Preprint 1997-018

Composite Schemes for Conservation Laws

R. Liska and B. Wendroff

Abstract: Global composition of several time steps of the two-step Lax-Wendroff scheme followed by a Lax-Friedrichs step seems to enhance the best features of both, although only first order accurate. We show this by means of some examples of one-dimensional shallow water flow over an obstacle. In two dimensions we present a new version of Lax-Friedrichs and an associated second order predictor-corrector method. Composition of these schemes is shown to be effective and efficient for some two-dimensional Riemann problems and for Noh's infinite strength cylindrical shock problem. We also show comparable results for composition of the predictor-corrector scheme with a modified second order accurate WENO scheme. That composition is second order but is more efficient and has better symmetry properties than WENO alone. For scalar advection in two dimensions the optimal stability of the new predictor-corrector scheme is shown using computer algebra. We also show that the generalization of this scheme to three dimensions is unstable, but using sampling we are able to show that the composites are sub-optimally stable.

Available as PostScript (1.2 Mbytes) or as gzipped PostScript (296 Kbytes; uncompress using gunzip).
Composite Schemes for Conservation Laws
R. Liska , <>
B. Wendroff , <>
Publishing information:
Los Alamos National Laboratory Report LA-UR 96-3589. To appear in SIAM J. Numer. Anal.
This was written in 1996, revised in 1997 following referees comments.
Submitted by:
<> July 11 1997.

[ 1996 Preprints | 1997 Preprints | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Fri Jul 11 09:35:50 1997