {SIAM}, ADDRESS = {}, YEAR = {2014}, PAGES = {viii+143}, ISBN = {ISBN 978-1-611973-79-2}, MRCLASS = {}, MRNUMBER = {}, DOI = {}, URL = {}, } @ARTICLE{Hage00, AUTHOR = {Hager, W.W.}, TITLE = {{R}unge-{K}utta methods in optimal control and the transformed adjoint system}, YEAR = {2000}, JOURNAL = {Numer. Math.}, VOLUME = {87}, NUMBER = {}, PAGES = {247-282} } @article {MR2444723, AUTHOR = {Hairer, Ernst}, TITLE = {Conjugate-symplecticity of linear multistep methods}, JOURNAL = {J. Comput. Math.}, FJOURNAL = {Journal of Computational Mathematics}, VOLUME = {26}, YEAR = {2008}, NUMBER = {5}, PAGES = {657--659}, ISSN = {0254-9409}, MRCLASS = {65L05 (65P10)}, MRNUMBER = {2444723}, MRREVIEWER = {Domingo Hern\'{a}ndez-Abreu}, } @article {MR2127929, AUTHOR = {Hairer, Ernst and Lubich, Christian}, TITLE = {Symmetric multistep methods over long times}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {97}, YEAR = {2004}, NUMBER = {4}, PAGES = {699--723}, ISSN = {0029-599X}, MRCLASS = {70-08 (37M15 37N05 65L06 65P10)}, MRNUMBER = {2127929}, MRREVIEWER = {Werner M. Seiler}, DOI = {10.1007/s00211-004-0520-2}, URL = {https://doi-org.pitt.idm.oclc.org/10.1007/s00211-004-0520-2}, } @book {MR2840298, AUTHOR = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard}, TITLE = {Geometric numerical integration}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {31}, NOTE = {Structure-preserving algorithms for ordinary differential equations, Reprint of the second (2006) edition}, PUBLISHER = {Springer, Heidelberg}, YEAR = {2010}, PAGES = {xviii+644}, ISBN = {978-3-642-05157-9}, MRCLASS = {65P10}, MRNUMBER = {2840298 (2012g:65290)}, } @book {MR2657217, AUTHOR = {Hairer, E. and Wanner, G.}, TITLE = {Solving ordinary differential equations. {II}}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {14}, NOTE = {Stiff and differential-algebraic problems, Second revised edition}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2010}, PAGES = {xvi+614}, ISBN = {978-3-642-05220-0}, MRCLASS = {65-02 (65Lxx)}, MRNUMBER = {2657217 (2011f:65001)}, DOI = {10.1007/978-3-642-05221-7}, URL = {http://dx.doi.org/10.1007/978-3-642-05221-7}, } @book {MR1227985, AUTHOR = {Hairer, E. and N{\o}rsett, S. P. and Wanner, G.}, TITLE = {Solving ordinary differential equations. {I}}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {8}, EDITION = {Second}, NOTE = {Nonstiff problems}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1993}, PAGES = {xvi+528}, ISBN = {3-540-56670-8}, MRCLASS = {65-02 (34A50 65L99)}, MRNUMBER = {1227985 (94c:65005)}, } @article {MR2259251, AUTHOR = {Hairer, Martin and Mattingly, Jonathan C.}, TITLE = {Ergodicity of the 2{D} {N}avier-{S}tokes equations with degenerate stochastic forcing}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {164}, YEAR = {2006}, NUMBER = {3}, PAGES = {993--1032}, ISSN = {0003-486X}, CODEN = {ANMAAH}, MRCLASS = {37L55 (35Q30 35R60 60H15 76D05 76M35)}, MRNUMBER = {2259251 (2008a:37095)}, MRREVIEWER = {Hakima Bessaih}, DOI = {10.4007/annals.2006.164.993}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.4007/annals.2006.164.993}, } @article {MR2111726, AUTHOR = {Hairer, Martin and Mattingly, Jonathan C.}, TITLE = {Ergodic properties of highly degenerate 2{D} stochastic {N}avier-{S}tokes equations}, JOURNAL = {C. R. Math. Acad. Sci. Paris}, FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, VOLUME = {339}, YEAR = {2004}, NUMBER = {12}, PAGES = {879--882}, ISSN = {1631-073X}, MRCLASS = {76D05 (35Q30 37L55 60H15 76M35)}, MRNUMBER = {2111726 (2005m:76047)}, MRREVIEWER = {Bohdan Maslowski}, DOI = {10.1016/j.crma.2004.09.035}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1016/j.crma.2004.09.035}, } @ARTICLE{HalMcc75, AUTHOR = {Haltiner, G. J. and McCollough, J. M.}, TITLE = {Experiments in the Initialization of a Global Primitive Equation Model}, YEAR = {1975}, JOURNAL = {J. Appl. Meteor.}, VOLUME = {14}, NUMBER = {3}, PAGES = {281--288} } @BOOK{HalWil1979, AUTHOR = {Haltiner, G.J. and Williams, R.T.}, TITLE = {Numerical prediction and dynamics meteorology}, PUBLISHER = {John Wiley \& Sons}, YEAR = {1980}, SERIES = {}, VOLUME = {}, EDITION = {2nd}, ADDRESS = {New York} } @Article{HaWaNaWa06, author="Hanspal, N. S. and Waghode, A. N. and Nassehi, V. and Wakeman, R. J.", title="Numerical Analysis of Coupled Stokes/Darcy Flows in Industrial Filtrations", journal="Transport in Porous Media", year="2006", month="Jul", day="01", volume="64", number="1", pages="73", abstract="Free flow channel confined by porous walls is a feature of many of the natural and industrial settings. Viscous flows adjacent to saturated porous medium occur in cross-flow and dead-end filtrations employed primarily in pharmaceutical and chemical industries for solid--liquid or gas--solid separations. Various mathematical models have been put forward to describe the conjugate flow dynamics based on theoretical grounds and experimental evidence. Despite this fact, there still exists a wide scope for extensive research in numerical solutions of these coupled models when applied to problems with industrial relevance. The present work aims towards the numerical analysis of coupled free/porous flow dynamics in the context of industrial filtration systems. The free flow dynamics has been expressed by the Stokes equations for the creeping, laminar flow regime whereas the flow behaviour in very low permeability porous media has been represented by the conventional Darcy equation. The combined free/porous fluid dynamical behaviour has been simulated using a mixed finite element formulation based on the standard Galerkin technique. A nodal replacement technique has been developed for the direct linking of Stokes and Darcy flow regimes which alleviates specification of any additional constraint at the free/porous interface. The simulated flow and pressure fields have been found for flow domains with different geometries which represent prototypes of actual industrial filtration equipment. Results have been obtained for varying values of permeability of the porous medium for generalised Newtonian fluids obeying the power law model. A series of numerical experiments has been performed in order to validate the coupled flow model. The developed model has been examined for its flexibility in dealing with complex geometrical domains and found to be generic in delivering convergent, stable and theoretically consistent results. The validity and accuracy of the simulated results has been affirmed by comparing with available experimental data.", issn="1573-1634", doi="10.1007/s11242-005-1457-3", url="https://doi.org/10.1007/s11242-005-1457-3" } @ARTICLE{HGSS04, AUTHOR = {Hansson, L.-A. and Gyllstr{\"o}m, M. and Stahl-Delbanco, A. and Svensson, M.}, TITLE = {Responses to fish predation and nutrients by plankton at different levels of taxonomic resolution}, YEAR = {2004}, JOURNAL = {Freshwater Biol.}, VOLUME = {49}, NUMBER = {}, PAGES = {1538-1550} } @article {MR2487575, AUTHOR = {Hattaf, K. and Rachik, M. and Saadi, S. and Tabit, Y. and Yousfi, N.}, TITLE = {Optimal control of tuberculosis with exogenous reinfection}, JOURNAL = {Appl. Math. Sci. (Ruse)}, FJOURNAL = {Applied Mathematical Sciences}, VOLUME = {3}, YEAR = {2009}, NUMBER = {5-8}, PAGES = {231--240}, ISSN = {1312-885X}, MRCLASS = {92C60 (49K15 49N90)}, MRNUMBER = {MR2487575 (2010c:92060)}, } @article{HBD04, title = {Simulations of nonhelical hydromagnetic turbulence}, author = {Haugen, Nils and Brandenburg, Axel and Dobler, Wolfgang}, journal = {Phys. Rev. E}, volume = {70}, issue = {1}, pages = {016308}, numpages = {14}, year = {2004}, month = {Jul}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.70.016308}, url = {http://link.aps.org/doi/10.1103/PhysRevE.70.016308} } @article {MR3327978, AUTHOR = {Hay, A. and Etienne, S. and Pelletier, D. and Garon, A.}, TITLE = {hp-adaptive time integration based on the {BDF} for viscous flows}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {291}, YEAR = {2015}, PAGES = {151--176}, ISSN = {0021-9991}, MRCLASS = {65M60 (65L06 65M20 76Nxx)}, MRNUMBER = {3327978}, MRREVIEWER = {Mapundi K. Banda}, DOI = {10.1016/j.jcp.2015.03.022}, URL = {https://doi.org/10.1016/j.jcp.2015.03.022}, } @article {MR4022323, AUTHOR = {He, Ying and Shen, Jie}, TITLE = {Unconditionally {S}table {P}ressure-{C}orrection {S}chemes for a {N}onlinear {F}luid-{S}tructure {I}nteraction {M}odel}, JOURNAL = {Commun. Appl. Math. Comput.}, FJOURNAL = {Communications on Applied Mathematics and Computation}, VOLUME = {1}, YEAR = {2019}, NUMBER = {1}, PAGES = {61--80}, ISSN = {2096-6385}, MRCLASS = {74F10 (35B30 35Q30 65M12 76D05)}, MRNUMBER = {4022323}, DOI = {10.1007/s42967-019-0004-0}, URL = {https://doi.org/10.1007/s42967-019-0004-0}, } @ARTICLE{HG98, AUTHOR = {He, J.W. and Glowinski, R.}, TITLE = {Neumann control of unstable parabolic systems: numerical approach}, YEAR = {1998}, JOURNAL = {J. Optim. Theory Appl.}, VOLUME = {96}, NUMBER = {1}, PAGES = {1-55} } @article {MR2034880, AUTHOR = {He, Yinnian}, TITLE = {Two-level method based on finite element and {C}rank-{N}icolson extrapolation for the time-dependent {N}avier-{S}tokes equations}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {41}, YEAR = {2003}, NUMBER = {4}, PAGES = {1263--1285}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65M60 (35Q30 76D05 76M10)}, MRNUMBER = {2034880 (2004k:65173)}, MRREVIEWER = {Long An Ying}, DOI = {10.1137/S0036142901385659}, URL = {http://dx.doi.org/10.1137/S0036142901385659}, } @ARTICLE{HePi, AUTHOR = {Hecht, F. and Pironneau, O.}, TITLE = {{FreeFEM++}}, YEAR = {\empty}, JOURNAL = {webpage: http://www.freefem.org}, VOLUME = {}, NUMBER = {}, PAGES = {} } H12 @article {MR3043640, AUTHOR = {Hecht, F.}, TITLE = {New development in freefem++}, JOURNAL = {J. Numer. Math.}, FJOURNAL = {Journal of Numerical Mathematics}, VOLUME = {20}, YEAR = {2012}, NUMBER = {3-4}, PAGES = {251--265}, ISSN = {1570-2820}, MRCLASS = {65Y15}, MRNUMBER = {3043640}, } @Article{Heister2017, author="Heister, Timo and Mohebujjaman, Muhammad and Rebholz, Leo G.", title="Decoupled, Unconditionally Stable, Higher Order Discretizations for {MHD} Flow Simulation", journal="Journal of Scientific Computing", year="2017", volume="71", number="1", pages="21--43", abstract="We propose, analyze, and test a new MHD discretization which decouples the system into two Oseen problems at each timestep yet maintains unconditional stability with respect to the time step size, is optimally accurate in space, and behaves like second order in time in practice. The proposed method chooses a parameter {\$}{\$}{\backslash}theta {\backslash}in [0,1]{\$}{\$} $\theta$ ∈ [ 0 , 1 ] , dependent on the viscosity {\$}{\$}{\backslash}nu {\$}{\$} $\nu$ and magnetic diffusivity {\$}{\$}{\backslash}nu {\_}m{\$}{\$} $\nu$ m , so that the explicit treatment of certain viscous terms does not cause instabilities, and gives temporal accuracy {\$}{\$}O({\backslash}Delta t^2 + (1-{\backslash}theta )|{\backslash}nu -{\backslash}nu {\_}m|{\backslash}Delta t){\$}{\$} O ( $\Delta$ t 2 + ( 1 - $\theta$ ) | $\nu$ - $\nu$ m | $\Delta$ t ) . In practice, {\$}{\$}{\backslash}nu {\$}{\$} $\nu$ and {\$}{\$}{\backslash}nu {\_}m{\$}{\$} $\nu$ m are small, and so the method behaves like second order. When {\$}{\$}{\backslash}theta =1{\$}{\$} $\theta$ = 1 , the method reduces to a linearized BDF2 method, but it has been proven by Li and Trenchea that such a method is stable only in the uncommon case of {\$}{\$}{\backslash}frac{\{}1{\}}{\{}2{\}}< {\backslash}frac{\{}{\backslash}nu {\}}{\{}{\backslash}nu {\_}m{\}} < 2{\$}{\$} 1 2 < $\nu$ $\nu$ m < 2 . For the proposed method, stability and convergence are rigorously proven for appropriately chosen {\$}{\$}{\backslash}theta {\$}{\$} $\theta$ , and several numerical tests are provided that confirm the theory and show the method provides excellent accuracy in cases where usual BDF2 is unstable.", issn="1573-7691", doi="10.1007/s10915-016-0288-4", url="http://dx.doi.org/10.1007/s10915-016-0288-4" } @ARTICLE{HeSt95, AUTHOR = {Henoch, C. and Stace, J.}, TITLE = {Experimental investigation of a salt water turbulent boundary layer modified by an applied streamwise magnetohydrodynamic body force}, YEAR = {1995}, JOURNAL = {Physics of Fluids}, VOLUME = {7}, NUMBER = {}, PAGES = {1371-1383} } @BOOK{Henr81, AUTHOR = {Henry, D.}, TITLE = {Geometric Theory of Semilinear Parabolic Equations}, PUBLISHER = {Springer-Verlag}, YEAR = {1981}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {840}, EDITION = {}, ADDRESS = {New York} } @ARTICLE{HK77, AUTHOR = {Hermann, R. and Krener, A.}, TITLE = {Nonlinear controllabillity and observability}, YEAR = {1977}, JOURNAL = {IEEE Trans. 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W.}, TITLE = {}, YEAR = {1969}, JOURNAL = {Physics of Fluids, {S}upplement, {II}}, VOLUME = {}, NUMBER = {}, PAGES = {219-227} } @ARTICLE{HMP87, AUTHOR = {Hollis, S.L. and Martin, R.H. and Pierre, M.}, TITLE = {Global existence and boundedness in reaction-diffusion systems}, YEAR = {1987}, JOURNAL = {SIAM J. Math. Anal.}, VOLUME = {18}, NUMBER = {3}, PAGES = {744-761} } @ARTICLE{H97, AUTHOR = {Horiuti, K.}, TITLE = {A new dynamic two-parameter mixed model for large eddy simulation}, YEAR = {1997}, JOURNAL = { Phys. Fluids}, VOLUME = {9}, NUMBER = {}, PAGES = {3443} } @INCOLLECTION{H01, AUTHOR = {Horiuti, K.}, TITLE = {Rotational transformation and geometrical correlation of {SGS} models}, BOOKTITLE = {Modern Simulation Strategies for Turbuylent Flows, Chapter 7}, PUBLISHER = {R.T. Edwards}, YEAR = {2001}, EDITOR = {B. J. 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Manouzi", keywords = "Distributed control", keywords = "Stochastic partial differential equation", keywords = "Finite element methods" } @ARTICLE{HM95, AUTHOR = {Hou, L. S. and Meir A. J.}, TITLE = {Boundary optimal control of {MHD} flows}, YEAR = {1995}, JOURNAL = {Appl. Math. Optim.}, VOLUME = {32}, NUMBER = {2}, PAGES = {143-162} } @ARTICLE{HP95, AUTHOR = {Hou, L. S. and Peterson J.}, TITLE = {Boundary optimal control for an electrically conducting fluid using boundary electrical potential controls}, YEAR = {1995}, JOURNAL = {Nonlinear Anal.}, VOLUME = {24}, NUMBER = {6}, PAGES = {857-874} } @ARTICLE{HR96, AUTHOR = {Hou, L. S. and Ravindran, S. S.}, TITLE = {Computations of boundary optimal control problems for an electrically conducting fluid}, YEAR = {1996}, JOURNAL = {J. Comput. Phys.}, VOLUME = {128}, NUMBER = {}, PAGES = {319-330} } @ARTICLE{H72, AUTHOR = {Howard, L.N.}, TITLE = {Bounds on flow quantities}, YEAR = {1972}, JOURNAL = {Ann. Rev. Fluid Mech.}, VOLUME = {4}, NUMBER = {}, PAGES = {473-494} } @ARTICLE{Hrin02, AUTHOR = {Hrinca, I.}, TITLE = {An optimal control problem for the {L}otka-{V}olterra system with diffusion}, YEAR = {2002}, JOURNAL = {Panamer. Math. J.