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:Ut+F(U)x+G(U)y=1εΨ(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.