cient stochastic chemistry approximation for the PDF transport equation

In this paper we present an e cient algorithm for the numerical treatment of the PDF transport equation. Using the partially stirred plug ow model in conjunction with the IEM mixing model we construct a numerical scheme that is based on a time splitting technique and a stochastic chemistry approximation. For this purpose a particle/sub-particle system is introduced. The dynamics of this particle system is determined by a mixing step and a chemistry step. The chemistry step is solved by a jump process where forward and reverse reactions are combined. Various numerical experiments are carried out to study convergence with respect to particle number and sub-particle number. In case of a linear reaction, the comparison between analytical solution and numerical approximation of the third moment reveals that the systematic error is inversely proportional to the number of particles and sub-particles, respectively. The performance of the algorithm is evaluated by studying the combustion of a premixed stoichiometric mixture of n-heptane and air. The stochastic chemistry algorithm is compared with a deterministic approach using the ODE solver DASSL and it is found, for the examples studied, that the stochastic algorithm is more e cient than the deterministic approach.