navier_stokes_2d_exact
navier_stokes_2d_exact,
a FORTRAN90 code which
evaluates exact solutions to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
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GMS: time dependent, vortices do not decay to zero;
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Lukas: steady, zero pressure;
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Poiseuille: steady, zero vertical velocity, zero source term;
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Spiral: time dependent, zero velocity on the unit square;
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Taylor: time dependent, zero source term, solution decays exponentially.
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Vortex: steady, same velocity pattern as Taylor.
Licensing:
The computer code and data files made available on this web page
are distributed under
the MIT license
Languages:
navier_stokes_2d_exact is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
navier_stokes_2d_exact_test
NAVIER_STOKES_3D_EXACT,
a FORTRAN90 code which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
NAVIER_STOKES_MESH2D,
MATLAB data files which
define triangular meshes for several
2D test problems involving the Navier Stokes equations (NSE)
for fluid flow, provided by Leo Rebholz.
SPIRAL_DATA,
a FORTRAN90 code which
computes a velocity vector field that satisfies the continuity
equation, writing the data to a file that can be plotted
by gnuplot.
STOKES_2D_EXACT,
a FORTRAN90 code which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
Reference:
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Jean-Luc Guermand, Peter Minev, Jie Shen,
An overview of projection methods for incompressible flows,
Computer methods in applied mechanics and engineering,
Volume 105, pages 6011-6045, 2006.
-
Maxim Olshanskii, Leo Rebholz,
Application of barycenter refined meshes in linear elasticity
and incompressible fluid dynamics,
ETNA: Electronic Transactions in Numerical Analysis,
Volume 38, pages 258-274, 2011.
-
Geoffrey Taylor,
On the decay of vortices in a viscous fluid,
Philosophical Magazine,
Volume 46, 1923, pages 671-674.
-
Geoffrey Taylor, Albert Green,
Mechanism for the production of small eddies from large ones,
Proceedings of the Royal Society of London,
Series A, Volume 158, 1937, pages 499-521.
Source Code:
Last revised on 21 August 2020.