BURGERS_SOLUTION
Exact Solution of Time Dependent 1D Viscous Burgers Equation

BURGERS_SOLUTION is a Python library 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 computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BURGERS_SOLUTION is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB 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];

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_viscous_time_exact1.py, evaluates solution #1 to the Burgers equation.
• burgers_viscous_time_exact2.py, evaluates solution #2 to the Burgers equation.
• hermite_ek_compute.py, computes a Gauss-Hermite quadrature rule.
• imtqlx.py, diagonalizes a symmetric tridiagonal matrix.
• r8_epsilon.py, returns the machine epsilon value.
• r8_gamma.py, evaluates the gamma function.
• r8_sign.py, returns the sign of an R8.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_write.py, writes an R8MAT file.
• r8vec_print.py, prints an R8VEC.
• timestamp.py, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• burgers_solution_test.py, calls all the tests.
• burgers_solution_test.sh, runs all the tests.
• burgers_solution_test.txt, the output file.
• burgers_solution_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_solution_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_solution_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_solution_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.

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