Journal of Statistical Physics

, Volume 66, Issue 3–4, pp 1011–1044 | Cite as

A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation

  • Wolfgang Wagner


Bird's direct simulation Monte Carlo method for the Boltzmann equation is considered. The limit (as the number of particles tends to infinity) of the random empirical measures associated with the Bird algorithm is shown to be a deterministic measure-valued function satisfying an equation close (in a certain sense) to the Boltzmann equation. A Markov jump process is introduced, which is related to Bird's collision simulation procedure via a random time transformation. Convergence is established for the Markov process and the random time transformation. These results, together with some general properties concerning the convergence of random measures, make it possible to characterize the limiting behavior of the Bird algorithm.

Key words

Boltzmann equation Bird's direct simulation Monte Carlo method stochastic numerical algorithm convergence of random measures Markov jump processes 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Wolfgang Wagner
    • 1
  1. 1.Laboratory for TechnomathematicsUniversity of KaiserslauternKaiserslauternGermany

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