NAVIER_STOKES_2D_EXACT
Exact solutions to the
2D Incompressible TimeDependent Navier Stokes Equations
NAVIER_STOKES_2D_EXACT,
a C code which
evaluates exact solutions to the incompressible timedependent
NavierStokes equations 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 GNU LGPL 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 timedependent
NavierStokes 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:

JeanLuc Guermand, Peter Minev, Jie Shen,
An overview of projection methods for incompressible flows,
Computer methods in applied mechanics and engineering,
Volume 105, pages 60116045, 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 258274, 2011.

Geoffrey Taylor,
On the decay of vortices in a viscous fluid,
Philosophical Magazine,
Volume 46, 1923, pages 671674.

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 499521.
Source Code:
Last revised on 14 July 2019.