}, VOLUME = {12}, NUMBER = {3}, PAGES = {23-46} } @misc{KY_Xu-2014, author = "Hu, Kaibo and Ma, Yicong and Xu, Jinchao", title = "Stable Finite Element Methods Preserving $\nabla\cdot {B}=0$ Exactly for {MHD} Models", howpublished = "arXiv:1410.1095v1 [math.NA]", year = "2014", month = "", note = "", } @article {MR1660141, AUTHOR = {Hughes, Thomas J. R. and Feij{\'o}o, Gonzalo R. and Mazzei, Luca and Quincy, Jean-Baptiste}, TITLE = {The variational multiscale method---a paradigm for computational mechanics}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {166}, YEAR = {1998}, NUMBER = {1-2}, PAGES = {3--24}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {65N55 (65M55 73V05 73V25)}, MRNUMBER = {1660141 (99m:65239)}, MRREVIEWER = {I. N. Molchanov}, DOI = {10.1016/S0045-7825(98)00079-6}, URL = {http://dx.doi.org/10.1016/S0045-7825(98)00079-6}, } @BOOK{HM76, AUTHOR = {Hughes, T. J. and Marsden, J.}, TITLE = {A {S}hort {C}ourse in {F}luid {M}echanics}, PUBLISHER = {Publish or Perish}, YEAR = {1976}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @article{0998.76040, author="Hughes, Thomas J.R. and Mazzei, Luca and Jansen, Kenneth E.", title="{Large eddy simulation and the variational multiscale method.}", language="English", journal="Comput. Vis. Sci.", volume="3", number="1-2", pages="47-59", year="2000", doi={10.1007/s007910050051}, abstract="{Summary: A large eddy simulation (LES) formulation is developed from the variational multiscale method. Modeling is confined to the effect of small-scale Reynolds stress, in contrast with classical LES in which the entire subgrid-scale stress is modeled. All other effects are accounted for exactly. It is argued that many shortcomings of the classical LES/constant-coefficient Smagorinsky model are eliminated by the scale separation inherent ab initio in the present approach.}", reviewer="{}", keywords="{large eddy simulation; variational multiscale method; small-scale Reynolds stress; Smagorinsky model; scale separation}", classmath="{76F65 (Direct numerical and large eddy simulation of turbulence) }", } @book {MR2002152, AUTHOR = {Hundsdorfer, Willem and Verwer, Jan}, TITLE = {Numerical solution of time-dependent advection-diffusion-reaction equations}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {33}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2003}, PAGES = {x+471}, ISBN = {3-540-03440-4}, MRCLASS = {65-02 (65L05 65Mxx)}, MRNUMBER = {2002152 (2004g:65001)}, MRREVIEWER = {Ian Gladwell}, } @article {MR2349693, AUTHOR = {Hundsdorfer, Willem and Ruuth, Steven J.}, TITLE = {I{MEX} extensions of linear multistep methods with general monotonicity and boundedness properties}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {225}, YEAR = {2007}, NUMBER = {2}, PAGES = {2016--2042}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65M06}, MRNUMBER = {2349693 (2009f:65185)}, DOI = {10.1016/j.jcp.2007.03.003}, URL = {http://dx.doi.org/10.1016/j.jcp.2007.03.003}, } @article {MR2196985, AUTHOR = {Hundsdorfer, Willem and Ruuth, Steven J.}, TITLE = {On monotonicity and boundedness properties of linear multistep methods}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {75}, YEAR = {2006}, NUMBER = {254}, PAGES = {655--672 (electronic)}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {65L05 (65L20)}, MRNUMBER = {2196985 (2007d:65061)}, MRREVIEWER = {J. C. Butcher}, DOI = {10.1090/S0025-5718-05-01794-1}, URL = {http://dx.doi.org/10.1090/S0025-5718-05-01794-1}, } HMK98 @article{CambridgeJournals:14193, author = {HUA,BACH LIEN and McWILLIAMS,JAMES C. and KLEIN,PATRICE}, title = {Lagrangian accelerations in geostrophic turbulence}, journal = {Journal of Fluid Mechanics}, volume = {366}, number = { }, pages = {87-108}, year = {1998}, doi = {null}, URL = {http://dx.doi.org/10.1017/S0022112098001001}, eprint = {http://journals.cambridge.org/article_S0022112098001001}, } @INPROCEEDINGS{1988stun.proc..193H, author = {{Hunt}, J.~C.~R. and {Wray}, A.~A. and {Moin}, P.}, title = "{Eddies, streams, and convergence zones in turbulent flows}", keywords = {DIGITAL SIMULATION, FLOW DISTRIBUTION, FLOW VELOCITY, SHEAR FLOW, TURBULENT FLOW, VELOCITY DISTRIBUTION, COMPUTATIONAL FLUID DYNAMICS, CONVERGENCE, FLOW STABILITY, STREAM FUNCTIONS (FLUIDS), VORTICES}, booktitle = {Studying Turbulence Using Numerical Simulation Databases, 2}, year = 1988, month = dec, pages = {193-208}, adsurl = {http://adsabs.harvard.edu/abs/1988stun.proc..193H}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article{HLLT13old, Author = {Hurl, N. and Layton, W. and Li, Y. and Trenchea, C.}, Institution = {University of Pittsburgh}, Year = {2013}, Title = {Stability Analysis of the {Crank-Nicolson-Leap-Frog Method} with the {Robert-Asselin-Williams} Time Filter}, url="http://www.mathematics.pitt.edu/sites/default/files/research-pdfs/CNLFraw.pdf" } @INPROCEEDINGS{LiTrenchea2015Venice, author = {Li, Yong and Trenchea, Catalin}, title = "{Analysis of time filters used with the leapfrog scheme}", keywords = {time filters, leapfrog, weather prediction}, booktitle = {Proceedings of the VI Conference on Computational Methods for Coupled Problems in Science and Engineering, Venice, Italy}, year = 2015, month = May, pages = {1261-1272}, adsurl = {}, adsnote = {} } @article {HLLT13, AUTHOR = {Hurl, Nicholas and Layton, William and Li, Yong and Trenchea, Catalin}, TITLE = {Stability analysis of the {C}rank--{N}icolson-{L}eapfrog method with the {R}obert--{A}sselin--{W}illiams time filter}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {54}, YEAR = {2014}, NUMBER = {4}, PAGES = {1009--1021}, ISSN = {0006-3835}, MRCLASS = {65L20 (86A10)}, MRNUMBER = {3292536}, DOI = {10.1007/s10543-014-0493-1}, URL = {http://dx.doi.org/10.1007/s10543-014-0493-1}, } @techreport{HLM13, Author = {Hurl, N. and Layton, W. and Li, Y. and Moraiti, M.}, Institution = {University of Pittsburgh}, Year = {2013}, Title = {The Unstable Mode in the Crank-Nicolson Leap-Frog Method is Stable} } @article {MR3557056, AUTHOR = {Hurl, Nick and Layton, William and Li, Yong and Moraiti, Marina}, TITLE = {The unstable mode in the {C}rank-{N}icolson leap-frog method is stable}, JOURNAL = {Int. J. Numer. Anal. Model.}, FJOURNAL = {International Journal of Numerical Analysis and Modeling}, VOLUME = {13}, YEAR = {2016}, NUMBER = {5}, PAGES = {753--762}, ISSN = {1705-5105}, MRCLASS = {65M20 (65L06 65M12)}, MRNUMBER = {3557056}, MRREVIEWER = {Erc\'{\i}lia Sousa}, } @techreport{ILT05, Author = {Ilyin, A.A. and Lunasin, E.M. and Titi, E.S.}, Institution = {}, Title = {A modified {L}eray-$\alpha$ subgrid-scale model of turbulence}, Year = {2005}} @ARTICLE{ILT06, AUTHOR = {Ilyin, A.A. and Lunasin, E.M. and Titi, E.S.}, TITLE = {A modified {L}eray-$\alpha$ subgrid model of turbulence}, YEAR = {2006}, JOURNAL = {Nonlinearity}, VOLUME = {19}, NUMBER = {}, PAGES = {879-897} } http://www.mathematics.pitt.edu/research/technical-reports.php @techreport{IngYuk10, Author = {Ingram, R. and Yuksel, G.}, Institution = {University of Pittsburgh}, Title = {Numerical Analysis of a Finite Element, {Crank-Nicolson} discretization for {MHD} flow at small magnetic {Reynolds} number}, Year = {2010}} @article {MR3055600, AUTHOR = {Ingram, Ross}, TITLE = {Unconditional convergence of high-order extrapolations of the {C}rank-{N}icolson, finite element method for the {N}avier-{S}tokes equations}, JOURNAL = {Int. J. Numer. Anal. Model.}, FJOURNAL = {International Journal of Numerical Analysis and Modeling}, VOLUME = {10}, YEAR = {2013}, NUMBER = {2}, PAGES = {257--297}, ISSN = {1705-5105}, MRCLASS = {65M60 (65M12 76D05)}, MRNUMBER = {3055600}, MRREVIEWER = {Daniele Boffi}, } YukselIngram13 @ARTICLE{MR3011862, AUTHOR = {Yuksel, Gamze and Ingram, Ross}, TITLE = {Numerical analysis of a finite element, {C}rank-{N}icolson discretization for {MHD} flows at small magnetic {R}eynolds numbers}, JOURNAL = {Int. J. Numer. Anal. Model.}, FJOURNAL = {International Journal of Numerical Analysis and Modeling}, VOLUME = {10}, YEAR = {2013}, NUMBER = {1}, PAGES = {74--98}, ISSN = {1705-5105}, MRCLASS = {65M60 (76W05)}, MRNUMBER = {3011862}, } @article {MR0180086, AUTHOR = {Iroshnikov, P. S.}, TITLE = {Turbulence of a conducting fluid in a strong magnetic field}, JOURNAL = {Soviet Astronom. AJ}, FJOURNAL = {Soviet Astronomy}, VOLUME = {7}, YEAR = {1964}, PAGES = {566--571}, ISSN = {0038-5301}, MRCLASS = {76.99}, MRNUMBER = {0180086 (31 \#4322)}, MRREVIEWER = {J. N. Kapur}, } MR2193218 @book {Is06, AUTHOR = {Isakov, V.}, TITLE = {Inverse problems for partial differential equations}, SERIES = {Applied Mathematical Sciences}, VOLUME = {127}, EDITION = {Second}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2006}, PAGES = {xiv+344}, ISBN = {978-0387-25364-0; 0-387-25364-5}, MRCLASS = {35R30 (35-02 65M32 74G75 74J25 76Q05 80A22 80A23)}, MRNUMBER = {MR2193218 (2006h:35279)}, } @book {MR1384977, AUTHOR = {Iserles, Arieh}, TITLE = {A first course in the numerical analysis of differential equations}, SERIES = {Cambridge Texts in Applied Mathematics}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1996}, PAGES = {xviii+378}, ISBN = {0-521-55376-8; 0-521-55655-4}, MRCLASS = {65-01 (65Fxx 65Lxx 65Mxx 65Nxx)}, MRNUMBER = {1384977}, MRREVIEWER = {Luis Verde-Star}, } MR2441683 @book {ItKu08, AUTHOR = {Ito, Kazufumi and Kunisch, Karl}, TITLE = {Lagrange multiplier approach to variational problems and applications}, SERIES = {Advances in Design and Control}, VOLUME = {15}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2008}, PAGES = {xviii+341}, ISBN = {978-0-898716-49-8}, MRCLASS = {49-02 (49J27 49K27 49K40 49M30 49M37)}, MRNUMBER = {MR2441683 (2009g:49001)}, MRREVIEWER = {Walter Alt}, } @article {MR1035975, AUTHOR = {Ito, Kazufumi and Kunisch, Karl}, TITLE = {The augmented {L}agrangian method for parameter estimation in elliptic systems}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {28}, YEAR = {1990}, NUMBER = {1}, PAGES = {113--136}, ISSN = {0363-0129}, MRCLASS = {35R30 (49K20 65P05)}, MRNUMBER = {1035975}, DOI = {10.1137/0328006}, URL = {http://dx.doi.org/10.1137/0328006}, } @INCOLLECTION{JabWil2011, AUTHOR = {Jablonowski, Christiane and Williamson, David}, TITLE = {The pros and cons of diffusion, filters and fixers in Atmospheric General Circulation Models}, BOOKTITLE = {Numerical Techniques for Global Atmospheric Models}, PUBLISHER ={Springer}, EDITOR = {Lauritzen, P. H. and Jablonowski, C. and Taylor, M. A. and Nair, R. D.}, YEAR = {2011}, SERIES = {Lecture Notes in Computational Science and Engineering}, VOLUME = {80}, EDITION = {}, PAGES = {381-493}, doi = {10.1007/978-3-642-11640-7_13} } abstract = {All atmospheric General Circulation Models (GCMs) need some form of dissipation, either explicitly specified or inherent in the chosen numerical schemes for the spatial and temporal discretizations. This dissipation may serve many purposes, including cleaning up numerical noise generated by dispersion errors or computational modes, and the Gibbs ringing in spectral models. Damping processes might also be used to crudely represent subgrid Reynolds stresses, eliminate undesirable noise due to poor initialization or grid-scale forcing from the physics parameterizations, cover up weak computational stability, damp tracer variance, and prevent the accumulation of potential enstrophy or energy at the smallest grid scales. This chapter critically reviews the wide selection of dissipative processes in GCMs. They are the explicitly added diffusion and hyper-diffusion mechanisms, divergence damping, vorticity damping, external mode damping, sponge layers, spatial and temporal filters, inherent diffusion properties of the numerical schemes, and a posteriori fixers used to restore lost conservation properties. All theoretical considerations are supported by many practical examples from a wide selection of GCMs. The examples utilize idealized test cases to isolate causes and effects, and thereby highlight the pros and cons of the diffusion, filters and fixers in GCMs.}, url = {http://nldr.library.ucar.edu/repository/collections/OSGC-000-000-003-591} } @article {MR1760028, AUTHOR = {J\"ager, Willi and Mikeli\'c, Andro}, TITLE = {On the interface boundary condition of {B}eavers, {J}oseph, and {S}affman}, JOURNAL = {SIAM J. Appl. Math.}, FJOURNAL = {SIAM Journal on Applied Mathematics}, VOLUME = {60}, YEAR = {2000}, NUMBER = {4}, PAGES = {1111--1127}, ISSN = {0036-1399}, MRCLASS = {76S05 (35B27 35Q35 76D07 76M50)}, MRNUMBER = {1760028}, MRREVIEWER = {Ma\l gorzata Peszy\'nska}, DOI = {10.1137/S003613999833678X}, URL = {https://doi.org/10.1137/S003613999833678X}, } @ARTICLE{Jame89, AUTHOR = {Jameson, A.}, TITLE = {Computational aerodynamics for aircraft design}, YEAR = {1989}, JOURNAL = {Science}, VOLUME = {245}, NUMBER = {}, PAGES = {361-371} } @ARTICLE{JaTeMa02, AUTHOR = {Jansen, K.E. and Tejada-Martinez, A.E.}, TITLE = {An evaluation of the variational multiscale model for large-eddy simulation while using a hierarchical basis}, YEAR = {2002}, JOURNAL = {AIAA Annual Meeting and Exhibit}, VOLUME = {}, NUMBER = {}, PAGES = {Paper No. 2002-0283} } @ARTICLE{JiangLayton2015, AUTHOR = {Jiang, Nan and Layton, William}, TITLE = {Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion}, YEAR = {2014}, JOURNAL = {Numerical Methods for Partial Differential Equations}, VOLUME = {to appear}, NUMBER = {}, PAGES = {}, DOI = {DOI: 10.1002/num.21908v}} @article {MR3332285, AUTHOR = {Jiang, Nan and Layton, William}, TITLE = {Numerical analysis of two ensemble eddy viscosity numerical regularizations of fluid motion}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {31}, YEAR = {2015}, NUMBER = {3}, PAGES = {630--651}, ISSN = {0749-159X}, MRCLASS = {65M32 (76D05)}, MRNUMBER = {3332285}, MRREVIEWER = {Dinh Nho H\`ao}, DOI = {10.1002/num.21908}, URL = {https://doi.org/10.1002/num.21908}, } @article {MR3260478, AUTHOR = {Jiang, Nan and Layton, William}, TITLE = {An algorithm for fast calculation of flow ensembles}, JOURNAL = {Int. J. Uncertain. Quantif.}, FJOURNAL = {International Journal for Uncertainty Quantification}, VOLUME = {4}, YEAR = {2014}, NUMBER = {4}, PAGES = {273--301}, ISSN = {2152-5080}, MRCLASS = {Expansion}, MRNUMBER = {3260478}, DOI = {10.1615/Int.J.UncertaintyQuantification.2014007691}, URL = {https://doi.org/10.1615/Int.J.UncertaintyQuantification.2014007691}, } @article{JKLMT15, title = "A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications ", journal = "J. Comput. Appl. Math. ", fjournal = "Journal of Computational and Applied Mathematics ", volume = "281", number = "0", pages = "263 - 276", year = "2015", note = "", issn = "0377-0427", doi = "http://dx.doi.org/10.1016/j.cam.2014.09.026", url = "http://www.sciencedirect.com/science/article/pii/S0377042714004336", author = "Nan Jiang and Michaela Kubacki and William Layton and Marina Moraiti and Hoang Tran", keywords = "{CNLF}, Stabilization, {CFL} condition" } @article {MR3365766, AUTHOR = {Jiang, Nan and Tran, Hoang}, TITLE = {Analysis of a stabilized {CNLF} method with fast slow wave splittings for flow problems}, JOURNAL = {Comput. Methods Appl. Math.