stokes_2d_exact

stokes_2d_exact, an Octave code which evaluates exact solutions (u,v,p)(x,y) to the incompressible steady Stokes equations in 2D, which are a system of partial differential equations (PDE) of the form: -uxx-uyy+px=f, -vxx-vyy+py=g, ux+vy=h.

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.