On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows

A. I. Khisamutdinov ; N. N. Velker

Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 65-88

Résumé

Publication describes Monte Carlo methods and algorithms for Boltzmann equation for rarefied gases problems in case of large-scale flow areas. We consider imitation or Continuous Time Monte Carlo methods where frequencies of interactions of particles’ pairs depend on difference of particles’ coordinates. The question about reduction computational costs of algorithms is examined using specificity of the problem. First, algorithms of an approximated method are constructed, analyzed and realized. This method is obtained using splitting (over groups of particles) of operator in master equations system. In the second place, we investigate fictitious collisions technique, where the upper bound for the number of interacting pairs is specified. Plane Poiseuille flow (in the field of external forces) problem, Heat transfer problem and Temperature discontinuity propagation problem are numerically solved using developed algorithms. Asymptotical estimates of the computational costs are confirmed with the data of the computational processes and comparative properties of the last one are fixed. Suggested algorithms of the method with splitting allow parallelization of the certain type.

Détail

Keywords: statistical modeling, Continuous Time Monte Carlo methods for Boltzmann equation, fictitious collisions technique, approximated method obtained using of splitting over groups of particles, reduction of computational cost.