The random projection method for a model problem of combustion with stiff chemical reactions

摘要

In this paper we extend the random projection method, recently proposed by the author and S. Jin [J. Comput. Phys. 163 (2000) 216] for under resolved numerical simulations of a qualitative model problem for combustion with stiff chemical reactions:ut+(f(u)−q0z)x=0,zx=1εφ(u)z.In this problem, the reaction time ε is small, making the problem numerically stiff. A classic spurious numerical phenomenon – the incorrect shock speed – occurs when the reaction time scale is not properly resolved numerically. The random projection method is introduced recently to handle this kind of numerical difficulty. The key idea in this method is to randomize the ignition temperature in a suitable domain. Several numerical experiments demonstrate the reliability and robustness of this method.