Numerical study of a stochastic particle method for homogeneous gas-phase reactions

Abstract

In this paper, we study a stochastic particle system that describes homogeneous gas-phase reactions of a number of chemical species. First, we introduce the system as a Markov jump process and discuss how relevant physical quantities are represented in terms of appropriate random variables. Then, we show how various deterministic equations, used in the literature, are derived from the stochastic system in the limit when the number of particles goes to infinity. Finally, we apply the corresponding stochastic algorithm to a toy problem, a simple formal reaction mechanism, and a real combustion problem. This problem is given by the isothermal combustion of a homogeneous mixture of heptane and air modelled by a detailed reaction mechanism with 107 chemical species and 808 reversible reactions. Heptane as described in this chemical mechanism serves as model-fuel for different types of internal combustion engines. In particular, we study the order of convergence with respect to the number of simulation particles, and illustrate the limitations of the method.