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
      

Three exact solution fields are provided here.

Licensing:

The information on this web page is 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

octave_exact, an Octave code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

Reference:

1. 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.