Preprint 1998-018

Unconditionally Stable Splitting Methods for the Shallow Water Equations

Abstract: The front tracking method for hyperbolic conservation laws is combined with operator splitting in order to study the shallow water equations. Furthermore, the method includes adaptive grid refinement. The front tracking method is unconditionally stable, but for practical computations feasible CFL numbers are moderately above unity (typically between 1 and 5). The method resolves shocks sharply and is highly efficient.

The numerical technique is applied to four test cases, the first being an expanding bore with rotational symmetry. The second problem addresses the question of describing the time-development of two constant water levels separated by a dam that breaks instantaneously. The third problem compares the front tracking method with an explicit analytic solution of water waves rotating over a parabolic bottom profile. Finally, we study flow over an obstacle in one-dimension.

Paper:

Available as PostScript (4.2 Mbytes) or gzipped PostScript (768 Kbytes; uncompress using gunzip).

Title:

Unconditionally stable splitting methods for the shallow water equations

Author(s):

Runar Holdahl

Helge Holden, <holden@math.ntnu.no>

Knut-Andreas Lie, <andreas@math.ntnu.no>

Publishing information:

Comments:

A MPEG movie of the dambreak problem is available on the web.

Submitted by:

<andreas@math.ntnu.no> May 4 1998.