WIAS Preprint No. 763, (2002)

A direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation


  • Garcia, Alejandro L.
  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 65C05 76P05 82C40


  • Uehling-Uhlenbeck-Boltzmann equation, Fermi-Dirac case, Bose-Einstein case, DSMC algorithm, numerical experiments




In this paper we describe a DSMC algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady state distribution.

Appeared in

  • Physical Review E,68, 056703 (2003), 11 pages

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