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

NAVIER_STOKES_3D_EXACT, a Python library which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.

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.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

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 Python 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 defining meshes for several 3D test problems involving the Navier Stokes equations for fluid flow, provided by Leo Rebholz.

Reference:

1. 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:

• r8vec_amax.py, returns the maximum absolute value entry in an R8VEC.
• r8vec_amin.py, returns the minimum absolute value entry in an R8VEC.
• r8vec_max.py, returns the maximum entry in an R8VEC.
• r8vec_min.py, returns the minimum entry in an R8VEC.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_ab.py, returns a scaled pseudorandom R8VEC.
• resid_ethier.py, evaluates the residual at any point (x,y,z) and time t.
• timestamp.py prints the YMDHMS date as a timestamp.
• uvwp_ethier.py, evaluates the velocity and pressure field at any point (x,y,z) and time t.

Examples and Tests:

• ns3de_test.py, calls all the tests.
• ns3de_test.sh, runs all the tests.
• ns3de_test_output.txt, the output file.

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