On the Stochastic Weighted Particle Method

Abstract

The stochastic weighted particle method is one of the particle methods recently developed to approximate the solution of the Boltzmann equation, one of the well known kinetic equations. The main idea is to use random weight transfer between particles during collisions. In order to reduce the stochastic fluctuations, this method provides a way to increase the number of particles. But if the additional particles cannot be compensated in some natural way, then the number of particles should be reduced. To improve the method for long time intervals, two reduction procedures are proposed. One of them is based on an appropriate clustering of the particle system in the velocity space, and the other one is a recently developed method based on the weight selection of the particles. Some theoretical and numerical aspects are presented.