BURGERS_SOLUTION
Exact Solutions of Time Dependent 1D Viscous Burgers Equation

BURGERS_SOLUTION is a FORTRAN90 library which evaluates exact solutions 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];

FD1D_BURGERS_LAX, a FORTRAN90 program which applies the finite difference method and the Lax-Wendroff method to solve the non-viscous Burgers equation in one spatial dimension and time.

FD1D_BURGERS_LEAP, a FORTRAN90 program which applies the finite difference method and the leapfrog approach to solve the non-viscous Burgers equation in one spatial dimension and time.

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_solution.f90, the source code.

Examples and Tests:

• burgers_solution_test.f90, a sample calling program.
• burgers_solution_test.txt, the output file.
• burgers_solution_test01.txt, a data file of values for exact solution #1 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 values for exact solution #1 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 values for exact solution #2 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 values for exact solution #2 for 0 <= x <= 2 Pi, 0 <= t <= 1, using 41 grid points in x and in t.

List of Routines:

• BURGERS_VISCOUS_TIME_EXACT1 evaluates solution #1 to the Burgers equation.
• BURGERS_VISCOUS_TIME_EXACT2 evaluates solution #2 to the Burgers equation.
• GET_UNIT returns a free FORTRAN unit number.
• HERMITE_EK_COMPUTE computes a Gauss-Hermite quadrature rule.
• IMTQLX diagonalizes a symmetric tridiagonal matrix.
• R8_GAMMA evaluates Gamma(X) for a real argument.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8MAT_WRITE writes an R8MAT file.
• R8VEC_EVEN returns an R8VEC of evenly spaced values.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.