Convergence of the stochastic weighted particle method for the Boltzmann equation
- Matheis, Ingo
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 65C05 76P05 82C80
- Boltzmann equation, stochastic weighted particle method, convergence, variance reduction, numerical experiment
This paper studies convergence of the stochastic weighted particle method for the Boltzmann equation. First the method is extended by introducing new stochastic reduction procedures, in order to control the number of simulation particles. Then, under rather general conditions, convergence to the solution of the Boltzmann equation is proved. Finally, numerical experiments are performed illustrating both convergence and considerable variance reduction, for the specific problem of calculating tails of the velocity distribution.
- SIAM J. Sci. Comput., 24 (2003), pp. 1589-1609