WIAS Preprint No. 672, (2001)

An efficient stochastic chemistry approximation for the PDF transport equation


  • Kraft, Markus
    ORCID: 0000-0002-4293-8924
  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 65C35 60K40


  • PDF transport equation, particle method, stochastic chemistry approximation, convergence, efficiency


In this paper we present an efficient algorithm for the numerical treatment of the PDF transport equation. Using the partially stirred plug flow 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 efficient than the deterministic approach.

Appeared in

  • Monte Carlo Methods Appl. 8 (2002), pp. 371-394

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