}, FJOURNAL = {Computational Methods in Applied Mathematics}, VOLUME = {15}, YEAR = {2015}, NUMBER = {3}, PAGES = {307--330}, ISSN = {1609-4840}, MRCLASS = {65M60 (65M12 76D05 86A05 86A10)}, MRNUMBER = {3365766}, MRREVIEWER = {Do Young Kwak}, DOI = {10.1515/cmam-2015-0010}, URL = {https://doi.org/10.1515/cmam-2015-0010}, } @article{doi:10.1029/2009WR008896, author = {Kavetski, Dmitri and Clark, Martyn P.}, title = {Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction}, journal = {Water Resources Research}, volume = {46}, number = {10}, pages = {}, keywords = {hydrological models, numerical artifacts, time stepping schemes, sensitivity analysis, parameter optimization, uncertainty assessment, validation}, doi = {10.1029/2009WR008896}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2009WR008896}, eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2009WR008896}, abstract = {Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using numerically unreliable methods. This paper considers the impact of the time stepping scheme on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on numerical accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping schemes, in particular, fixed-step explicit methods, suffer from troublesome numerical artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by numerical errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping schemes generally produce “better behaved” objective functions, free of spurious local optima, and with sufficient numerical continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and numerical errors provide “the right result for the wrong reason” and the calibrated model performance appears adequate, unreliable time stepping schemes make the model unnecessarily fragile in predictive mode, undermining validation assessments and operational use. Erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable, especially given that robust numerics are accepted as mainstream in other areas of science and engineering. We hope that the vivid empirical findings will encourage the conceptual hydrological community to close its Pandora's box of numerical problems, paving the way for more meaningful model application and interpretation.}, year = {2010} } @techreport{kaya02, Author = {Kaya, S.}, Institution = {University of Pittsburgh}, Title = {Numerical analysis of a subgrid scale eddy viscosity method for higher {R}eynolds number flow problem}, Year = {2002}} MR1678201 @book {Kell99, AUTHOR = {Kelley, C. T.}, TITLE = {Iterative methods for optimization}, SERIES = {Frontiers in Applied Mathematics}, VOLUME = {18}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1999}, PAGES = {xvi+180}, ISBN = {0-89871-433-8}, MRCLASS = {90-02 (65K05 90-01 90C30)}, MRNUMBER = {MR1678201 (2000h:90003)}, MRREVIEWER = {William W. Hager}, } @article {MR1191146, AUTHOR = {Kunisch, K. and Sachs, E. W.}, TITLE = {Reduced {SQP} methods for parameter identification problems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {29}, YEAR = {1992}, NUMBER = {6}, PAGES = {1793--1820}, ISSN = {0036-1429}, MRCLASS = {65J05 (65K05)}, MRNUMBER = {1191146}, MRREVIEWER = {C. Ilioi}, DOI = {10.1137/0729100}, URL = {http://dx.doi.org/10.1137/0729100}, } MR1745475 @book {LaTr00, AUTHOR = {Lasiecka, Irena and Triggiani, Roberto}, TITLE = {Control theory for partial differential equations: continuous and approximation theories. {I}}, SERIES = {Encyclopedia of Mathematics and its Applications}, VOLUME = {74}, NOTE = {Abstract parabolic systems}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {2000}, PAGES = {xxii+644+I4}, ISBN = {0-521-43408-4}, MRCLASS = {93-02 (35B37 47D06 47N70 49N10 93C20 93C25)}, MRNUMBER = {MR1745475 (2001m:93002)}, MRREVIEWER = {Luciano Pandolfi}, } @phdthesis{HLin2008, Author = {Lin, Haomin}, Date-Added = {}, Date-Modified = {}, School = {Florida State Universtiy}, Title = {An optimal control problem for a time-dependent {Ginzburg-Landau} model of superconductivity}, Year = {2008}} @ARTICLE{Jero84, AUTHOR = {Jerome, J.}, TITLE = {Fully discrete stability and invariant rectangular regions for reaction-diffusion systems}, YEAR = {1984}, JOURNAL = {SIAM J. Numer. Anal.}, VOLUME = {21}, NUMBER = {6}, PAGES = {1054-1065} } @article {MR2498862, AUTHOR = {Jiang, Bin}, TITLE = {A parallel domain decomposition method for coupling of surface and groundwater flows}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {198}, YEAR = {2009}, NUMBER = {9-12}, PAGES = {947--957}, ISSN = {0045-7825}, MRCLASS = {76D05 (65N55 65Y05 76M25)}, MRNUMBER = {2498862}, DOI = {10.1016/j.cma.2008.11.001}, URL = {https://doi.org/10.1016/j.cma.2008.11.001}, } @article {MR1769136, AUTHOR = {Jiang, Cheng Shun and Zhang, Yan Xiao}, TITLE = {A parameter identification and inversion method for a class of reaction-diffusion systems}, JOURNAL = {Control Theory Appl.}, FJOURNAL = {Control Theory \& Applications. Kongzhi Lilun yu Yingyong}, VOLUME = {17}, YEAR = {2000}, NUMBER = {2}, PAGES = {193--197}, ISSN = {1000-8152}, CODEN = {KLYYEB}, MRCLASS = {93B30 (93C20)}, MRNUMBER = {MR1769136}, } @ARTICLE{Jian06, AUTHOR = {Jiang, Huiqiang}, TITLE = {Global Existence of Solutions of an activator-inhibitor system}, YEAR = {2006}, JOURNAL = {Discrete and Continuous Dynamical Systems}, VOLUME = {14}, NUMBER = {4}, PAGES = {737-751} } @techreport{JiTr2013, Author = {Jiang, Nan and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Analysis of a family of regularization methods for {Navier-Stokes} equations}, Year = {2013}} @article {MR0166936, AUTHOR = {Johansson, Olov and Kreiss, Heinz-Otto}, TITLE = {\"{U}berdas {V}erfahren der zentralen {D}ifferenzen zur {L}\"osung des {C}auchy problems f\"ur partielle {D}ifferentialgleichungen}, JOURNAL = {Nordisk Tidskr. Informations-Behandling}, VOLUME = {3}, YEAR = {1963}, PAGES = {97--107}, MRCLASS = {65.65}, MRNUMBER = {0166936 (29 \#4209)}, MRREVIEWER = {G. Dahlquist}, } MR2018955 @book {J04, AUTHOR = {John, V.}, TITLE = {Large eddy simulation of turbulent incompressible flows}, SERIES = {Lecture Notes in Computational Science and Engineering}, VOLUME = {34}, NOTE = {Analytical and numerical results for a class of LES models}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2004}, PAGES = {xii+261}, ISBN = {3-540-40643-3}, MRCLASS = {76F65 (65M60)}, MRNUMBER = {MR2018955 (2004k:76069)}, MRREVIEWER = {Bernard J. Geurts}, } @article{1085.76510, author="John, Volker", title="{Reference values for drag and lift of a two-dimensional time-dependent flow around a cylinder.}", language="English", journal="Int. J. Numer. Methods Fluids ", volume="44", number="7", pages="777-788", year="2004", doi={10.1002/fld.679}, abstract="{Summary: This paper presents a numerical study of a two-dimensional time-dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied.}", keywords="{time-dependent incompressible Navier-Stokes equations; drag coefficient; lift coefficient}", classmath="{*76D05 (Navier-Stokes equations (fluid dynamics)) 76M10 (Finite element methods) 76M20 (Finite difference methods) }", } @article {MR1949402, AUTHOR = {John, V. and Layton, W. J.}, TITLE = {Analysis of numerical errors in large eddy simulation}, JOURNAL = {SIAM J. Numer. 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The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit, and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. Copyright © 2016 John Wiley \& Sons, Ltd.}, year = {2017} } @BOOK{LaLi59, AUTHOR = {Landau, L.D. and Lifschitz, E.M.}, TITLE = {Fluid {M}echanics}, PUBLISHER = {Pergamon}, YEAR = {1959}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @book {MR961259, AUTHOR = {Landau, L. D. and Lifshitz, E. M.}, TITLE = {Course of theoretical physics. {V}ol. 6}, EDITION = {Second}, NOTE = {Fluid mechanics, Translated from the third Russian edition by J. B. Sykes and W. H. 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Layton", keywords = "Eddy viscosity", keywords = "Subgrid scales" } @article{layton:916, author = {Layton, W.}, collaboration = {}, title = {Bounds on Energy and Helicity Dissipation Rates of Approximate Deconvolution Models of Turbulence}, publisher = {SIAM}, year = {2007}, journal = {SIMA}, fjournal = {SIAM Journal on Mathematical Analysis}, volume = {39}, number = {3}, pages = {916-931}, keywords = {energy dissipation rate; helicity; helicity dissipation rate; large eddy simulation; turbulence; deconvolution}, url = {http://link.aip.org/link/?SJM/39/916/1}, doi = {10.1137/06066223X} } @article {MR2338532, AUTHOR = {Layton, William}, TITLE = {Superconvergence of finite element discretization of time relaxation models of advection}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {47}, YEAR = {2007}, NUMBER = {3}, PAGES = {565--576}, ISSN = {0006-3835}, MRCLASS = {65M60}, MRNUMBER = {2338532 (2009g:65127)}, DOI = {10.1007/s10543-007-0142-z}, URL = {http://dx.doi.org/10.1007/s10543-007-0142-z}, } @book {MR2442411, AUTHOR = {Layton, William}, TITLE = {Introduction to the numerical analysis of incompressible viscous flows}, SERIES = {Computational Science \& Engineering}, VOLUME = {6}, NOTE = {With a foreword by Max Gunzburger}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {2008}, PAGES = {xx+213}, ISBN = {978-0-898716-57-3}, MRCLASS = {76Mxx (65Mxx 65Nxx 76D05)}, MRNUMBER = {MR2442411}, } @techreport{Layt07, Author = {Layton, W.}, Institution = {University of Pittsburgh}, Title = {A remark on regularity of an elliptic-elliptic singular perturbation problem}, Year = {http://www.mathematics.pitt.edu/research/technical-reports.php, 2007}} MR2015713 - LL03 @article {LL03, AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {A simple and stable scale-similarity model for large eddy simulation: energy balance and existence of weak solutions}, JOURNAL = {Appl. Math. Lett.}, FJOURNAL = {Applied Mathematics Letters. An International Journal of Rapid Publication}, VOLUME = {16}, YEAR = {2003}, NUMBER = {8}, PAGES = {1205--1209}, ISSN = {0893-9659}, CODEN = {AMLEEL}, MRCLASS = {76F65 (35D05 35Q35 76D03)}, MRNUMBER = {MR2015713 (2004j:76095)}, MRREVIEWER = {Bernard J. Geurts}, } AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {A simple and stable scale similarity model for large eddy simulation: energy balance and existence of weak solutions}, YEAR = {2003}, JOURNAL = {Applied Math. letters}, VOLUME = {16}, NUMBER = {}, PAGES = {1205-1209} } @techreport{LL04c, Author = {Layton, W. and Lewandowski, R.}, Institution = {}, Title = {Consistency and feasibility of approximate de-convolution models of turbulence}, Year = {2004}} @ARTICLE{LaLe04, AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {On a well-posed turbulence model}, YEAR = {2006}, JOURNAL = { Discrete Contin. Dyn. Syst. Ser. B}, VOLUME = {6}, NUMBER = {1}, PAGES = {111-128} } @ARTICLE{LL06, AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {Residual stress of approximate deconvolution large eddy simulation models of turbulence}, YEAR = {2006}, JOURNAL = {J. Turbul.}, FJOURNAL = {Journal of Turbulence}, VOLUME = {46}, NUMBER = {2}, PAGES = {1-21} } @ARTICLE{LL06a, AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {On a well-posed turbulence model}, YEAR = {2006}, JOURNAL = {Discrete and Continuous Dynamical Systems - Series B}, VOLUME = {6}, NUMBER = {}, PAGES = {111-128} } MR2380885 @article {LL07, AUTHOR = {Layton, W. and Lewandowski, R.}, TITLE = {A high accuracy {L}eray-deconvolution model of turbulence and its limiting behavior}, JOURNAL = {Anal. Appl. (Singap.)}, FJOURNAL = {Analysis and Applications}, VOLUME = {6}, YEAR = {2008}, NUMBER = {1}, PAGES = {23--49}, ISSN = {0219-5305}, MRCLASS = {76F02 (35Q30 76D05)}, MRNUMBER = {MR2380885 (2008m:76063)}, MRREVIEWER = {Luigi Carlo Berselli}, } LLMNR @ARTICLE{oooo, AUTHOR = {Layton, W. and Labovschii, A. and Manica, C. and Neda, M. and Rebholz, L.}, TITLE = {The Stabilized, Extrapolated Trapezoidal Finite Element Method for the Navier-Stokes Equations}, YEAR = {2007}, JOURNAL = {submitted to Theoretical and Computational Fluid Dynamics}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{LMNR06, AUTHOR = {Layton, W.J. and Manica, C. and Neda, M. and Rebholz, L.}, TITLE = {Helicity and energy conservation and dissipation in approximate deconvolution {LES} models of turbulence}, JOURNAL = {Adv. Appl. Fluid Mech.}, FJOURNAL = {Advances and Applications in Fluid Mechanics}, VOLUME = {4}, YEAR = {2008}, NUMBER = {1}, PAGES = {1--46}, ISSN = {0973-4686}, MRCLASS = {76F05 (76F65 76M55)}, MRNUMBER = {2488583 (2010c:76074)}, } LMNR06b @ARTICLE{ooooo, Author = {Layton, W. and Manica, C. and Neda, M. and Rebholz, L.}, Title = {Numerical analysis of a high accuracy {L}eray-deconvolution model of turbulence}, Year = {2007}, PAGES = {to appear: Numerical Methods for PDEs} } @techreport{LMNR007, Author = {Layton, W. and Manica, C. and Neda, M. and Rebholz, L.}, Institution = {University of Pittsburgh}, Title = {Numerical Analysis and Computational Comparisons of the {NS}-alpha and {NS}-omega regularizations}, Year = {2007}} @ARTICLE{LMNR07, Author = {Layton, W. and Manica, C. and Neda, M. and Rebholz, L.}, Title = {On the {NS}-omega regularization of the {Navier-Stokes} equations}, Year = {2007}, JOURNAL = {}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{LMNR07c, AUTHOR = {Layton, W. and Manica, C. and Neda, M. and Rebholz, L.}, TITLE = {Numerical analysis and computational testing of a high accuracy {L}eray-deconvolution model of turbulence}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {24}, YEAR = {2008}, NUMBER = {2}, PAGES = {555--582}, ISSN = {0749-159X}, MRCLASS = {76F02 (35Q35 65M06 76D05 76F65 76M25)}, MRNUMBER = {2382797 (2009b:76064)}, DOI = {10.1002/num.20281}, URL = {http://dx.doi.org/10.1002/num.20281}, } @ARTICLE{LMNR008, AUTHOR = {Layton, W. and Manica, C. and Neda, M. and Rebholz, L.}, TITLE = {Numerical analysis and computational comparisons of the {NS}-alpha and {NS}-omega regularizations}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {199}, YEAR = {2010}, NUMBER = {13-16}, PAGES = {916--931}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {76F65 (65M60 76D05)}, MRNUMBER = {2581353}, MRREVIEWER = {Bartosz Protas}, DOI = {10.1016/j.cma.2009.01.011}, URL = {http://dx.doi.org/10.1016/j.cma.2009.01.011}, } @article {LaMaNeTr11, AUTHOR = {Layton, William and Mays, Nathaniel and Neda, Monika and Trenchea, Catalin}, TITLE = {Numerical analysis of modular regularization methods for the {BDF}2 time discretization of the {N}avier-{S}tokes equations}, JOURNAL = {ESAIM Math. Model. Numer. Anal.