NAVIER_STOKES_3D_EXACT Exact solutions to the 3D Incompressible Time-Dependent Navier Stokes Equations

NAVIER_STOKES_3D_EXACT, a FORTRAN77 library 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.

Languages:

NAVIER_STOKES_3D_EXACT is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

NAVIER_STOKES_2D_EXACT, a FORTRAN77 library which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.

NAVIER_STOKES_MESH3D, MATLAB data files which define meshes for several 3D test problems involving the Navier Stokes equations for flow flow, provided by Leo Rebholz.

Reference:

1. Martin Bazant, Henry Moffatt,
Exact solutions of the Navier-Stokes equations having steady vortex structures,
Journal of Fluid Mechanics,
Volume 541, pages 55-64, 2005.
2. Johannes Burgers,
A mathematical model illustrating the theory of turbulence,
Volume 1, pages 171-199, 1948.
3. C Ross Ethier, David Steinman,
Exact fully 3D Navier-Stokes solutions for benchmarking,
International Journal for Numerical Methods in Fluids,
Volume 19, Number 5, March 1994, pages 369-375.

Source Code:

• ns3de.f, the source code.
• ns3de.sh, BASH commands to compile the source code.

List of Routines:

• R8VEC_MAX returns the maximum value in an R8VEC.
• R8VEC_MIN returns the minimum value in an R8VEC.
• R8VEC_UNIFORM_AB returns a scaled pseudorandom R8VEC.
• RESID_ETHIER evaluates the residual of the Ethier exact Navier Stokes solution.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• UVWP_ETHIER evaluates the Ethier exact Navier Stokes solution.

You can go up one level to the FORTRAN77 source codes.

Last revised on 16 January 2015.