A short note on the counter-intuitive spurious behaviors in stiff reacting flow

A well known spurious numerical phenomenon may occur in solving stiff detonation problems due to the under-resolved numerical solution in both space and time. Most people believe that decreasing numerical dissipation or stiffness will delay or eliminate the onset of spurious numerical phenomenon. However, several counter-intuitive spurious behaviors were observed by H.C. Yee et al. (2013) [10] recently and the mechanism of the generation of these strange phenomena remains an open question. The goal of this short note is to give a reasonable explanation for these counter-intuitive spurious behaviors existing in the detonation problems (the simplified 2×2 system and the reactive Euler equations) with stiff reacting source terms and discontinuities. In developing the mechanism of spurious numerical phenomenon in detonation problems, we find the parameters of the intermediate state are very important because they determine whether the spurious phenomenon will happen or not. Furthermore, these counter-intuitive spurious behaviors are mainly due to the oscillation of those intermediate state parameters as the time step or grid is refined gradually. These findings may help us to get a further understanding of some of the difficulties in numerical combustion and problems with stiff nonlinear source terms and discontinuities in general.