}, FJOURNAL = {ESAIM. Mathematical Modelling and Numerical Analysis}, VOLUME = {48}, YEAR = {2014}, NUMBER = {3}, PAGES = {765--793}, ISSN = {0764-583X}, MRCLASS = {65M60 (76D05)}, MRNUMBER = {3264334}, DOI = {10.1051/m2an/2013120}, URL = {http://dx.doi.org/10.1051/m2an/2013120}, } @article{LMNT14, author = {Layton, William and Mays, Nathaniel and Neda, Monika and Trenchea,Catalin}, title = {Numerical analysis of modular regularization methods for the BDF2 time discretization of the {Navier-Stokes} equations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis}, volume = {eFirst}, month = {2}, year = {2014}, issn = {1290-3841}, doi = {10.1051/m2an/2013120}, URL = {http://www.esaim-m2an.org/article_S0764583X13001209}, } @article {MR3264334, AUTHOR = {Layton, William and Mays, Nathaniel and Neda, Monika and Trenchea, Catalin}, TITLE = {Numerical analysis of modular regularization methods for the {BDF}2 time discretization of the {N}avier-{S}tokes equations}, JOURNAL = {ESAIM Math. Model. Numer. Anal.}, FJOURNAL = {ESAIM. Mathematical Modelling and Numerical Analysis}, VOLUME = {48}, YEAR = {2014}, NUMBER = {3}, PAGES = {765--793}, ISSN = {0764-583X}, MRCLASS = {65M60 (76D05)}, MRNUMBER = {3264334}, DOI = {10.1051/m2an/2013120}, URL = {https://doi.org/10.1051/m2an/2013120}, } %MR2270051- LN07, @article {LN07, AUTHOR = {Layton, W. and Neda, M.}, TITLE = {Truncation of scales by time relaxation}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {325}, YEAR = {2007}, NUMBER = {2}, PAGES = {788--807}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {76F65 (35Q35 76D05)}, MRNUMBER = {MR2270051}, } @ARTICLE{LN07a, AUTHOR = {Layton, W. and Neda, M.}, TITLE = {The energy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models}, YEAR = {2007}, JOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {}, NUMBER = {}, PAGES = {} } MR2323499 - LN07b, @article {LN07b, AUTHOR = {Layton, W. and Neda, M.}, TITLE = {A similarity theory of approximate deconvolution models of turbulence}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {333}, YEAR = {2007}, NUMBER = {1}, PAGES = {416--429}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {76Fxx (35Q30 76Dxx)}, MRNUMBER = {MR2323499}, } @techreport{LMNT10, Author = {Layton, William and Mays, Nathaniel and Neda, M. and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Filter based stabilization of the {BDF2} time discretization of {Navier-Stokes} equations}, Year = {2011}} @article{Layton20103728, title = "Temporally regularized direct numerical simulation", journal = "Applied Mathematics and Computation", volume = "216", number = "12", pages = "3728 - 3738", year = "2010", note = "", issn = "0096-3003", doi = "DOI: 10.1016/j.amc.2010.05.031", url = "http://www.sciencedirect.com/science/article/pii/S0096300310005758", author = "William J. Layton and C. David Pruett and Leo G. Rebholz", keywords = "Temporal filtering", keywords = "Turbulence", keywords = "Deconvolution", keywords = "Time relaxation" } @BOOK{LaRe11, AUTHOR = {Layton, William and Rebholz, Leo}, TITLE = {Approximate Deconvolution Models of Turbulence : Analysis, Phenomenology and Numerical Analysis}, PUBLISHER = {Springer-Verlag}, YEAR = {2011}, SERIES = {Springer Lecture Notes in Mathematics}, VOLUME = {}, EDITION = {}, ADDRESS = {Berlin} } @techreport{LaReTr10, Author = {Layton, William and Rebholz, Leo G. and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Modular Nonlinear Filter Stabilization of Methods for Higher {Reynolds} Numbers Flow}, Year = {2010} } @article {LaReTr11, AUTHOR = {Layton, William and Rebholz, Leo G. and Trenchea, Catalin}, TITLE = {Modular nonlinear filter stabilization of methods for higher {R}eynolds numbers flow}, JOURNAL = {J. Math. Fluid Mech.}, FJOURNAL = {Journal of Mathematical Fluid Mechanics}, VOLUME = {14}, YEAR = {2012}, NUMBER = {2}, PAGES = {325--354}, ISSN = {1422-6928}, MRCLASS = {76D05 (35Q30 65M60 76F65 76M10)}, MRNUMBER = {2925112}, MRREVIEWER = {Lorenzo H{\'e}ctor Ju{\'a}rez}, DOI = {10.1007/s00021-011-0072-z}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1007/s00021-011-0072-z}, } @techreport{LaRoTr_10, Author = {Layton, W. and R\"{o}he, L. and Tran, H.}, Institution = {University of Pittsburgh}, Title = {Explicitly uncoupled {VMS} stabilization of fluid flow}, Year = {2010}} @article {MR2844045, AUTHOR = {Layton, William and R{\"o}he, Lars and Tran, Hoang}, TITLE = {Explicitly uncoupled {VMS} stabilization of fluid flow}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, FJOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {200}, YEAR = {2011}, NUMBER = {45-46}, PAGES = {3183--3199}, ISSN = {0045-7825}, CODEN = {CMMECC}, MRCLASS = {76F99 (76D05)}, MRNUMBER = {2844045 (2012i:76054)}, MRREVIEWER = {Iuliana Stanculescu}, DOI = {10.1016/j.cma.2011.06.015}, URL = {http://dx.doi.org/10.1016/j.cma.2011.06.015}, } @ARTICLE{LaRoTr_10b, AUTHOR = {Layton, W. and R\"{o}he, L. and Tran, H.}, TITLE = {A modular, postprocessed induced VMS method}, YEAR = {2010}, JOURNAL = {submitted: CMAME}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{LS07, AUTHOR = {Layton, W. and Stanculescu, I.}, TITLE = {K-41 Optimized Approximate Deconvolution Models}, YEAR = {2007}, JOURNAL = {I.J. Comp. Sci. and Math.}, VOLUME = {}, NUMBER = {}, PAGES = {to appear} } @article {MR1974181, AUTHOR = {Layton, William J. and Schieweck, Friedhelm and Yotov, Ivan}, TITLE = {Coupling fluid flow with porous media flow}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {40}, YEAR = {2002}, NUMBER = {6}, PAGES = {2195--2218 (2003)}, ISSN = {0036-1429}, MRCLASS = {76D07 (35Q30 65N30 76M10 76S05)}, MRNUMBER = {1974181 (2004c:76048)}, MRREVIEWER = {Klaus Johannsen}, DOI = {10.1137/S0036142901392766}, URL = {http://dx.doi.org/10.1137/S0036142901392766}, } @techreport{LaTrTr11, Author = {Layton, W. and Tran, H. and Trenchea, C.}, Institution = {University of Pittsburgh}, Title = {Two stable partitioned methods for uncoupling evolutionary groundwater-surfacewater flows}, Year = {2011}} @article{LaTrTr12longtime, AUTHOR = {Layton, William and Tran, Hoang and Trenchea, Catalin}, TITLE = {Analysis of long time stability and errors of two partitioned methods for uncoupling evolutionary groundwater-surface water flows}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {51}, YEAR = {2013}, NUMBER = {1}, PAGES = {248--272}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {65M60 (65M12 76S05)}, MRNUMBER = {3033010}, MRREVIEWER = {Ma{\l}gorzata Peszy{\'n}ska}, DOI = {10.1137/110834494}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1137/110834494}, } @article {MR3033010, AUTHOR = {Layton, William and Tran, Hoang and Trenchea, Catalin}, TITLE = {Analysis of long time stability and errors of two partitioned methods for uncoupling evolutionary groundwater-surface water flows}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {51}, YEAR = {2013}, NUMBER = {1}, PAGES = {248--272}, ISSN = {0036-1429}, MRCLASS = {65M60 (65M12 76S05)}, MRNUMBER = {3033010}, MRREVIEWER = {Ma\l gorzata Peszy\'nska}, DOI = {10.1137/110834494}, URL = {https://doi.org/10.1137/110834494}, } @article {LaTr09a, AUTHOR = {Layton, William and Trenchea, Catalin}, TITLE = {The {D}as-{M}oser commutator closure for filtering through a boundary is well-posed}, JOURNAL = {Math. Comput. Modelling}, FJOURNAL = {Mathematical and Computer Modelling}, VOLUME = {53}, YEAR = {2011}, NUMBER = {5-6}, PAGES = {566--573}, ISSN = {0895-7177}, CODEN = {MCMOEG}, MRCLASS = {76F65 (35A15 35Q35 76D05)}, MRNUMBER = {2769427}, DOI = {10.1016/j.mcm.2010.09.004}, URL = {http://dx.doi.org/10.1016/j.mcm.2010.09.004}, } @article{LaTr11, AUTHOR = {Layton, William and Trenchea, Catalin}, TITLE = {Stability of two {IMEX} methods, {CNLF} and {BDF}2-{AB}2, for uncoupling systems of evolution equations}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {62}, YEAR = {2012}, NUMBER = {2}, PAGES = {112--120}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {65M06 (65M12 76M20)}, MRNUMBER = {2863095 (2012j:65257)}, DOI = {10.1016/j.apnum.2011.10.006}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1016/j.apnum.2011.10.006}, } @article {LTS077, AUTHOR = {Layton, William and Stanculescu, Iuliana and Trenchea, Catalin}, TITLE = {Theory of the {$\text{NS-}\overline\omega$} model: a complement to the {$\text{NS-}\alpha$} model}, JOURNAL = {Commun. Pure Appl. Anal.}, FJOURNAL = {Communications on Pure and Applied Analysis}, VOLUME = {10}, YEAR = {2011}, NUMBER = {6}, PAGES = {1763--1777}, ISSN = {1534-0392}, MRCLASS = {76D05 (65M06 76F02)}, MRNUMBER = {2805338}, DOI = {10.3934/cpaa.2011.10.1763}, URL = {http://dx.doi.org/10.3934/cpaa.2011.10.1763}, } @ARTICLE{LST14, AUTHOR = {Layton, W. and Sussman, M. and A. Takhirov}, TITLE = {Instability of {Crank-Nicolson Leap-Frog} for Non-autonomous Systems}, YEAR = {2014}, JOURNAL = {Int. J. Numer. Anal. Model. Ser. B}, FJOURNAL = {International Journal of Numerical Analysis and Modeling, Series B}, VOLUME = {5}, NUMBER = {3}, PAGES = {289--298} } @ARTICLE{LaSuTr09, AUTHOR = {Layton, W. and Sussman, M. and Trenchea, C.}, TITLE = {Bounds on Energy, Magnetic Helicity and Cross Helicity Dissipation Rates of Approximate Deconvolution Models of Turbulence for {MHD} Flows}, YEAR = {2010}, JOURNAL = {Numer. Funct. Anal. Optim.}, FJOURNAL = { Numerical Functional Analysis and Optimization}, VOLUME = {31}, NUMBER = {4-6}, PAGES = {577-595} } @INCOLLECTION{LaTrTr2012, AUTHOR = {Layton, William and Tran, Hoang and Trenchea, Catalin}, TITLE = {Stability of partitioned methods for magnetohydrodynamics flows at small magnetic {R}eynolds number}, BOOKTITLE = {Recent advances in scientific computing and applications}, SERIES = {Contemp. Math.}, VOLUME = {586}, PAGES = {231--238}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {2013}, MRCLASS = {76W05 (65M06 65M12 76M20)}, MRNUMBER = {3075873}, DOI = {10.1090/conm/586/11636}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1090/conm/586/11636}, } @ARTICLE{LaTrTr2013, AUTHOR = {Layton, William and Tran, Hoang and Trenchea, Catalin}, TITLE = {Numerical analysis of two partitioned methods for uncoupling evolutionary {MHD} flows}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {30}, YEAR = {2014}, NUMBER = {4}, PAGES = {1083--1102}, ISSN = {0749-159X}, MRCLASS = {65M60 (76W05)}, MRNUMBER = {3200267}, } @article{ISI:000303700000011, Author = {Layton, William and Hoang Tran and Xiong, Xin}, Title = {{Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems}}, Journal = {{Journal of Computational and Applied Mathematics}}, Year = {{2012}}, Volume = {{236}}, Number = {{13}}, Pages = {{3198-3217}}, Month = {{JUL}}, Abstract = {{This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each timestep into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based partitioned methods under timestep restrictions depending on the problem parameters. The methods include those that are stable uniformly in S-0, the storativity coefficient, for moderate k(min), the minimum hydraulic conductivity, uniformly in k(min) for moderate S-0 and with no coupling between the timestep and the spacial meshwidth. (C) 2012 Elsevier B.V. All rights reserved.}}, Publisher = {{ELSEVIER SCIENCE BV}}, Address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}}, Type = {{Article}}, Language = {{English}}, Affiliation = {{Layton, W (Reprint Author), Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA.. Layton, William; Hoang Tran; Xiong, Xin, Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA.}}, DOI = {{10.1016/j.cam.2012.02.019}}, ISSN = {{0377-0427}}, Keywords = {{Stokes-Darcy coupling; Partitioned methods; Splitting methods}}, Keywords-Plus = {{POROUS-MEDIA FLOW; FINITE-ELEMENT METHODS; COUPLING FLUID-FLOW; PARABOLIC EQUATIONS; BOUNDARY-CONDITION; GROUNDWATER FLOWS; MODEL; SURFACE; EXPLICIT; IMPLICIT}}, Research-Areas = {{Mathematics}}, Web-of-Science-Categories = {{Mathematics, Applied}}, Author-Email = {{wjl@pitt.edu hat25@pitt.edu xix21@pitt.edu}}, Funding-Acknowledgement = {{NSF\{{[}\}DMS 0810385]}}, Funding-Text = {{The author WL had a stimulating E-mail exchange with Professor Jan Verwer in January 2011 on the Stokes-Darcy coupling. This exchange led to the consideration of splitting methods and the development of the ideas herein. We gratefully acknowledge our discussion with Professor Verwer which inspired our work. The work of WL, HT and XX was partially supported by NSF grant DMS 0810385.}}, Number-of-Cited-References = {{61}}, Times-Cited = {{0}}, Journal-ISO = {{J. Comput. Appl. Math.}}, Doc-Delivery-Number = {{937YL}}, Unique-ID = {{ISI:000303700000011}}, } @ARTICLE{Layton12Citt, AUTHOR = {Layton, William}, TITLE = {The interior error of {van Cittert} deconvolution is optimal}, YEAR = {2012}, JOURNAL = {Appl. Math.}, VOLUME = {E-notes 12}, NUMBER = {12}, PAGES = {88-93} } @article {MR3452847, AUTHOR = {Layton, William and Li, Yong and Trenchea, Catalin}, TITLE = {Recent developments in {IMEX} methods with time filters for systems of evolution equations}, JOURNAL = {J. Comput. Appl. Math.}, FJOURNAL = {Journal of Computational and Applied Mathematics}, VOLUME = {299}, YEAR = {2016}, PAGES = {50--67}, ISSN = {0377-0427}, MRCLASS = {65L05 (65L04 65L06 65L20)}, MRNUMBER = {3452847}, MRREVIEWER = {Bernhard A. Schmitt}, DOI = {10.1016/j.cam.2015.09.038}, URL = {http://dx.doi.org/10.1016/j.cam.2015.09.038}, } @ARTICLE{LPTa05, AUTHOR = {Lazarev, Yu.N. and Petrov, P.V. and Tartakovsky, D.M.}, TITLE = {Interface dynamics in randomly heterogeneous porous media}, YEAR = {2005}, JOURNAL = {Advances in Water Resources}, VOLUME = {28}, NUMBER = {}, PAGES = {393-403} } @ARTICLE{LeLe07, AUTHOR = {Lederer, J. and Lewandowski, R.}, TITLE = {On the {RANS} 3{D} model with unbounded eddy viscosities}, YEAR = {2007}, JOURNAL = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis}, VOLUME = {24}, NUMBER = {3}, PAGES = {413-441} } @book{lefebvre1983gas, title={Gas turbine combustion}, author={Lefebvre, A.H.}, isbn={9780070370296}, lccn={82018727}, series={Energy, Combustion, and Environment Series}, url={https://books.google.com/books?id=rNNSAAAAMAAJ}, year={1983}, publisher={Hemisphere Pub. 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Mech.}, VOLUME = {8}, NUMBER = {}, PAGES = {398-422} } @ARTICLE{LL04b, AUTHOR = {Lewandowski, R. and Layton, W.}, TITLE = {Un Filtre pour la {SGE} \'{E}tudi\'{e} \`{a} la Lumi\`{e}re du K41}, YEAR = {2004}, JOURNAL = {Journ\'{e}es AUM AFM}, VOLUME = {}, NUMBER = {}, PAGES = {} } @ARTICLE{LeReDr06, AUTHOR = {Lewis, M. and Renclawowicz, J. and Driessche, P. Van den}, TITLE = {Traveling waves and spread rates for a West Nile virus model}, YEAR = {2006}, JOURNAL = {Bull. Math. Biol.}, VOLUME = {68}, NUMBER = {1}, PAGES = {3-23} } @article {MR1353521, AUTHOR = {Li, S. and Qin, Meng Zhao}, TITLE = {Lie-{P}oisson integration for rigid body dynamics}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {30}, YEAR = {1995}, NUMBER = {9}, PAGES = {105--118}, ISSN = {0898-1221}, MRCLASS = {70-08 (58F05 70E15 70H05)}, MRNUMBER = {1353521}, MRREVIEWER = {B. M. Herbst}, DOI = {10.1016/0898-1221(95)00150-W}, URL = {https://doi.org/10.1016/0898-1221(95)00150-W}, } @book {MR3611231, AUTHOR = {Li, Yong}, TITLE = {Time filters for numerical weather prediction}, NOTE = {Thesis (Ph.D.)