navier_stokes_2d_exact

navier_stokes_2d_exact, a C++ code which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.

• GMS: time dependent, vortices do not decay to zero;
• Lukas: steady, zero pressure;
• Poiseuille: steady, zero vertical velocity, zero source term;
• Spiral: time dependent, zero velocity on the unit square;
• Taylor: time dependent, zero source term, solution decays exponentially.
• 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 C++ code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.

SPIRAL_DATA, a C++ 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 C++ code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.

Reference:

1. 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.
2. 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.
3. Geoffrey Taylor,
   On the decay of vortices in a viscous fluid,
   Philosophical Magazine,
   Volume 46, 1923, pages 671-674.
4. 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:

• navier_stokes_2d_exact.cpp, the source code.
• navier_stokes_2d_exact.sh, compiles the source code.
• navier_stokes_2d_exact.hpp, the include file.