Numerical solution of the Boltzmann equation on the uniform grid
Sergej Rjasanow (Uni Saarbrücken)
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
for the most general model of interaction and of the order for the
Variable Hard Spheres (VHS) interaction model, while the formal accuracy is
of the order . 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 comparison
with DSMC computations.
[1] Rjasanow, S. and Ibragimov, I., Numerical solution of the Boltzmann equation
on the uniform grid, Preprint 63, University of Saarland, 2002,
to appear in "`Computing"'
This talk presents joint work with Ilgis Ibragimow.
