STOKES_2D_EXACT\
Exact solutions to the\
2D Incompressible Steady Stokes Equations {#stokes_2d_exact-exact-solutions-to-the-2d-incompressible-steady-stokes-equations align=”center”}
=========================================
STOKES_2D_EXACT, a C++ 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: {#licensing align=”center”}
The computer code and data files made available on this web page are
distributed under the GNU LGPL license.
Languages: {#languages align=”center”}
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.
NAVIER_STOKES_2D_EXACT,
a C++ library which evaluates an exact solution to the incompressible
time-dependent Navier-Stokes 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 C++
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: {#reference align=”center”}
- Junping Wang, Yanqiu Wang, Xiu Ye,\
A robust numerical method for Stokes equations based on
divergence-free H(div) finite element methods,\
SIAM Journal on Scientific Computing,\
Volume 31, Number 4, 2009, pages 2784-2802.
- Howard Elman, Alison Ramage, David Silvester,\
Finite Elements and Fast Iterative Solvers with Applications in
Incompressible Fluid Dynamics,\
Oxford, 2005,\
ISBN: 978-0198528678,\
LC: QA911.E39.
Source Code: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
Graphics files:
List of Routines: {#list-of-routines align=”center”}
- GRID_2D returns a regular 2D grid.
- R8VEC_AMAX returns the maximum absolute value in an R8VEC.
- R8VEC_AMIN returns the minimum absolute value in an R8VEC.
- R8VEC_MAX returns the value of the maximum element in a R8VEC.
- R8VEC_MIN returns the value of the minimum element in a R8VEC.
- R8VEC_NORM_L2 returns the L2 norm of an R8VEC.
- R8VEC_UNIFORM_AB_NEW returns a scaled pseudorandom R8VEC.
- RESID_STOKES1 returns residuals of the exact Stokes solution
#1.
- RESID_STOKES2 returns residuals of the exact Stokes solution
#2.
- RESID_STOKES3 returns residuals of the exact Stokes solution
#3.
- RHS_STOKES1 returns the right hand sides of the exact Stokes
solution #1.
- RHS_STOKES2 returns the right hand sides of the exact Stokes
solution #2.
- RHS_STOKES3 returns the right hand sides of the exact Stokes
solution #3.
- STOKES_GNUPLOT writes the Stokes velocity field to files for
GNUPLOT.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
- UVP_STOKES1 evaluates the exact Stokes solution #1.
- UVP_STOKES2 evaluates the exact Stokes solution #2.
- UVP_STOKES3 evaluates the exact Stokes solution #3.
You can go up one level to the C++ source codes.
Last revised on 11 February 2015.