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.
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.
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.
You can go up one level to the DATASETS directory.