navier_stokes_2d_exact

navier_stokes_2d_exact, a FORTRAN77 code which evaluates exact solutions to the incompressible time-dependent Navier-Stokes Equations (NSE) over an arbitrary domain in 2D.

• Lukas: steady flow, pressure is zero everywhere;
• Spiral: velocity is zero on the boundary of the unit square;
• Taylor: source term is zero everywhere.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

navier_stokes_2d_exact is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

navier_stokes_2d_exact_test

navier_stokes_3d_exact, a FORTRAN77 library 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 FORTRAN77 library 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 FORTRAN77 library which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.

Reference:

1. 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.
2. Geoffrey Taylor,
   On the decay of vortices in a viscous fluid,
   Philosophical Magazine,
   Volume 46, 1923, pages 671-674.
3. Geoffrey Taylor, A E 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.f, the source code.
• navier_stokes_2d_exact.sh, BASH commands to compile the source code.