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 ⁶log(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 pseudo-molecules and for the hard spheres model illustrate the accuracy and the efficiency of the method in comparison with DSMC computations in the spatially homogeneous case.