NAVIER_STOKES_2D_EXACT
Exact solutions to the
2D Incompressible TimeDependent Navier Stokes Equations
NAVIER_STOKES_2D_EXACT,
a MATLAB library which
evaluates exact solutions to the incompressible timedependent
NavierStokes equations over an arbitrary domain in 2D.

Lukas: steady flow, pressure is zero everywhere;

Poiseuille: steady flow, vertical velocity and right hand side are zero everywhere;

Spiral: velocity is zero on the boundary of the unit square;

Taylor: source term is zero everywhere.

Vortex: a steady flow with the 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
a Python version.
Related Data and Programs:
navier_stokes_2d_exact_test
NAVIER_STOKES_3D_EXACT,
a MATLAB library which
evaluates exact solutions to the incompressible timedependent
NavierStokes equations over an arbitrary domain in 3D.
NAVIER_STOKES_MESH2D,
MATLAB data files defining meshes for several
2D test problems involving the Navier Stokes equations
for fluid flow, provided by Leo Rebholz.
SPIRAL_DATA,
a MATLAB 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 MATLAB library which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
Reference:

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, 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 499521.
Source Code:

grid_2d.m,
returns a regular 2D grid.

ns2de_gnuplot.m,
writes the velocity vector field to files for GNUPLOT.

r8vec_uniform_ab.m,
returns a scaled pseudorandom R8VEC.

resid_lukas.m,
evaluates the Lukas Bystricky residuals.

resid_poiseuille.m,
evaluates the Poiseuille residuals.

resid_spiral.m,
evaluates the Spiral residuals.

resid_taylor.m,
evaluates the Taylor residuals.

resid_vortex.m,
evaluates the Vortex residuals.

rhs_lukas.m,
evaluates the Lukas Bystricky right hand sides.

rhs_poiseuille.m,
evaluates the Poiseuille right hand sides.

rhs_spiral.m,
evaluates the Spiral right hand sides.

rhs_taylor.m,
evaluates the Taylor right hand sides.

rhs_vortex.m,
evaluates the Vortex right hand sides.

timestamp.m
prints the YMDHMS date as a timestamp.

uvp_lukas.m,
evaluates the Lukas Bystricky flow field.

uvp_poiseuille.m,
evaluates the Poiseuille flow field.

uvp_spiral.m,
evaluates the Spiral flow field.

uvp_taylor.m,
evaluates the Taylor flow field.

uvp_vortex.m,
evaluates the Vortex flow field.
Last revised on 17 February 2019.