The random projection method for stiff detonation capturing

Abstract

In this paper we present a simple and robust random projection method for under-resolved numerical simulation of stiff detonation waves in chemically reacting flows. This method is based on the random projection method proposed by the authors for general hyperbolic systems with stiff reaction terms [W. Bao and S. Jin, J. Comput. Phys., 163 (2000), pp. 216-248], where the ignition temperature is randomized in a suitable domain. It is simplified using the equations of instantaneous reaction and then extended to handle the interactions of detonations. Extensive numerical experiments, including interaction of detonation waves, and in two dimensions, demonstrate the reliability and robustness of this novel method.