A Temperature Time Counter Scheme for the Boltzmann Equation

Abstract

This paper gives a rigorous derivation of a new stochastic particle method for the Boltzmann equation and illustrates its numerical efficiency. Using estimates based on the local temperature of the simulation cells, any truncation error related to large velocities is avoided. Moreover, time steps between collisions are larger than in the standard direct simulation method. This fact and an efficient modelling procedure for the index distribution of the collision partners lead to a considerable reduction of computational effort in certain applications.