Numerical solution of the Boltzmann equation on the uniform grid

Abstract

In the present paper a new numerical method for the Boltzmann equation is developed. The gain part of the collision integral is written in a form which allows its numerical computation on the uniform grid to be carried out efficiently. The amount of numerical work is shown to be of the order O(n^{6}\log(n)) for the most general model of interaction and of the order O(n^{6}) for the Variable Hard Spheres (VHS) interaction model, while the formal accuracy is of the order O(n^{-2}). Here n denotes the number of discretisation points in one direction of the velocity space. Some numerical examples for Maxwell pseudomolecules and for the hard spheres model illustrate the accuracy and the efficiency of the method in comparision with DSMC computations.