BURGERS_SOLUTION\
Exact Solutions of Time Dependent 1D Viscous Burgers Equation {#burgers_solution-exact-solutions-of-time-dependent-1d-viscous-burgers-equation align=”center”}
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BURGERS_SOLUTION is a C++ 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
for -1.0 < x < +1.0, and 0.0 < t.
Licensing: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
BURGERS_SOLUTION 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.
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 C++ 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 C++ 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: {#reference align=”center”}
- 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: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
- burgers_solution_prb.cpp, a sample
calling program.
- burgers_solution_prb_output.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.
List of Routines: {#list-of-routines align=”center”}
- BURGERS_VISCOUS_TIME_EXACT1 evaluates solution #1 to the
Burgers equation.
- BURGERS_VISCOUS_TIME_EXACT1 evaluates solution #2 to the
Burgers equation.
- HERMITE_EK_COMPUTE computes a Gauss-Hermite quadrature rule.
- IMTQLX diagonalizes a symmetric tridiagonal matrix.
- R8_ABS returns the absolute value of an R8.
- R8_EPSILON returns the R8 roundoff unit.
- R8_MAX returns the maximum of two R8’s.
- R8_MIN returns the minimum of two R8’s.
- R8_SIGN returns the sign of an R8.
- R8MAT_PRINT prints an R8MAT.
- R8MAT_PRINT_SOME prints some of an R8MAT.
- R8MAT_WRITE writes an R8MAT file.
- R8VEC_EVEN_NEW returns an R8VEC of values evenly spaced
between ALO and AHI.
- R8VEC_PRINT prints an R8VEC.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the C++ source codes.
Last revised on 26 September 2015.