STOKES_2D_EXACT
Exact solutions to the
2D Incompressible Steady Stokes Equations
STOKES_2D_EXACT,
a Python library which
evaluates exact solutions to the incompressible steady
Stokes equations in 2D.
The incompressible steady 2D Stokes equations seek functions u(x,y),
v(x,y), (the velocity vector) and p(x,y) (the pressure) such that
 uxx  uyy + dpdx = f
 vxx  vyy + dpdy = g
ux + vy = h
while satisfying boundary conditions for u and v, and a normalization
condition for p, such as specifying its value at one point, or requiring
that the integral of p over the region be 0.
Three exact solution fields are provided here.
Licensing:
The computer code and data files made available on this web page
are distributed under
the GNU LGPL license.
Languages:
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,
a Python library which
evaluates an exact solution to the incompressible timedependent
NavierStokes equations over an arbitrary domain in 2D.
NAVIER_STOKES_MESH2D,
MATLAB data files which
define triangular meshes for several
2D test problems involving the Navier Stokes equations
for fluid flow, provided by Leo Rebholz.
SPIRAL_DATA,
a Python library which
computes a velocity vector field that satisfies the continuity
equation, writing the data to a file that can be plotted
by gnuplot.
Reference:

Junping Wang, Yanqiu Wang, Xiu Ye,
A robust numerical method for Stokes equations based on divergencefree
H(div) finite element methods,
SIAM Journal on Scientific Computing,
Volume 31, Number 4, 2009, pages 27842802.

Howard Elman, Alison Ramage, David Silvester,
Finite Elements and Fast Iterative Solvers with
Applications in Incompressible Fluid Dynamics,
Oxford, 2005,
ISBN: 9780198528678,
LC: QA911.E39.
Source Code:

grid_2d.py,
returns a regular 2D grid.

r8vec_amax.py,
returns the maximum absolute value entry in an R8VEC.

r8vec_amin.py,
returns the minimum absolute value entry in an R8VEC.

r8vec_max.py,
returns the maximum entry in an R8VEC.

r8vec_min.py,
returns the minimum entry in an R8VEC.

r8vec_norm_l2.py,
returns the L2 norm of an R8VEC.

r8vec_print.py,
prints an R8VEC.

r8vec_uniform_ab.py,
returns a scaled pseudorandom R8VEC.

resid_stokes1.py,
evaluates the residual at any point (x,y) for flow #1.

resid_stokes2.py,
evaluates the residual at any point (x,y) for flow #2.

resid_stokes3.py,
evaluates the residual at any point (x,y) for flow #3.

rhs_stokes1.py,
evaluates the residual at any point (x,y) for flow #1.

rhs_stokes2.py,
evaluates the residual at any point (x,y) for flow #2.

rhs_stokes3.py,
evaluates the residual at any point (x,y) for flow #3.

stokes_gnuplot.py,
writes files to create a GNUPLOT image of the flow.

stokes_matplotlib.py,
writes files to create a MATPLOTLIB image of the flow.

timestamp.py
prints the YMDHMS date as a timestamp.

uvp_stokes1.py,
evaluates the velocity and pressure field at any point (x,y) for flow #1.

uvp_stokes2.py,
evaluates the velocity and pressure field at any point (x,y) for flow #2.

uvp_stokes3.py,
evaluates the velocity and pressure field at any point (x,y) for flow #3.
Examples and Tests:
Graphics files for flow #1:
Graphics files for flow #2:
Graphics files for flow #3:
You can go up one level to
the MATLAB source codes.
Last revised on 12 February 2015.