Preprint 1998-018

An Unconditionally Stable Method for the Euler Equations

Helge Holden, Knut-Andreas Lie, and Nils Henrik Risebro

Abstract: We discuss how to combine a front tracking method with dimensional splitting to solve numerically systems of conservation laws in two space dimensions. In addition we present an adaptive grid refinement strategy. The method is unconditionally stable and allows for moderately high CFL numbers (typically 1--4), and thus it is highly efficient.

The method is applied to the Euler equations of gas dynamics. In particular, it is tested on an expanding circular gas front, a wind tunnel with a step, a double Mach reflection as well as a shock-bubble interaction. The method shows very sharp resolution of shocks.

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An unconditionally stable method for the Euler equations
Helge Holden, <>
Knut-Andreas Lie, <>
Nils Henrik Risebro, <>
Publishing information:
More numerical examples are available on the web.
Submitted by:
<> May 4 1998.

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Last modified: Mon May 4 11:01:39 1998