Numerical solution of the Boltzmann equation by time relaxed Monte Carlo (TRMC) methods

Lorenzo Pareschi, Stefano Trazzi

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A new family of Monte Carlo schemes has been recently introduced for the numerical solution of the Boltzmann equation of rarefied gas dynamics (SIAM J. Sci. Comput. 2001; 23:1253-1273). After a splitting of the equation the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high-order terms in the expansion with the equilibrium Maxwellian distribution. The corresponding time relaxed Monte Carlo (TRMC) schemes allow the use of time steps larger than those required by direct simulation Monte Carlo (DSMC) and guarantee consistency in the fluid-limit with the compressible Euler equations. Conservation of mass, momentum, and energy are also preserved by the schemes. Applications to a two-dimensional gas dynamic flow around an obstacle are presented which show the improvement in terms of computational efficiency of TRMC schemes over standard DSMC for regimes close to the fluid-limit.

Original languageEnglish
Pages (from-to)947-983
Number of pages37
JournalInternational Journal for Numerical Methods in Fluids
Issue number9
StatePublished - 30 Jul 2005
Externally publishedYes


  • Boltzmann equation
  • Euler equations
  • Fluid-dynamic limit
  • Monte Carlo methods
  • Stiff systems
  • Time relaxed schemes


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