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:
U_t+F(U)_x+G(U)_y=\fl{1}{\vep}\Psi(U).
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.


Paper:
Available as PostScript (8.5 Mbytes) or gzipped PostScript (1.0 Mbytes; uncompress using gunzip).
Author(s):
Weizhu Bao
Shi Jin, <jin@math.gatech.edu>
Publishing information:
Comments:
Submitted by:
<jin@math.gatech.edu> December 6 1999.


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