stokes_2d_exact

stokes_2d_exact, an Octave code 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 MIT license

Languages:

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:

stokes_2d_exact_test

navier_stokes_2d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2d.

spiral_data, an Octave code 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 divergence-free H(div) finite element methods,
SIAM Journal on Scientific Computing,
Volume 31, Number 4, 2009, pages 2784-2802.

Source Code:

grid_2d.m, returns a regular 2D grid.
r8vec_uniform_ab.m, returns a scaled pseudorandom R8VEC.
resid_stokes1.m, evaluates the residuals at any point (x,y) for flow #1.
resid_stokes2.m, evaluates the residuals at any point (x,y) for flow #2.
resid_stokes3.m, evaluates the residuals at any point (x,y) for flow #3.
rhs_stokes1.m, evaluates the riht hand side functions at any point (x,y) for flow #1.
rhs_stokes2.m, evaluates the riht hand side functions at any point (x,y) for flow #2.
rhs_stokes3.m, evaluates the riht hand side functions at any point (x,y) for flow #3.
stokes_gnuplot.m, writes the velocity vector field to files for GNUPLOT.
uvp_stokes1.m, evaluates the velocity and pressure field at any point (x,y) for flow #1.
uvp_stokes2.m, evaluates the velocity and pressure field at any point (x,y) for flow #2.
uvp_stokes3.m, evaluates the velocity and pressure field at any point (x,y) for flow #3.

Last revised on 04 November 2023.