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:

ut + u   ux = nu   uxx

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.

Related Data and Programs:

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.

Tar File:

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


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 interp
The 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.

You can go up one level to the DATASETS directory.

Last revised on 22 September 2006.