--University of Pittsburgh}, PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, YEAR = {2016}, PAGES = {75}, ISBN = {978-1369-41820-0}, MRCLASS = {Thesis}, MRNUMBER = {3611231}, URL = {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10298805}, } @conference{LiTr2015Venezzia, author = "Li, Yong and Trenchea, Catalin", title = "Analysis of time filters used with the Leapfrog scheme", booktitle = "Coupled Problems in Science and Engineering VI COUPLED PROBLEMS 2015", editor = "B. Schrefler, E. O\~{n}̃ate and M. Papadrakakis", volume = "", number = "", series = "", pages = "1261-1272", address = "Barcelona, Spain", year = "2015", month = "april", publisher= "International Center for Numerical Methods in Engineering (CIMNE)", note = "", ISBN = {978-84-943928-3-2} } @phdthesis{LiThesis, Author = {Li, Yong}, Date-Added = {}, Date-Modified = {}, School = {University of Pittsburgh}, Title = {Time filters for numerical weather prediction}, Year = {2016}} @ARTICLE{YLCTstochBoussinesq, AUTHOR = {Li, Yong and Trenchea, Catalin}, TITLE = {Existence and Ergodicity for the Two-Dimensional Stochastic Boussinesq equation}, JOURNAL = {International Journal of Numerical Analysis and Modeling}, FJOURNAL = {}, VOLUME = {}, YEAR = {2017}, PAGES = {to appear}, ISSN = {}, MRCLASS = {}, MRNUMBER = {}, DOI = {}, URL = {}, } @article {MR3789587, AUTHOR = {Li, Yong and Trenchea, Catalin}, TITLE = {Existence and ergodicity for the two-dimensional stochastic {B}oussinesq equation}, JOURNAL = {Int. J. Numer. Anal. Model.}, FJOURNAL = {International Journal of Numerical Analysis and Modeling}, VOLUME = {15}, YEAR = {2018}, NUMBER = {4-5}, PAGES = {715--728}, ISSN = {1705-5105}, MRCLASS = {60H15 (35Q35 35R60)}, MRNUMBER = {3789587}, MRREVIEWER = {Dominic Breit}, } YLCT-mhd-15 @article {MR3831959, AUTHOR = {Li, Yong and Trenchea, Catalin}, TITLE = {Partitioned second order method for magnetohydrodynamics in {E}ls\"{a}sser variables}, JOURNAL = {Discrete Contin. Dyn. Syst. Ser. B}, FJOURNAL = {Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences}, VOLUME = {23}, YEAR = {2018}, NUMBER = {7}, PAGES = {2803--2823}, ISSN = {1531-3492}, MRCLASS = {65M60 (65M12 65M15 76W05)}, MRNUMBER = {3831959}, MRREVIEWER = {Hamdullah Y\"{u}cel}, DOI = {10.3934/dcdsb.2018106}, URL = {https://doi.org/10.3934/dcdsb.2018106}, } @articleInfo{1531-3492_2018_7_2803, AUTHOR = {Li, Yong and Trenchea, Catalin}, TITLE = {Partitioned second order method for magnetohydrodynamics in {E}ls\"{a}sser variables}, JOURNAL = {Discrete Contin. Dyn. Syst. Ser. B}, FJOURNAL = {Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences}, VOLUME = {23}, YEAR = {2018}, NUMBER = {7}, PAGES = {2803--2823}, ISSN = {1531-3492}, MRCLASS = {65M60 (65M12 65M15 76W05)}, MRNUMBER = {3831959}, DOI = {10.3934/dcdsb.2018106}, URL = {https://doi.org/10.3934/dcdsb.2018106}, } @techreport{YLCT-hoRA-15, Author = {Li, Yong and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {A higher order {Robert-Asselin} type time filter in the semi-explicit integrations}, Year = {2015}} @ARTICLE{YLCT14, AUTHOR = {Li, Yong and Trenchea, Catalin}, TITLE = {A higher-order {R}obert--{A}sselin type time filter}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {259}, YEAR = {2014}, PAGES = {23--32}, ISSN = {0021-9991}, MRCLASS = {Preliminary Data}, MRNUMBER = {3148557}, DOI = {10.1016/j.jcp.2013.11.022}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1016/j.jcp.2013.11.022}, } @techreport{YLPD14, AUTHOR = {Li, Yong and Williams, Paul D.}, Institution = {University of Pittsburgh}, TITLE = {Analysis of the {RAW} Filter in Composite-Tendency Leapfrog Integrations}, YEAR = {2014}, } @article {MR3957886, AUTHOR = {Li, Xiaoli and Shen, Jie and Rui, Hongxing}, TITLE = {Energy stability and convergence of {SAV} block-centered finite difference method for gradient flows}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {88}, YEAR = {2019}, NUMBER = {319}, PAGES = {2047--2068}, ISSN = {0025-5718}, MRCLASS = {65M06 (35K20 35K35 65M12 65M15)}, MRNUMBER = {3957886}, DOI = {10.1090/mcom/3428}, URL = {https://doi.org/10.1090/mcom/3428}, } @article {MR2684726, AUTHOR = {Lieberman, Chad and Willcox, Karen and Ghattas, Omar}, TITLE = {Parameter and state model reduction for large-scale statistical inverse problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {32}, YEAR = {2010}, NUMBER = {5}, PAGES = {2523--2542}, ISSN = {1064-8275}, MRCLASS = {65C05 (35R30 37M99 62F15 62J07 65C20)}, MRNUMBER = {2684726 (2011h:65007)}, MRREVIEWER = {Laura Scrimali}, DOI = {10.1137/090775622}, URL = {http://dx.doi.org/10.1137/090775622}, } @article{lilly1965computational, title={On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems}, author={Lilly, D.K.}, fjournal={Monthly Weather Review}, journal = {Mon. Wea. 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Sciences}, VOLUME = {43}, NUMBER = {}, PAGES = {126-140} } @book{lin1990sea, title={Sea-Water Magnetohydrodynamic Propulsion for Next-Generation Undersea Vehicles}, author={Lin, T.F. and Gilbert, J.B. and Kossowsky, R. and PENNSYLVANIA STATE UNIV STATE COLLEGE.}, url={http://books.google.com/books?id=GvhwNwAACAAJ}, year={1990}, publisher={Defense Technical Information Center} } @book{LinYL2007, author = {Lin, Yuh-Lang}, Title = {Mesoscale Dynamics}, publisher = {Cambridge University Press}, year = {2007}, url = {http://dx.doi.org/10.1017/CBO9780511619649} } Cambridge Books Online @BOOK{Lin94, AUTHOR = {Lindeberg, T.}, TITLE = {Scale-space theory in computer vision}, PUBLISHER = {Kluwer}, YEAR = {1994}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {Dordrecht} } @article {MR2802099, AUTHOR = {Linke, Alexander and Rebholz, Leo G. and Wilson, Nicholas E.}, TITLE = {On the convergence rate of grad-div stabilized {T}aylor-{H}ood to {S}cott-{V}ogelius solutions for incompressible flow problems}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {381}, YEAR = {2011}, NUMBER = {2}, PAGES = {612--626}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {76D03 (35Q35)}, MRNUMBER = {2802099 (2012g:76041)}, DOI = {10.1016/j.jmaa.2011.03.019}, URL = {http://dx.doi.org/10.1016/j.jmaa.2011.03.019}, } MR2337020 @article {LiTi07, AUTHOR = {Linshiz, J.S. and Titi, E.S.}, TITLE = {Analytical study of certain magnetohydrodynamic-{$\alpha$} models}, JOURNAL = {J. Math. Phys.}, FJOURNAL = {Journal of Mathematical Physics}, VOLUME = {48}, YEAR = {2007}, NUMBER = {6}, PAGES = {065504, 28}, ISSN = {0022-2488}, CODEN = {JMAPAQ}, MRCLASS = {76W05 (35Q35 76D03 76F02)}, MRNUMBER = {MR2337020 (2008i:76211)}, MRREVIEWER = {Xiaoming Wang}, } @article {MR1325825, AUTHOR = {Lions, Jacques-Louis and Temam, Roger and Wang, Shou Hong}, TITLE = {Mathematical theory for the coupled atmosphere-ocean models. ({CAO} {III})}, JOURNAL = {J. Math. Pures Appl. (9)}, FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`eme S\'{e}rie}, VOLUME = {74}, YEAR = {1995}, NUMBER = {2}, PAGES = {105--163}, ISSN = {0021-7824}, MRCLASS = {35Q35 (35D05 35K50 76C99 86A05)}, MRNUMBER = {1325825}, MRREVIEWER = {Bruno Scheurer}, } @article {MR1282364, AUTHOR = {Lions, Jacques-Louis and Temam, Roger and Wang, Shou Hong}, TITLE = {Probl\`eme \`a fronti\`ere libre pour les mod\`eles coupl\'{e}s de l'oc\'{e}an et de l'atmosph\`ere}, JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'{e}mie des Sciences. S\'{e}rie I. Math\'{e}matique}, VOLUME = {318}, YEAR = {1994}, NUMBER = {12}, PAGES = {1165--1171}, ISSN = {0764-4442}, MRCLASS = {86A10 (35Q35 35R35 76D99 76V05)}, MRNUMBER = {1282364}, } @article {MR1252502, AUTHOR = {Lions, J.-L. and Temam, R. and Wang, S.}, TITLE = {Models for the coupled atmosphere and ocean. ({CAO} {I},{II})}, JOURNAL = {Comput. Mech. Adv.}, FJOURNAL = {Computational Mechanics Advances}, VOLUME = {1}, YEAR = {1993}, NUMBER = {1}, PAGES = {120}, ISSN = {0927-7951}, MRCLASS = {35Q35 (65N50 76M25 76U05 86-08 86A05)}, MRNUMBER = {1252502}, MRREVIEWER = {Bruno Scheurer}, } @book {JLL69, AUTHOR = {Lions, J.-L.}, TITLE = {Quelques m\'ethodes de r\'esolution des probl\`emes aux limites non lin\'eaires}, PUBLISHER = {Dunod}, YEAR = {1969}, PAGES = {xx+554}, MRCLASS = {47.80 (35.00)}, MRNUMBER = {0259693 (41 \#4326)}, MRREVIEWER = {L. Cesari}, } MR0244606 @book {JLL68, AUTHOR = {Lions, J.-L.}, TITLE = {Contr\^ole optimal de syst\`emes gouvern\'es par des \'equations aux d\'eriv\'ees partielles}, SERIES = {Avant propos de P. Lelong}, PUBLISHER = {Dunod}, ADDRESS = {Paris}, YEAR = {1968}, PAGES = {xiii+426}, MRCLASS = {35.15 (49.00)}, MRNUMBER = {MR0244606 (39 \#5920)}, MRREVIEWER = {L. Cesari}, } MR664760 @book {Lion81, AUTHOR = {Lions, J.-L.}, TITLE = {Some methods in the mathematical analysis of systems and their control}, PUBLISHER = {Kexue Chubanshe (Science Press)}, ADDRESS = {Beijing}, YEAR = {1981}, PAGES = {xxiii+542}, ISBN = {0-677-60200-6}, MRCLASS = {49-01}, MRNUMBER = {MR664760 (84m:49003)}, } @ARTICLE{LP64, AUTHOR = {Lions, J.L. and Peetre, J.}, TITLE = {Sur une classe d'espaces d'interpolation}, YEAR = {1964}, JOURNAL = {Pub. de {I}.{H}.{E}.{S}.}, VOLUME = {19}, NUMBER = {}, PAGES = {5-68} } @book {MR0479526, AUTHOR = {Lions, J.-L.}, TITLE = {Some aspects of the optimal control of distributed parameter systems}, NOTE = {Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 6}, PUBLISHER = {Society for Industrial and Applied Mathematics}, ADDRESS = {Philadelphia, Pa.}, YEAR = {1972}, PAGES = {vi+92}, MRCLASS = {93C05 (93C20)}, MRNUMBER = {0479526 (57 \#18950)}, } @ARTICLE{LW04, AUTHOR = {Liu, J.-G. and Wang, W.-C.}, TITLE = {Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry}, YEAR = {2004}, JOURNAL = {JCP}, VOLUME = {200}, NUMBER = {}, PAGES = {8-33} } @book {MR3410409, AUTHOR = {Liu, Wei and R{\"o}ckner, Michael}, TITLE = {Stochastic partial differential equations: an introduction}, SERIES = {Universitext}, PUBLISHER = {Springer, Cham}, YEAR = {2015}, PAGES = {vi+266}, ISBN = {978-3-319-22353-7; 978-3-319-22354-4}, MRCLASS = {60H15 (35Q30 35Q53 35R60 60-01 60H05 60H10 60J25)}, MRNUMBER = {3410409}, MRREVIEWER = {Mark C. Veraar}, DOI = {10.1007/978-3-319-22354-4}, URL = {http://dx.doi.org.pitt.idm.oclc.org/10.1007/978-3-319-22354-4}, } @BOOK{Loeve_77, Author = {Lo{\`e}ve, M.}, Title = {Probability theory}, Publisher = {Springer-Verlag}, Year = {1977}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {45 and 46}, Edition = {4$^{th}$}, Address = {New York} } @article{lorenz1963deterministic, title={Deterministic nonperiodic flow}, author={Lorenz, Edward N}, journal={Journal of the atmospheric sciences}, volume={20}, number={2}, pages={130--141}, year={1963}, url={http://dx.doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2} } @ARTICLE{LD00, AUTHOR = {Lund, M.A. and Davis, J.A.}, TITLE = {Seasonal dynamics of plankton communities and water chemistry in a eutrophic wetland ({L}ake {M}onger, {W}estern {A}ustralia): implications for biomanipulation}, YEAR = {2000}, JOURNAL = {Mar. Freshwater Res.}, VOLUME = {51}, NUMBER = {}, PAGES = {321-332} } @ARTICLE{LLP99, AUTHOR = {Lenhart, S. and Liang, M. and Protopopescu, V.}, TITLE = {Optimal control of boundary habitat hostility for interacting species}, YEAR = {1999}, JOURNAL = {Math. Method. Appl. Sci.}, VOLUME = {22}, NUMBER = {}, PAGES = {1061-1077} } LeWo07 @book {MR2316829, AUTHOR = {Lenhart, Suzanne and Workman, John T.}, TITLE = {Optimal control applied to biological models}, SERIES = {Chapman \& Hall/CRC Mathematical and Computational Biology Series}, PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL}, YEAR = {2007}, PAGES = {xii+261}, ISBN = {978-1-58488-640-2; 1-58488-640-4}, MRCLASS = {49-01 (49-04 49N90 92-02)}, MRNUMBER = {MR2316829 (2008f:49001)}, MRREVIEWER = {Stefan Miric{\u{a}}}, } @book {MR1817225, AUTHOR = {Lieb, E.H. and Loss, M.}, TITLE = {Analysis}, SERIES = {Graduate Studies in Mathematics}, VOLUME = {14}, EDITION = {Second}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {2001}, PAGES = {xxii+346}, ISBN = {0-8218-2783-9}, MRCLASS = {00A05 (26-01 28-01 31-01 35J10 42-01)}, MRNUMBER = {MR1817225 (2001i:00001)}, } @book {MR1465184, AUTHOR = {Lieberman, G.M.}, TITLE = {Second order parabolic differential equations}, PUBLISHER = {World Scientific Publishing Co. Inc.}, ADDRESS = {River Edge, NJ}, YEAR = {1996}, PAGES = {xii+439}, ISBN = {981-02-2883-X}, MRCLASS = {35-02 (35Bxx 35Dxx 35Kxx)}, MRNUMBER = {MR1465184 (98k:35003)}, MRREVIEWER = {Siegfried Carl}, } @BOOK{LMW11, AUTHOR = {A. Logg, K.-A. Mardal, G. N. Wells et al.}, TITLE = {Automated Solution of Differential Equations By the Finite Element Method}, PUBLISHER = {Springer}, YEAR = {2011}, SERIES = {webpage: http://fenicsproject.org/}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @inproceedings{Lombardi2012NumericalSO, title={Numerical Simulation of Sailing Boats: Dynamics, {FSI}, and Shape Optimization}, author={Matteo Lombardi and Nicola Parolini and Alfio Quarteroni and Gianluigi Rozza}, year={2012} } @article {Lucor:2007p5253, AUTHOR = {Lucor, Didier and Meyers, Johan and Sagaut, Pierre}, TITLE = {Sensitivity analysis of large-eddy simulations to subgrid-scale-model parametric uncertainty using polynomial chaos}, JOURNAL = {J. Fluid Mech.}, FJOURNAL = {Journal of Fluid Mechanics}, VOLUME = {585}, YEAR = {2007}, PAGES = {255--279}, ISSN = {0022-1120}, CODEN = {JFLSA7}, MRCLASS = {76F65}, MRNUMBER = {2346736 (2008i:76101)}, MRREVIEWER = {Richard Pasquetti}, DOI = {10.1017/S0022112007006751}, URL = {http://dx.doi.org/10.1017/S0022112007006751}, } @ARTICLE{Luen64, AUTHOR = {Luenberger, D.}, TITLE = {Observing the state of a linear system}, YEAR = {1964}, JOURNAL = {IEEE Trans. Military Electronics, MIL-8}, VOLUME = {}, NUMBER = {}, PAGES = {74-80} } @article{10.1115/1.2720483, author = {Luo, Jiang and Razinsky, Eli H.}, title = "{Conjugate Heat Transfer Analysis of a Cooled Turbine Vane Using the V2F Turbulence Model}", journal = {Journal of Turbomachinery}, volume = {129}, number = {4}, pages = {773-781}, year = {2006}, month = {07}, abstract = "{The conjugate heat transfer methodology has been employed to predict the flow and thermal properties including the metal temperature of a NASA turbine vane at three operating conditions. The turbine vane was cooled internally by air flowing through ten round pipes. The conjugate heat transfer methodology allows a simultaneous solution of aerodynamics and heat transfer in the external hot gas and the internal cooling passages and conduction within the solid metal, eliminating the need for multiple/decoupled solutions in a typical industry design process. The model of about 3 million computational meshes includes the gas path and the internal cooling channels, comprising hexa cells, and the solid metal comprising hexa and prism cells. The predicted aerodynamic loadings were found to be in close agreement with the data for all the cases. The predicted metal temperature, external, and internal heat transfer distributions at the midspan compared well with the measurement. The differences in the heat transfer rates and metal temperature under different running conditions were also captured well. The V2F turbulence model has been compared with a low-Reynolds-number k-ε model and a nonlinear quadratic k-ε model. The V2F model is found to provide the closest agreement with the data, though it still has room for improvement in predicting the boundary layer transition and turbulent heat transfer, especially on the suction side. The overall results are quite encouraging and indicate that conjugate heat transfer simulation with proper turbulence closure has the potential to become a viable tool in turbine heat transfer analysis and cooling design.