Weakly nonlinear asymptotic models and analogs of detonation processes

Abstract

Two simplified, qualitative models of combustion and detonation processes have been developed and studied in recent years. One is an analog, posed independently by Fickett and Majda, and one is an asymptotic model, derived by Rosales and Majda, that is valid near a Mach 1 regime where the reaction front is moving close to the sound speed in the material ahead and the particle velocity is small in comparison. In this paper, after reviewing the recent literature on these two models, we analyze the scalings required to obtain the asymptotic equations, thereby revealing the range of parameter values for which the asymptotic model is valid. Along with the analysis we give a simple one-dimensional derivation of the asymptotic equations, and it is indicated how the formulation of the model changes when the chemical kinetics is reversible.