navier_stokes_3d_exact, a Python code which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.
The given velocity and pressure fields are exact solutions for the 3D incompressible time-dependent Navier Stokes equations over any region.
To define a typical problem, one chooses a bounded spatial region and a starting time, and then imposes boundary and initial conditions by referencing the exact solution appropriately.
In the Ethier reference, a calculation is made for the cube centered at (0,0,0) with a "radius" of 1 unit, and over the time interval from t = 0 to t = 0.1, with parameters a = PI/4 and d = PI/2, and with Dirichlet boundary conditions on all faces of the cube.
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
navier_stokes_3d_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 exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.