}", issn = {0889-504X}, doi = {10.1115/1.2720483}, url = {https://doi.org/10.1115/1.2720483}, eprint = {https://asmedigitalcollection.asme.org/turbomachinery/article-pdf/129/4/773/5843264/773\_1.pdf}, } @article {MR2480183, AUTHOR = {Ma, Xiang and Zabaras, Nicholas}, TITLE = {An efficient {B}ayesian inference approach to inverse problems based on an adaptive sparse grid collocation method}, JOURNAL = {Inverse Problems}, FJOURNAL = {Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data}, VOLUME = {25}, YEAR = {2009}, NUMBER = {3}, PAGES = {035013, 27}, ISSN = {0266-5611}, CODEN = {INPEEY}, MRCLASS = {65J22 (62C10 62H35 62P30)}, MRNUMBER = {2480183 (2010e:65082)}, DOI = {10.1088/0266-5611/25/3/035013}, URL = {http://dx.doi.org/10.1088/0266-5611/25/3/035013}, } @article {MR1949885, AUTHOR = {Machihara, Shuji and Ozawa, Tohru}, TITLE = {Interpolation inequalities in {B}esov spaces}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {131}, YEAR = {2003}, NUMBER = {5}, PAGES = {1553--1556 (electronic)}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {46B70 (46E35 46M35)}, MRNUMBER = {MR1949885 (2004i:46030)}, } @article {MR2208679, AUTHOR = {Madzvamuse, Anotida}, TITLE = {Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {214}, YEAR = {2006}, NUMBER = {1}, PAGES = {239--263}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65M60 (76M10)}, MRNUMBER = {MR2208679 (2006j:65289)}, } @ARTICLE{MaWaMa03, AUTHOR = {Madzvamuse, A. and Wathen, A. and Maini, P.}, TITLE = {A moving grid finite element method applied to a model biological pattern generator}, YEAR = {2003}, JOURNAL = {J. Comput. Phys.}, VOLUME = {2}, NUMBER = {2}, PAGES = {478-500} } @ARTICLE{Magaz1980, AUTHOR = {Magazenkov, L.N.}, TITLE = {{Trudy Glavnoi Geofizicheskoi Observatorii}}, YEAR = {1980}, JOURNAL = {(Transactions of the Main Geophysical Observatory)}, VOLUME = {410}, NUMBER = {}, PAGES = {120--129} } @article{Mahesh:2004:NML:1016237.1016248, author = {Mahesh, K. and Constantinescu, G. and Moin, P.}, title = {A Numerical Method for Large-eddy Simulation in Complex Geometries}, journal = {J. Comput. Phys.}, issue_date = {10 June 2004}, volume = {197}, number = {1}, month = jun, year = {2004}, issn = {0021-9991}, pages = {215--240}, numpages = {26}, url = {http://dx.doi.org/10.1016/j.jcp.2003.11.031}, doi = {10.1016/j.jcp.2003.11.031}, acmid = {1016248}, publisher = {Academic Press Professional, Inc.}, address = {San Diego, CA, USA}, keywords = {complex geometries, energy-conserving schemes, gas-turbine combustor, large-eddy simulation, unstructured grids}, } @ARTICLE{Malc00, AUTHOR = {Malchow, H.}, TITLE = {Motional Instabilities in Prey-Predator Systems}, YEAR = {2000}, JOURNAL = {J. Theor. Biol.}, VOLUME = {204}, NUMBER = {}, PAGES = {639-647} } @ARTICLE{MHP04, AUTHOR = {Malchow, H. and Hilker, F.M. and Petrovskii, S.V.}, TITLE = {Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system}, YEAR = {2004}, JOURNAL = {Discrete Cont. Dyn.-B}, VOLUME = {4}, NUMBER = {3}, PAGES = {705-711} } @book {MR1409366, AUTHOR = {M{\'{a}}lek, J. and Ne{\v{c}}as, J. and Rokyta, M. and R{u}{\v{z}}i{\v{c}}ka, M.}, TITLE = {Weak and measure-valued solutions to evolutionary {PDE}s}, SERIES = {Applied Mathematics and Mathematical Computation}, VOLUME = {13}, PUBLISHER = {Chapman \& Hall}, ADDRESS = {London}, YEAR = {1996}, PAGES = {xii+317}, ISBN = {0-412-57750-X}, MRCLASS = {35-02 (35D05 35K60 35L65 35Q35)}, MRNUMBER = {MR1409366 (97g:35002)}, MRREVIEWER = {Vladimir V. Shelukhin}, } @techreport{MKM06, Author = {Manica, C.C. and Kaya-Merdan, S.}, Institution = {University of Pittsburgh}, Title = {Convergence Analysis of the Finite Element Method for a Fundamental Model in Turbulence}, Year = {http://www.math.pitt.edu/techreports.html, 2006}} @techreport{MM07, Author = {Manica, C.C. and Stanculescu, I.}, Institution = {University of Pittsburgh}, Title = {report in preparation}, Year = {http://www.math.pitt.edu/techreports.html, 2007}} @article {MR1107016, AUTHOR = {Maremonti, Paolo}, TITLE = {Existence and stability of time-periodic solutions to the {N}avier-{S}tokes equations in the whole space}, JOURNAL = {Nonlinearity}, FJOURNAL = {Nonlinearity}, VOLUME = {4}, YEAR = {1991}, NUMBER = {2}, PAGES = {503--529}, ISSN = {0951-7715}, CODEN = {NONLE5}, MRCLASS = {35Q30 (35B10 35B35 76D05)}, MRNUMBER = {1107016 (92d:35227)}, MRREVIEWER = {Pavel Krej{\v{c}}{\'{\i}}}, URL = {http://stacks.iop.org/0951-7715/4/503}, } @incollection{Marsch91, year={1991}, isbn={978-3-642-76752-4}, booktitle={Reviews in Modern Astronomy}, volume={4}, series={Reviews in Modern Astronomy}, editor={Klare, Gerhard}, doi={10.1007/978-3-642-76750-0_10}, title={Turbulence in the Solar Wind}, url={http://dx.doi.org/10.1007/978-3-642-76750-0_10}, publisher={Springer Berlin Heidelberg}, author={Marsch, E.}, pages={145-156}, language={English} } @article {MR2970260, AUTHOR = {Martin, James and Wilcox, Lucas C. and Burstedde, Carsten and Ghattas, Omar}, TITLE = {A stochastic {N}ewton {MCMC} method for large-scale statistical inverse problems with application to seismic inversion}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {34}, YEAR = {2012}, NUMBER = {3}, PAGES = {A1460--A1487}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {65C40 (35Q62 62F15 90C15)}, MRNUMBER = {2970260}, MRREVIEWER = {Bruno Betr{\`o}}, DOI = {10.1137/110845598}, URL = {http://dx.doi.org/10.1137/110845598}, } @ARTICLE{Marxen, AUTHOR = {Marxen, O.}, TITLE = {Numerical studies of physical effects related to the controlled transition process in laminar separation bubbles}, YEAR = {2004}, JOURNAL = {Dissertation for Doctorate of Engineering, Institute of Aerodynamics and Gasdynamics, University of Stuttgart}, VOLUME = {}, NUMBER = {}, PAGES = {} } @article{PhysRevE.77.036403, journal = {Phys. Rev. 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E. and Politano, H. and Pouquet, A.", title = "Dynamo action in the {Taylor-Green} vortex near threshold", journal = "Physics of Plasmas (1994-present)", year = "1997", volume = "4", number = "1", eid = "", pages = "1-3", url = "http://scitation.aip.org/content/aip/journal/pop/4/1/10.1063/1.872578", doi = "http://dx.doi.org/10.1063/1.872578" } @article {MR3273270, AUTHOR = {Norton, Terence J. T. and Hill, Adrian T.}, TITLE = {An iterative starting method to control parasitism for the leapfrog method}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {87}, YEAR = {2015}, PAGES = {145--156}, ISSN = {0168-9274}, MRCLASS = {65M06 (65M12)}, MRNUMBER = {3273270}, MRREVIEWER = {Sergio Amat}, DOI = {10.1016/j.apnum.2014.09.005}, URL = {https://doi.org/10.1016/j.apnum.2014.09.005}, } @book {MR2084891, AUTHOR = {Novotn{\'y}, A. and Stra{\v{s}}kraba, I.}, TITLE = {Introduction to the mathematical theory of compressible flow}, SERIES = {Oxford Lecture Series in Mathematics and its Applications}, VOLUME = {27}, PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = {2004}, PAGES = {xx+506}, ISBN = {0-19-853084-6}, MRCLASS = {35Q35 (35Q30 76N10)}, MRNUMBER = {MR2084891 (2005i:35220)}, MRREVIEWER = {Rapha{\"e}l Danchin}, } @article {MR2242955, AUTHOR = {Odasso, Cyril}, TITLE = {Ergodicity for the stochastic complex {G}inzburg-{L}andau equations}, JOURNAL = {Ann. Inst. H. Poincar\'e Probab. Statist.}, FJOURNAL = {Annales de l'Institut Henri Poincar\'e. 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An International Journal}, VOLUME = {29}, YEAR = {2013}, NUMBER = {6}, PAGES = {2061--2080}, ISSN = {0749-159X}, MRCLASS = {65M60 (65M12 65M15 76D05 76M10)}, MRNUMBER = {3116558}, MRREVIEWER = {Dmitriy Leykekhman}, } @ARTICLE{OsLa96, AUTHOR = {Osnes, H. and Langtangen, H.P.}, TITLE = {An Efficient Probabilistic Finite Element Method for Stochastic Groundwater Flow}, YEAR = {1998}, JOURNAL = {Advances in Water Resources}, VOLUME = {22}, NUMBER = {}, PAGES = {185-195} } @article {MR2068272, AUTHOR = {\O sterby, Ole}, TITLE = {Five ways of reducing the {C}rank-{N}icolson oscillations}, JOURNAL = {BIT}, FJOURNAL = {BIT. 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Panchev }, edition = { [1st ed.] }, isbn = { 0080158269 }, publisher = { Pergamon Press Oxford, New York, }, pages = { xiii, 444 p. }, year = { 1971 }, type = { Book }, language = { English }, subjects = { Turbulence.; Stochastic processes. }, life-dates = { 1971 - }, catalogue-url = { http://nla.gov.au/nla.cat-vn2531140 }, } @article{PAPANICOLAOU20013413, title = "A conservation-based discretization approach for conjugate heat transfer calculations in hot-gas ducting turbomachinery components", journal = "International Journal of Heat and Mass Transfer", volume = "44", number = "18", pages = "3413 - 3429", year = "2001", issn = "0017-9310", doi = "https://doi.org/10.1016/S0017-9310(01)00017-5", url = "http://www.sciencedirect.com/science/article/pii/S0017931001000175", author = "E. Papanicolaou and D. Giebert and R. Koch and A. Schulz", abstract = "A numerical procedure has been developed for simulation of conjugate heat transfer in generalized coordinates and used in some typical turbomachinery applications. Discretized equations for nodes located exactly on the solid–fluid interface were derived using energy conservation principles, yielding the corresponding temperatures directly, without the need for inter- or extrapolation from adjacent nodes. A finite-volume-based computer code was used along with the SIMPLE algorithm and the k–ϵ turbulence model. The turbulent flow and heat transfer in a stepped labyrinth seal and in an effusion-cooled combustor liner have been studied and results were compared with measured data showing good agreement. In the labyrinth-seal case, the comparisons were in terms of surface temperatures and Nusselt numbers, while for the effusion-cooling case in terms of the streamwise velocity and the film-cooling effectiveness for different blowing and density ratios. 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ASME)}, VOLUME = {115}, NUMBER = {}, PAGES = {302-310 } } @book {MR2329435, AUTHOR = {Pr{\'e}v{\^o}t, Claudia and R{\"o}ckner, Michael}, TITLE = {A concise course on stochastic partial differential equations}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {1905}, PUBLISHER = {Springer, Berlin}, YEAR = {2007}, PAGES = {vi+144}, ISBN = {978-3-540-70780-6; 3-540-70780-8}, MRCLASS = {60H15 (60-01)}, MRNUMBER = {2329435}, MRREVIEWER = {Sandra Cerrai}, } @article {MR0126088, AUTHOR = {Prodi, G.}, TITLE = {Un teorema di unicit\`a per le equazioni di {N}avier-{S}tokes}, JOURNAL = {Ann. Mat. Pura Appl. (4)}, FJOURNAL = {Annali di Matematica Pura ed Applicata. Serie Quarta}, VOLUME = {48}, YEAR = {1959}, PAGES = {173--182}, ISSN = {0003-4622}, MRCLASS = {35.79}, MRNUMBER = {MR0126088 (23 \#A3384)}, MRREVIEWER = {J. L. Lions}, } @book {PrWe84, AUTHOR = {Protter, Murray H. and Weinberger, Hans F.}, TITLE = {Maximum principles in differential equations}, NOTE = {Corrected reprint of the 1967 original}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1984}, PAGES = {x+261}, ISBN = {0-387-96068-6}, MRCLASS = {35B50 (35-01)}, MRNUMBER = {MR762825 (86f:35034)}, } @ARTICLE{P06, AUTHOR = {Pruett, C.}, TITLE = {Temporal large-eddy simulation: theory and implementation}, YEAR = {2008}, JOURNAL = {Theor. Comput. Fluid Dyn.}, VOLUME = {22}, NUMBER = {}, PAGES = {275--304} } @ARTICLE{Pru04, AUTHOR = {Pruett, C.D.}, TITLE = {On Eulerian time-domain filtering for spatial large-eddy simulation}, YEAR = {2000}, JOURNAL = {AIAA J.}, VOLUME = {38}, NUMBER = {}, PAGES = {1634} } @ARTICLE{PGGT03, AUTHOR = {Pruett, C.D. and Gatski, T.B. and Grosch, C.E. and Thacker, W.D.}, TITLE = {The temporally filtered {N}avier-{S}tokes equations: properties of the residual stress}, YEAR = {2003}, JOURNAL = {Phys. Fluids}, VOLUME = {15}, NUMBER = {}, PAGES = {2127-2140} } @ARTICLE{PTGG06, AUTHOR = {Pruett, C.D. and Thomas, B.C. and Grosch, C.E. and Gatski, T.B.}, TITLE = {A temporal approximate deconvolution model for large-eddy simulation}, YEAR = {2006}, JOURNAL = {Phys. Fluids}, VOLUME = {18}, NUMBER = {}, PAGES = {1-4} } @book {MR2729936, AUTHOR = {Punsly, Brian}, TITLE = {Black hole gravitohydromagnetics}, SERIES = {Astrophysics and Space Science Library}, VOLUME = {355}, EDITION = {Second}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2008}, PAGES = {xiv+399}, ISBN = {978-3-540-76955-2}, MRCLASS = {83C55 (76W05 76Y05 83C57 85A30)}, MRNUMBER = {2729936 (2012b:83029)}, MRREVIEWER = {Elizabeth Winstanley}, } @book {MR1299729, AUTHOR = {Quarteroni, Alfio and Valli, Alberto}, TITLE = {Numerical approximation of partial differential equations}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {23}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1994}, PAGES = {xvi+543}, ISBN = {3-540-57111-6}, MRCLASS = {65-01 (65Mxx 65Nxx 76D05 76Mxx)}, MRNUMBER = {1299729 (95i:65005)}, MRREVIEWER = {Ji{\v{r}}{\'{\i}} Nedoma}, } @article {MR1885704, AUTHOR = {Quarteroni, Alfio and Veneziani, Alessandro and Zunino, Paolo}, TITLE = {Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {39}, YEAR = {2001/02}, NUMBER = {5}, PAGES = {1488--1511}, ISSN = {0036-1429}, MRCLASS = {76Z05 (65M60 76D05 76M10 76R50 92C35)}, MRNUMBER = {1885704}, DOI = {10.1137/S0036142900369714}, URL = {https://doi.org/10.1137/S0036142900369714}, } @book {MR2522375, AUTHOR = {Quarteroni, Alfio}, TITLE = {Numerical models for differential problems}, SERIES = {MS\&A. Modeling, Simulation and Applications}, VOLUME = {2}, PUBLISHER = {Springer-Verlag Italia, Milan}, YEAR = {2009}, PAGES = {xvi+601}, ISBN = {978-88-470-1070-3}, NOTE = {Translated from the 4th (2008) Italian edition by Silvia Quarteroni}, MRCLASS = {65-02 (65Mxx 65Nxx)}, MRNUMBER = {MR2522375}, DOI = {10.1007/978-88-470-1071-0}, URL = {http://dx.doi.org/10.1007/978-88-470-1071-0}, } @book {QSS07, AUTHOR = {Quarteroni, Alfio and Sacco, Riccardo and Saleri, Fausto}, TITLE = {Numerical mathematics}, SERIES = {Texts in Applied Mathematics}, VOLUME = {37}, EDITION = {Second}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2007}, PAGES = {xviii+655}, ISBN = {978-3-540-34658-6; 3-540-34658-9}, MRCLASS = {65-01}, MRNUMBER = {MR2265914 (2007f:65001)}, } @techreport{QuTr02, Author = {Quincampoix, M. and Trenchea, C.