SHALLOW_WATER_1D
The Shallow Water Equations in 1D

SHALLOW_WATER_1D is a MATLAB program which simulates a system governed by the shallow water equations in 1D.

Licensing:

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

Languages:

SHALLOW_WATER_1D is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

SHALLOW_WATER_1D_DISPLAY, a MATLAB program which can display a solution of the shallow water equations in 1D, generally as computed by the program shallow_water_1d.

SHALLOW_WATER_2D, a MATLAB program which solves the 2D shallow water equations.

Reference:

Cleve Moler,
Experiments with MATLAB,
http://www.mathworks.com/moler/exm/index.html

Source Code:

make_animation.m, a script that calls shallow_water_1d to compute the data arrays, and then shallow_water_1d_animation to create a sequence of JPG image files.
shallow_water_1d.m, the source code.
shallow_water_1d_animation.m, a program to animate the solution by creating a series of JPEG files.

A simple dataset was created by the command

        [ h_array, uh_array, x, t ] = shallow_water_1d ( 41, 100, 1.0, 0.2, 9.8 )

This was then animated by the command

        shallow_water_1d_animation ( h_array, uh_array, x, t )

and the resulting JPG files were turned into QuickTime movies.

h_reflective.mov, a QuickTime movie of H for 101 steps.
uh_reflective.mov, a QuickTime movie of UH for 101 steps.

An internal switch was modified so that the code used periodic boundary conditions. In this case, we can expect momentum conservation. The dataset was created by the command

        [ h_array, uh_array, x, t ] = shallow_water_1d ( 41, 100, 1.0, 0.2, 9.8 )