navier_stokes_3d_exact, a MATLAB 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.
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.
For the Poiseuille flow, a typical region is the infinite cylinder along the x axis, with radius 1, for which the velocity is zero on the boundary.
The computer code and data files made available on this web page are distributed under the MIT 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 MATLAB code which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.
navier_stokes_mesh3d, MATLAB data files defining meshes for several 3D test problems involving the Navier Stokes equations for flow flow, provided by Leo Rebholz.