}, Institution = {Universit\'{e} de Bretagne Occidentale}, Title = {Hamilton-{J}acobi equation and optimality conditions for control systems governed by semilinear parabolic equations with boundary control}, Year = {2003}} @mastersthesis{Ramon2014, author = "Ramon, A.C.", title = "Modeling Transport Phenomena at the Interface Between a Free Fluid and a Porous Medium", school = "Universitat Politecnica de Catalunya", type = "Master thesis in advanced mathematics and mathematical engineering", address = "", year = "2014", month = "", note = "", } @article{10.1115/1.1928287, author = {Rahman, Faisal and Visser, Jan A. and Morris, Reuben M.}, title = "{Capturing Sudden Increase in Heat Transfer on the Suction Side of a Turbine Blade Using a Navier-Stokes Solver}", journal = {Journal of Turbomachinery}, volume = {127}, number = {3}, pages = {552-556}, year = {2005}, month = {01}, abstract = "{The numerical modeling of heat transfer on the suction side of a cooled gas turbine blade is one of the more difficult problems in engineering. The main reason is believed to be the transition from laminar to turbulent flow and the inability of standard Navier–Stokes solvers to predict the transition. This paper proves that sudden changes in heat transfer on the suction side of a turbine blade can indeed also be caused by localized shocks disrupting the boundary layer. In contrast to transition, the position of these shocks and the effect of the shocks on the pressure distribution and heat transfer rate can be predicted to within an acceptable degree of accuracy using standard Navier–Stokes solvers. Two well-documented case studies from the literature are used to prove that the pressure distribution around the profile can be predicted accurately when compared to experimental data. At the same time this method can be used to capture sudden changes in heat transfer rate caused by localized shocks. The conclusion from this study is that localized shock waves close to the suction side surface of a turbine blade can have the same effect on the heat transfer rate to the blade as transition.}", issn = {0889-504X}, doi = {10.1115/1.1928287}, url = {https://doi.org/10.1115/1.1928287}, eprint = {https://asmedigitalcollection.asme.org/turbomachinery/article-pdf/127/3/552/5942254/552\_1.pdf}, } @ARTICLE{RM04, AUTHOR = {Rapaport, A. and Maloum, A.}, TITLE = {Design of exponential observers for nonlinear systems by embedding}, YEAR = {2004}, JOURNAL = {Internat. J. Robust Nonlinear Control}, VOLUME = {14}, NUMBER = {3}, PAGES = {273-288} } @ARTICLE{Ravi05, AUTHOR = {Ravindran, S.S.}, TITLE = {Real-time computational algorithm for optimal control of an {MHD} flow system}, YEAR = {2005}, JOURNAL = {SIAM J. Sci. Comput}, VOLUME = {26}, NUMBER = {4}, PAGES = {1369-1388} } @ARTICLE{Ravi11, AUTHOR = {Ravindran, S.S.}, TITLE = {Convergence of Extrapolated {BDF2} Finite Element Schemes for Unsteady Penetrative Convection Model}, YEAR = {2012}, JOURNAL = {Numerical Functional Analysis and Optimization}, VOLUME = {33}, NUMBER = {1}, PAGES = {48-79} } @article {MR2758268, AUTHOR = {Ray, J. and Marzouk, Y. M. and Najm, H. N.}, TITLE = {A {B}ayesian approach for estimating bioterror attacks from patient data}, JOURNAL = {Stat. Med.}, FJOURNAL = {Statistics in Medicine}, VOLUME = {30}, YEAR = {2011}, NUMBER = {2}, PAGES = {101--126}, ISSN = {0277-6715}, MRCLASS = {Database Expansion Item}, MRNUMBER = {2758268}, DOI = {10.1002/sim.4090}, URL = {http://dx.doi.org/10.1002/sim.4090}, } @article {MR1665668, AUTHOR = {Raymond, J. P. and Zidani, H.}, TITLE = {Hamiltonian {P}ontryagin's principles for control problems governed by semilinear parabolic equations}, JOURNAL = {Appl. Math. Optim.}, FJOURNAL = {Applied Mathematics and Optimization. An International Journal with Applications to Stochastics}, VOLUME = {39}, YEAR = {1999}, NUMBER = {2}, PAGES = {143--177}, ISSN = {0095-4616}, CODEN = {AMOMBN}, MRCLASS = {49K20 (35K55 65K10)}, MRNUMBER = {MR1665668 (99j:49050)}, MRREVIEWER = {J. Fr{\'e}d{\'e}ric Bonnans}, DOI = {10.1007/s002459900102}, URL = {http://dx.doi.org/10.1007/s002459900102}, } @techreport{JiangRebholzTre2015, Author = {Jiang, Nan and Rebholz, Leo G. and Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Analysis of a family of regularization methods for {Navier-Stokes} equations}, Year = {2014}} @unpublished{JiangRebholzTre2014, author = {Jiang, Nan and Rebholz, Leo G. and Trenchea, Catalin}, title = {Analysis of a family of regularization methods for {Navier-Stokes} equations}, year = {2014}, month = "", note = {Preprint}, } JiangRebholzTre2016 @article{Jiang2016388, title = "An optimally accurate discrete regularization for second order timestepping methods for {Navier-Stokes} equations", journal = "Computer Methods in Applied Mechanics and Engineering ", volume = "310", number = "", pages = "388 - 405", year = "2016", note = "", issn = "0045-7825", doi = "http://dx.doi.org/10.1016/j.cma.2016.07.017", url = "http://www.sciencedirect.com/science/article/pii/S0045782516307587", author = "Nan Jiang and Muhammad Mohebujjaman and Leo G. Rebholz and Catalin Trenchea", keywords = "Navier-€“Stokes", keywords = "Unconditional stability", keywords = "IMEX methods", keywords = "Second order convergence", keywords = "Crank-Nicolson", keywords = "BDF2 " } @article {MR2234494, AUTHOR = {Rebholz, L.G.}, TITLE = {A multiscale {$V$}-{$P$} discretization for flow problems}, JOURNAL = {Appl. Math. Comput.}, FJOURNAL = {Applied Mathematics and Computation}, VOLUME = {177}, YEAR = {2006}, NUMBER = {1}, PAGES = {24--35}, ISSN = {0096-3003}, CODEN = {AMHCBQ}, MRCLASS = {76M10 (65M06 76D05)}, MRNUMBER = {MR2234494 (2007a:76075)}, } MR2277764 - R07, @article {R07, AUTHOR = {Rebholz, L.G.}, TITLE = {Conservation laws of turbulence models}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {326}, YEAR = {2007}, NUMBER = {1}, PAGES = {33--45}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {76F65 (35L65 35Q35 76D05)}, MRNUMBER = {MR2277764}, } @Article{Reb07b, author = {L. Rebholz}, title = {A family of new high order {NS-alpha} models arising from helicity correction in {Leray} turbulence models }, journal = {submitted}, note = {TR MATH 06-19, University of Pittsburgh}, year = {2007} } @article {MR3867387, AUTHOR = {Rebollo, T. Chacon and Yakoubi, D.}, TITLE = {A three-dimensional model for two coupled turbulent fluids: numerical analysis of a finite element approximation}, JOURNAL = {IMA J. Numer. Anal.}, FJOURNAL = {IMA Journal of Numerical Analysis}, VOLUME = {38}, YEAR = {2018}, NUMBER = {4}, PAGES = {1927--1958}, ISSN = {0272-4979}, MRCLASS = {65N30 (65N12 76F65 86A05 86A10)}, MRNUMBER = {3867387}, MRREVIEWER = {Beny Neta}, DOI = {10.1093/imanum/drx049}, URL = {https://doi.org/10.1093/imanum/drx049}, } %MR07b @article {MR2732395, AUTHOR = {Miles, William W. and Rebholz, Leo G.}, TITLE = {An enhanced-physics-based scheme for the {$\text{NS-}\alpha$} turbulence model}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {26}, YEAR = {2010}, NUMBER = {6}, PAGES = {1530--1555}, ISSN = {0749-159X}, MRCLASS = {76Fxx (65M60 76Mxx)}, MRNUMBER = {2732395}, } RJH06 - MR2201563 @article {MR2201563, AUTHOR = {van Reeuwijk, M. and Jonker, H.J.J. and Hanjali{\'c}, K.}, TITLE = {Incompressibility of the {L}eray-{$\alpha$} model for wall-bounded flows}, JOURNAL = {Phys. Fluids}, FJOURNAL = {Physics of Fluids}, VOLUME = {18}, YEAR = {2006}, NUMBER = {1}, PAGES = {018103, 4}, ISSN = {1070-6631}, CODEN = {PHFLE6}, MRCLASS = {76F02 (76F40)}, MRNUMBER = {MR2201563 (2006i:76043)}, } @ARTICLE{RDATM05, AUTHOR = {Rejas, D. and Declerck, S. and Auwerkerken, J. and Tak, P. and Meester, L.D.}, TITLE = {Plankton dynamics in a tropical floodplain lake: fish, nutrients, and the relative importance of bottom-up and top-down control}, YEAR = {2005}, JOURNAL = {Freshwater Biol.}, VOLUME = {50}, NUMBER = {}, PAGES = {52-69} } @ARTICLE{RenLeslie11, AUTHOR = {Ren, Diandong and Leslie, Lance M.}, TITLE = {Three positive feedback mechanisms for ice-sheet melting in a warming climate}, YEAR = {2011}, JOURNAL = {J. Glaciol.}, VOLUME = {57}, NUMBER = {206}, PAGES = {1057--1066} } @ARTICLE{R95, AUTHOR = {Reynolds, O.}, TITLE = {On the dynamic theory of incompressible viscous fluids and the determination of the criterium}, YEAR = {1895}, JOURNAL = {Phil. Trans. R. Soc. London A}, VOLUME = {186}, NUMBER = {}, PAGES = {123-164} } !! Scientific Papers II, pp. 535\D0577. @book {MR2358797, AUTHOR = {Richardson, Lewis F.}, TITLE = {Weather prediction by numerical process}, SERIES = {Cambridge Mathematical Library}, EDITION = {Second}, NOTE = {}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2007}, PAGES = {xiv+236}, ISBN = {978-0-521-68044-8; 0-521-68044-1}, MRCLASS = {86A10}, MRNUMBER = {2358797 (2008g:86013)}, DOI = {10.1017/CBO9780511618291}, URL = {http://dx.doi.org/10.1017/CBO9780511618291}, } @ARTICLE{Ritchie1832, AUTHOR = {Ritchie, William}, TITLE = {Experimental Researches in Voltaic Electricity and Electro-Magnetism}, YEAR = {1832}, JOURNAL={Phil. Trans. R. Soc. 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Japan}, FJOURNAL = {Journal of the Meteorological Society of Japan}, VOLUME = {44, Ser. 2}, NUMBER = {5}, PAGES = {237-245} } @ARTICLE{Robert69, AUTHOR = {Robert, Andr\'{e} J.}, TITLE = {The integration of a spectral model of the atmosphere by the implicit method}, YEAR = {1969}, JOURNAL = { Proc. WMO-IUGG Symp. on NWP, Tokyo, Japan Meteorological Agency}, VOLUME = {\empty}, NUMBER = {VII}, PAGES = {19-24} } @ARTICLE{RobLep97, AUTHOR = {Robert, Andr\'{e} and L\'{e}pine, Mario}, TITLE = {An Anomaly in the Behaviour of the Time Filter Used with the Leapfrog Scheme in Atmospheric Models}, YEAR = {1997}, JOURNAL = {Atmosphere-Ocean}, VOLUME = {35}, NUMBER = {sup2}, PAGES = {S3--S15} } @BOOK{Roberts67, AUTHOR = {Roberts, P. 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Ruth}, title = {A canonical integration technique}, journal = {IEEE Trans. Nucl. Sci}, year = {1983}, pages = {2669--2671} } @article{MR1366356, AUTHOR = {Ruuth, Steven J.}, TITLE = {Implicit-explicit methods for reaction-diffusion problems in pattern formation}, JOURNAL = {J. Math. Biol.}, FJOURNAL = {Journal of Mathematical Biology}, VOLUME = {34}, YEAR = {1995}, NUMBER = {2}, PAGES = {148--176}, ISSN = {0303-6812}, CODEN = {JMBLAJ}, MRCLASS = {92C15}, MRNUMBER = {MR1366356 (96j:92008)}, DOI = {10.1007/BF00178771}, URL = {http://dx.doi.org/10.1007/BF00178771}, } @article {MR2145787, AUTHOR = {Ruuth, Steven J. and Hundsdorfer, Willem}, TITLE = {High-order linear multistep methods with general monotonicity and boundedness properties}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {209}, YEAR = {2005}, NUMBER = {1}, PAGES = {226--248}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65L06 (76M20)}, MRNUMBER = {2145787 (2005m:65143)}, DOI = {10.1016/j.jcp.2005.02.029}, URL = {http://dx.doi.org/10.1016/j.jcp.2005.02.029}, } @ARTICLE{RyYa01, AUTHOR = {Ryu, S.-U. and Yagi, A.}, TITLE = {Optimal control of {K}eller-{S}egel equations}, YEAR = {2001}, JOURNAL = {JMAA}, VOLUME = {256}, NUMBER = {}, PAGES = {45-66} } @ARTICLE{SV94, AUTHOR = {Saddoughi, S.G. and Veeravalli, S.V.}, TITLE = {Local isotropy in turbulent boundary layers at high {R}eynolds number}, YEAR = {1994}, JOURNAL = {Fluid Mech.}, VOLUME = {268}, NUMBER = {}, PAGES = {333-372} } @article{Saffman71, author = {Saffman, Philip Geoffrey}, title = {On the Boundary Condition at the Surface of a Porous Medium}, journal = {Studies in Applied Mathematics}, year = {1971}, volume = {50}, number = {2}, pages = {93-101}, doi = {10.1002/sapm197150293}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sapm197150293}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sapm197150293}, abstract = {A theoretical justification is given for an empirical boundary condition proposed by Beavers and Joseph [1]. 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Publ., Hackensack, NJ}, YEAR = {2010}, MRCLASS = {76F65 (76M25)}, MRNUMBER = {2765985}, } @book {MR2541719, AUTHOR = {Sagaut, Pierre and Cambon, Claude}, TITLE = {Homogeneous turbulence dynamics}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2008}, PAGES = {xvi+463}, ISBN = {978-0-521-85548-8}, MRCLASS = {76-02 (76Fxx)}, MRNUMBER = {2541719 (2010g:76002)}, MRREVIEWER = {Anatoliy Prykarpatsky}, DOI = {10.1017/CBO9780511546099}, URL = {http://dx.doi.org/10.1017/CBO9780511546099}, } @incollection {MR2759433, AUTHOR = {Sagaut, P. and Meyers, J. and Lucor, D.}, TITLE = {Uncertainty modeling, error charts and improvement of subgrid models}, BOOKTITLE = {Advances in hybrid {RANS}-{LES} modelling}, SERIES = {Notes Numer. Fluid Mech. Multidiscip. Des.}, VOLUME = {97}, PAGES = {37--44}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2008}, MRCLASS = {76M25 (76F65)}, MRNUMBER = {2759433}, } @article{S13, author={S. 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An International Journal}, VOLUME = {25}, YEAR = {1996}, NUMBER = {7}, PAGES = {647--665}, ISSN = {0045-7930}, CODEN = {CPFLB1}, MRCLASS = {65N06 (76D05 76M20)}, MRNUMBER = {1416431 (97i:65156)}, DOI = {10.1016/0045-7930(96)00015-1}, URL = {http://dx.doi.org/10.1016/0045-7930(96)00015-1}, } @article{8bb544d8bed34aeb8f62e4d06527ccb5, title = "Computational Methods for Parachute Fluid-Structure Interactions", abstract = "The computational challenges posed by fluid-structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of {"}ringsail{"} parachutes the geometric complexities created by the construction of the canopy from {"}rings{"} and {"}sails{"} with hundreds of ring {"}gaps{"} and sail {"}slits{"}, and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has successfully addressed these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the T*AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T*AFSM, which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the T*AFSM. The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the T*AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T*AFSM. We provide an overview of the core and special techniques developed by the T*AFSM, present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters.", author = "Kenji Takizawa and Tezduyar, {Tayfun E.}", year = "2012", month = "3", doi = "10.1007/s11831-012-9070-4", language = "English", volume = "19", pages = "125--169", journal = "Archives of Computational Methods in Engineering", issn = "1134-3060", publisher = "Springer Netherlands", number = "1", } @article {MR3532381, AUTHOR = {Takhirov, Aziz}, TITLE = {Voigt regularization for the explicit time stepping of the {H}all effect term}, JOURNAL = {Geophys. Astrophys. 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Velte}, } @BOOK{Tema79, AUTHOR = {Temam, Roger}, TITLE = {{N}avier-{S}tokes {E}quations. {T}heory and {N}umerical {A}nalysis}, PUBLISHER = {North-Holland}, YEAR = {1979}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {Amsterdam} } @book {MR1846644, AUTHOR = {Temam, Roger}, TITLE = {Navier-{S}tokes equations}, NOTE = {Theory and numerical analysis, Reprint of the 1984 edition}, PUBLISHER = {AMS Chelsea Publishing, Providence, RI}, YEAR = {2001}, PAGES = {xiv+408}, ISBN = {0-8218-2737-5}, MRCLASS = {76-02 (35Q30 65Mxx 65Nxx 76D03 76D05 76N10)}, MRNUMBER = {1846644 (2002j:76001)}, MRREVIEWER = {Tom{\'a}s Chac{\'o}n Rebollo}, } MR1441312 @book {Tema97, AUTHOR = {Temam, R.