burgers_exact

burgers_exact, a Python code which evaluates an exact solution of the time-dependent 1D viscous Burgers equation.

The form of the Burgers equation considered here is:

        du       du        d^2 u
        -- + u * -- = nu * -----
        dt       dx        dx^2
      

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

burgers_exact is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

burgers, a dataset directory which contains 40 solutions of the Burgers equation in one space dimension and time at equally spaced times from 0 to 1, with values at 41 equally spaced nodes in [0,1];

python_exact, a Python code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

Reference:

1. Claude Basdevant, Michel Deville, Pierre Haldenwang, J Lacroix, J Ouazzani, Roger Peyret, Paolo Orlandi, Anthony Patera,
   Spectral and finite difference solutions of the Burgers equation,
   Computers and Fluids,
   Volume 14, Number 1, 1986, pages 23-41.

Source Code:

• burgers_exact.py, the source code.
• burgers_exact.sh, runs all the tests.
• burgers_exact.txt, the output file.

• burgers_exact_test01.txt, a data file of solution #1 values for -1 <= x <= +1, 0 <= t <= 3/pi, using 11 grid points in x and in t.
• burgers_exact_test02.txt, a data file of solution #1 values for -1 <= x <= +1, 0 <= t <= 3/pi, using 41 grid points in x and in t.
• burgers_exact_test03.txt, a data file of solution #2 values for 0 <= x <= 2 Pi, 0 <= t <= 1, using 11 grid points in x and in t.
• burgers_exact_test04.txt, a data file of solution #2 values for 0 <= x <= 2 Pi, 0 <= t <= 1, using 41 grid points in x and in t.