Preprint 1999-041

The Random Projection Method for Hyperbolic Systems with Stiff Reaction Terms

Weizhu Bao and Shi Jin

Abstract: In this paper we propose the random projection method for numerical simulations of the hyperbolic conservation laws with stiff source terms arising from chemically reactive flows:
In this problem, the chemical time scales may be orders of magnitude faster than the fluid dynamical time scales, making the problem numerically stiff. A classic spurious numerical phenomenon, the incorrect propagation speeds of discontinuities, occurs in underresolved numerical solutions. We introduce a random projection method for the reaction term by replacing the ignition temperature with a uniformly distributed random variable. The statistical average of this method corrects the spurious shock speed, as will be proved with a scalar model problem and demonstrated by a wide range of numerical examples in inviscid denotation waves in both one and two space dimensions.

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Weizhu Bao
Shi Jin, <>
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<> December 6 1999.

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