}, TITLE = {Infinite-dimensional dynamical systems in mechanics and physics}, SERIES = {Applied Mathematical Sciences}, VOLUME = {68}, EDITION = {Second}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1997}, PAGES = {xxii+648}, ISBN = {0-387-94866-X}, MRCLASS = {58Fxx (34G20 35K55 35Q30 47H20 58D25 76D05)}, MRNUMBER = {MR1441312 (98b:58056)}, MRREVIEWER = {Bruno Scheurer}, } @BOOK{Tema95, AUTHOR = {Temam, R.}, TITLE = {{N}avier-{S}tokes Equations and Nonlinear Functional Analysis}, PUBLISHER = {Society for Industrial and Applied Mathematics}, YEAR = {1995}, SERIES = {CBMS-NSF Regional Conference Series in Applied Mathematics}, VOLUME = {}, EDITION = {}, ADDRESS = {Philadelphia} } @INCOLLECTION{Tema76PER, AUTHOR = {Temam, R.}, TITLE = {Une propriet\'{e} g\'{e}n\'{e}rique des solutions stationnaries ou p\'{e}riodiques des \8Equations de {Navier\D0 Stokes}}, BOOKTITLE = {Functional Analysis and Numerical Analysis, Symposium Franco\D0Japonais, Septembre, 1976}, PUBLISHER = {Japan Society for the Promotion of Science}, YEAR = {1978}, EDITOR = {}, SERIES = {}, VOLUME = {}, EDITION = {}, PAGES = {}, ADDRESS = {} } @ARTICLE{TS06, AUTHOR = {Templeton, J.A. and Shoeybi, M.}, TITLE = {Towards wall-normal filtering for large eddy simulation}, YEAR = {2006}, JOURNAL = {Multiscale Modeling and Simulation}, VOLUME = {5}, NUMBER = {}, PAGES = {420-444} } @ARTICLE{TMW05, AUTHOR = {Templeton, J.A. and Wang, M. and Moin, P.}, TITLE = {An efficient wall model for large eddy simulation based on optimal control}, YEAR = {2005}, JOURNAL = {Phys. Fluids}, VOLUME = {18}, NUMBER = {}, PAGES = {025101-025113} } @book{Thiriet2012, author = {Marc, Thiriet}, year = {2012}, month = {01}, pages = {}, title = {Control of Cell Fate in the Circulatory and Ventilatory Systems}, doi = {10.1007/978-1-4614-0329-6} } @INCOLLECTION{Thom75, AUTHOR = {Thomas, D.}, TITLE = {Artificial enzyme membranes, transport, memory and oscillatory phenomena}, BOOKTITLE = {Analysis and control of immobilized enzyme systems}, PUBLISHER = {Springer}, YEAR = {1975}, EDITOR = {D. Thomas and J. P. Kernevez}, SERIES = {}, VOLUME = {}, EDITION = {}, PAGES = {115-150}, ADDRESS = {Berlin} } @article {MR2231953, AUTHOR = {Thomas, S. J. and Loft, R. D.}, TITLE = {The {NCAR} spectral element climate dynamical core: semi-implicit {E}ulerian formulation}, JOURNAL = {J. Sci. 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H. Winston \& Sons}, ADDRESS = {Washington, D.C.: John Wiley \& Sons, New York}, YEAR = {1977}, PAGES = {xiii+258}, MRCLASS = {65J05 (65R05 65NXX)}, MRNUMBER = {MR0455365 (56 \#13604)}, MRREVIEWER = {M. Z. Nashed}, } @ARTICLE{TLMM03, AUTHOR = {Tikhonova, I.A. and Li, B.L. and Malchow, H. and Medvinsky, A.B.}, TITLE = {The impact of the phytoplankton growth rate on spatial and temporal dynamics of plankton communities in a heterogeneous environment}, YEAR = {2003}, JOURNAL = {Biofizika}, VOLUME = {48}, NUMBER = {5}, PAGES = {891-899} } @ARTICLE{TMKPPP03, AUTHOR = {T{\'a}trai, I. and M{\'a}ty{\'a}s, K. and Korponai, J. and Paulovits, G. and Pomogyi, P. and Pek{\'a}r, F.}, TITLE = {Management of fish communities and its impacts on the lower trophic levels in shallow ecosystems in {H}ungary}, YEAR = {2003}, JOURNAL = {Hydrobiologia}, VOLUME = {506-509}, NUMBER = {}, PAGES = {489-496} } @phdthesis{todor_thesis_05, Author = {R.A. Todor}, Date-Added = {2006-05-29 05:37:37 -0400}, Date-Modified = {2006-05-29 05:39:17 -0400}, School = {Swiss Federal Institute of Technology Zurich}, Title = {Sparse Perturbation Algorithms for Elliptic {PDE}'s with Stochastic Data}, Year = {2005}} @BOOK{To71, AUTHOR = {Tokaty, G.A.}, TITLE = {A history and philosophy of fluid mechanics}, PUBLISHER = {Dover}, YEAR = {1971}, SERIES = {}, VOLUME = {}, EDITION = {}, ADDRESS = {} } @article{TothKalnay1997, Abstract = {Abstract The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first-guess forecasts, is ?scaled down? at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred vectors from independent breeding cycles. Experimental runs with a 10-member ensemble (five independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium-range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04?0.11 in pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool. The two methods used so far to produce operational ensemble forecasts?that is, breeding and the adjoint (or ?optimal perturbations?) technique applied at the European Centre for Medium-Range Weather Forecasts?have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.}, Annote = {doi: 10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2}, Annote1 = {Abstract The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first-guess forecasts, is ?scaled down? at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred vectors from independent breeding cycles. Experimental runs with a 10-member ensemble (five independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium-range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04?0.11 in pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool. The two methods used so far to produce operational ensemble forecasts?that is, breeding and the adjoint (or ?optimal perturbations?) technique applied at the European Centre for Medium-Range Weather Forecasts?have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.}, Author = {Toth, Zoltan and Kalnay, Eugenia}, Booktitle = {Monthly Weather Review}, Da = {1997/12/01}, Date = {1997/12/01}, Date-Added = {2014-12-16 16:43:22 +0000}, Date-Modified = {2014-12-16 16:43:22 +0000}, Doi = {10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2}, Isbn = {0027-0644}, Journal = {Monthly Weather Review}, Journal1 = {Mon. Wea. Rev.}, M3 = {doi: 10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2}, Month = {2014/12/16}, Number = {12}, Pages = {3297--3319}, Publisher = {American Meteorological Society}, Title = {Ensemble Forecasting at {NCEP} and the Breeding Method}, Ty = {JOUR}, Url = {http://dx.doi.org/10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2}, Volume = {125}, Year = {1997}, Year1 = {1997}, Bdsk-Url-1 = {http://dx.doi.org/10.1175/1520-0493(1997)125%3C3297:EFANAT%3E2.0.CO;2}} @techreport{TranTren10, Author = {Tran, H. and Trenchea, C.}, Institution = {University of Pittsburgh}, Title = {Parameter identification for {Brinkman} equation}, Year = {in preparation}} @ARTICLE{TranTren09, AUTHOR = {Tran, H. and Trenchea, C.}, TITLE = {Stochastic collocation method for the {Oseen} equations with random viscosity}, YEAR = {2010}, JOURNAL = {in preparation}, VOLUME = {}, NUMBER = {}, PAGES = {} } @techreport{TranTrenWeb2014, Author = {Tran, Hoang A. and Trenchea, Catalin and Webster, Clayton G.}, Institution = {Oak Ridge National Laboratories}, Title = {A convergence analysis of stochastic collocation method for {N}avier-{S}tokes equations with random input data}, Year = {2014}} @techreport{2019-midpoint, author = "Burkardt, John and Trenchea, Catalin", Institution = {University of Pittsburgh}, title = "Variable-step Unconditionally Stable Second-Order Approximations", year = "2019", month = "", note = "", } @techreport{2019-midpointMHD, author = {Trenchea, Catalin}, Institution = {University of Pittsburgh}, title = {Unconditionally stable partitioned second-order variable step method for magnetohydrodynamics in {E}ls\"asser variables}, year = "2019", month = "", note = "", } @article {MR1992405, AUTHOR = {Trenchea, Catalin}, TITLE = {Periodic optimal control of the {B}oussinesq equation}, JOURNAL = {Nonlinear Anal.}, FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods}, VOLUME = {53}, YEAR = {2003}, NUMBER = {1}, PAGES = {81--96}, ISSN = {0362-546X}, CODEN = {NOANDD}, MRCLASS = {49K20 (35Q35 76D55)}, MRNUMBER = {MR1992405 (2004j:49041)}, MRREVIEWER = {Carlos Castro Barbero}, } @article {MR1954908, AUTHOR = {Trenchea, Catalin}, TITLE = {Internal optimal control of the periodic {E}uler-{B}ernoulli equation}, JOURNAL = {Commun. Appl. Anal.}, FJOURNAL = {Communications in Applied Analysis. An International Journal for Theory and Applications}, VOLUME = {7}, YEAR = {2003}, NUMBER = {1}, PAGES = {115--125}, ISSN = {1083-2564}, MRCLASS = {49J20 (35B10 35G05)}, MRNUMBER = {MR1954908 (2003j:49011)}, MRREVIEWER = {Alexander V. Arguchintsev}, } @article {MR2150330, AUTHOR = {Trenchea, Catalin}, TITLE = {Optimal control of an elliptic equation under periodic conditions}, JOURNAL = {Mem. Sec\c{t}. \c{S}tiin\c{t}. Acad. Rom\mbox{\^{a}n{\u{a} Ser. IV}}}, FJOURNAL = {Academia Rom\^{a}n\u{a}. Memoriile Sec\c{t}iilor \c{S}tiin\c{t}ifice. Seria IV}, VOLUME = {25}, YEAR = {2002}, PAGES = {23--35 (2005)}, ISSN = {1224-1407}, MRCLASS = {49K20 (49J20)}, MRNUMBER = {MR2150330 (2006f:49036)}, MRREVIEWER = {Monica Motta}, } @article {MR1839799, AUTHOR = {Moro\c{s}anu, C. and Trenchea, C.}, TITLE = {Identification for a nonlinear periodic wave equation}, JOURNAL = {Appl. Math. Optim.}, FJOURNAL = {Applied Mathematics and Optimization. An International Journal with Applications to Stochastics}, VOLUME = {44}, YEAR = {2001}, NUMBER = {2}, PAGES = {87--104}, ISSN = {0095-4616}, CODEN = {AMOMBN}, MRCLASS = {35R30 (35B10 35L70 65M32 93B30 93C20)}, MRNUMBER = {MR1839799 (2002e:35241)}, MRREVIEWER = {Valeri G. Yakhno}, } @article {MR1684678, AUTHOR = {Trenchea, Catalin}, TITLE = {Optimal control of the periodic string equation with internal control}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {101}, YEAR = {1999}, NUMBER = {2}, PAGES = {429--447}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {49J20 (49K20)}, MRNUMBER = {MR1684678 (2000b:49009)}, MRREVIEWER = {Vilmos Komornik}, } @article {TrWe_07b, AUTHOR = {Trenchea, C. and Webster, C.G.}, TITLE = {On the regularity of the stochastic Navier-Stokes equations}, JOURNAL = {In progress}, VOLUME = {}, YEAR = {2007}, NUMBER = {}, PAGES = {429--447}, } @techreport{Tren2011, Author = {Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Theta method: {Crank-Nicolson Leap Frog, BDF2} Linear Extrapolation}, Year = {2012}} @ARTICLE{Tren12IMEXmhd, AUTHOR = {Trenchea, Catalin}, TITLE = {Unconditional stability of a partitioned {IMEX} method for magnetohydrodynamic flows}, JOURNAL = {Appl. Math. Lett.}, FJOURNAL = {Applied Mathematics Letters. An International Journal of Rapid Publication}, VOLUME = {27}, YEAR = {2014}, PAGES = {97--100}, ISSN = {0893-9659}, MRCLASS = {65M06 (65M12 76W05)}, MRNUMBER = {3111615}, DOI = {10.1016/j.aml.2013.06.017}, URL = {http://dx.doi.org/10.1016/j.aml.2013.06.017}, } MR3337109 @article {Tren12IMEXskew, AUTHOR = {Trenchea, Catalin}, TITLE = {Stability of partitioned {IMEX} methods for systems of evolution equations with skew-symmetric coupling}, JOURNAL = {ROMAI J.}, FJOURNAL = {ROMAI Journal}, VOLUME = {10}, YEAR = {2014}, NUMBER = {2}, PAGES = {175--189}, ISSN = {1841-5512}, MRCLASS = {65J08}, MRNUMBER = {3337109}, } @ARTICLE{Tren12IMEXenhancedstab, AUTHOR = {Trenchea, Catalin}, TITLE = {Second order implicit for local effects and explicit for nonlocal effects is unconditionally stable}, JOURNAL = {submitted}, YEAR = {2013}, VOLUME = {}, NUMBER = {}, PAGES = {\empty} } Tren12IMEXenhancedstab @article {MR3601311, AUTHOR = {Trenchea, Catalin}, TITLE = {Second-order unconditionally stable {I}m{E}x schemes: implicit for local effects and explicit for nonlocal effects}, JOURNAL = {ROMAI J.}, FJOURNAL = {ROMAI Journal}, VOLUME = {12}, YEAR = {2016}, NUMBER = {1}, PAGES = {163--178}, ISSN = {1841-5512}, MRCLASS = {65L06 (65L20 65M20)}, MRNUMBER = {3601311}, MRREVIEWER = {Benjamin Wi-Lian Ong}, } @techreport{Tren12IMEXenhancedstab-TR, Author = {Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Second order implicit for local effects and explicit for nonlocal effects is unconditionally stable}, Year = {2012}, URL = {http://www.mathematics.pitt.edu/research/technical-reports}} @techreport{trenchea-midpoint, Author = {Trenchea, Catalin}, Institution = {University of Pittsburgh}, Title = {Midpoint rule}, Year = {2019}, URL = {http://www.mathematics.pitt.edu/research/technical-reports}} @INCOLLECTION{Tsin90, AUTHOR = {Tsinober, A.}, TITLE = {{MHD} flow drag reduction}, BOOKTITLE = {Viscous Drag Reduction in Boundary Layers}, PUBLISHER = {American Institute of Astronautics and Aeronautics}, YEAR = {1990}, EDITOR = {Busnell, D.M. and Hefner, J.N.}, SERIES = {Progress in Astronautics and Aeronautics}, VOLUME = {123}, EDITION = {}, PAGES = {327-349}, ADDRESS = {Reston, VA} } @ARTICLE{TS67, AUTHOR = {Tsinober, A. 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Space Sci.", volume="277", number="1-2", pages="219-224", year="2001", doi={10.1023/A:1012240621065}, abstract="{Summary: A short review is presented of the dissipative and radiative MHD, electromagnetic and plasma kinetic scaling approaches which are useful for sorting out different physical processes according to their relative importance. The `velocity-emission' ratio $Ve$, the Faraday number $F$ and `Trieste numbers' $T$ are described together with more familiar dimensionless parameters. 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Translation.}, year = 1983, volume = 3, editor = {{Zeldovich}, I.~B. and {Ruzmaikin}, A.~A. and {Sokolov}, D.~D. }, adsurl = {http://adsabs.harvard.edu/abs/1983flma....3.....Z}, adsnote = {Provided by the SAO/NASA Astrophysics Data System} } @article{ZhaiChen2003, author = {Zhai, Z. and Chen, Q.}, year = {2003}, month = {01}, pages = {1467-1474}, title = {Impact of determination of convective heat transfer coefficient on the coupled energy and CFD simulation for buildings}, volume = {3}, journal = {Proc. Build. Simul. 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Low frequency magnetic turbulence in the solar wind is relatively well characterized and understood. The situation is more complicated for magnetic turbulence in and around the Earth's magnetosphere, where the turbulence feature can vary widely with the location. Recent spacecraft observations of magnetic turbulence in the magnetosheath, in the polar cusp regions and in the magnetotail are considered. Turbulence features like the fluctuation level, the spectral power law index, the turbulence drivers and the turbulence anisotropy and intermittency are addressed. The influence of such a turbulence on the plasma transport and dynamics is briefly described, also using the results of numerical simulations.} } @ARTICLE{Zuaz93, AUTHOR = {Zuazua, E.}, TITLE = {Exact controllability for semilinear wave equations in one space dimension}, YEAR = {1993}, JOURNAL = {Ann. Inst. H. Poincar\'{e} Anal. 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