stokes_2d_exact, a Python 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 = hwhile 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.
The computer code and data files made available on this web page are distributed under the MIT license
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.
navier_stokes_2d_exact, a Python code 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 Python code which computes a velocity vector field that satisfies the continuity equation, writing the data to a file that can be plotted by gnuplot.
Graphics files for flow #1:
Graphics files for flow #2:
Graphics files for flow #3: