40 Solutions of the Burgers Equation

**BURGERS**
is a dataset directory which
contains solutions to the time-dependent
Burgers equation in one dimension.

The Burgers equation has the form:

u_{t}+ u u_{x}= nu u_{xx}

The Burgers equations is sometimes called "the poor man's
Navier Stokes equation"; it can be regarded as a cousin of that
equation, which still includes nonlinearity controlled by the
magnitude of a viscosity parameter **nu**, and whose solution
exhibits wave-like behavior.

Each solution in this dataset contains data evaluated at 41 equally spaced nodes in the interval from 0.0 to 1.0; successive solutions represent snapshots of the data at 40 equally spaced times from 0 to 1.

The initial condition is a square wave which is equal to 1 from 0 to 1/2, and to 0 from 1/2 to 1. As time progresses, the wave travels and smooths out.

This data was computed, and graciously supplied, by Professor Hyung-Chun Lee of Ajou University, Korea.

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

BURGERS_SOLUTION, a FORTRAN90 library which evaluates an exact solution of the time-dependent 1D Burgers equation.

SVD_BASIS, a C++ program which applies the Singular Value Decomposition (SVD) to a collection of data vectors, extracting dominant modes;

SVD_BASIS_WEIGHT, a FORTRAN90 program which is similar to SVD_BASIS, but which allows the user to assign weights to each data vector.

A GZIP'ed TAR file of the contents of this directory is available.

- burgers.tar.sh the commands used to create the GZIP'ed TAR file.
- burgers.tar.gz the GZIP'ed TAR file.

The full data set is available in a single file of 41 rows
and 40 columns, which is awkward to read, but good for loading
into MATLAB with a single **load** statement:
burgers_full.txt.

MATLAB can be used to display the full data set using commands like

data = load ( 'burgers_full.txt' ); [ t, x ] = meshgrid ( 1:40, 1:41 ); surf ( t, x, data ); shading interpThe results of such a series of commands can be viewed in burgers_full.png, which is a PNG image.

The data is also available as one X coordinate file, and 40 "snapshots" of the solution at a sequence of times.

- burgers_x.txt, the spatial coordinates of the 41 nodes between 0.0 and 1.0.
- burgers_01.txt.
- burgers_02.txt.
- burgers_03.txt.
- burgers_04.txt.
- burgers_05.txt.
- burgers_06.txt.
- burgers_07.txt.
- burgers_08.txt.
- burgers_09.txt.
- burgers_10.txt.
- burgers_11.txt.
- burgers_12.txt.
- burgers_13.txt.
- burgers_14.txt.
- burgers_15.txt.
- burgers_16.txt.
- burgers_17.txt.
- burgers_18.txt.
- burgers_19.txt.
- burgers_20.txt.
- burgers_21.txt.
- burgers_22.txt.
- burgers_23.txt.
- burgers_24.txt.
- burgers_25.txt.
- burgers_26.txt.
- burgers_27.txt.
- burgers_28.txt.
- burgers_29.txt.
- burgers_30.txt.
- burgers_31.txt.
- burgers_32.txt.
- burgers_33.txt.
- burgers_34.txt.
- burgers_35.txt.
- burgers_36.txt.
- burgers_37.txt.
- burgers_38.txt.
- burgers_39.txt.
- burgers_40.txt.

You can go up one level to the DATASETS directory.