The random projection method for hyperbolic conservation laws with stiff reaction terms

We propose a random projection method for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows: U-t + F(U)(x) + G(U)(y) = 1/epsilon 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 detonation waves in both one and two space dimensions. (C) 2000 Academic Press.