07/04/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Sergej Rjasanow, Universität Saarbrücken, Alemanha
The Boltzmann equation. Theory and numerics
In the first part of the talk we introduce the Boltzmann
equation, discuss its properties and give an overview on existence
and uniqueness of solutions. Especially our new results on mapping
properties of the Boltzmann collision operator will be presented.
Then the Direct Simulation Monte Carlo method (DSMC) which is
widely applied in numerics will be explained. In the third part of
the talk we present the Stochastic Weighted Particle Method (SWPM)
which was introduced in 90's by Rjasanow and Wagner. We apply this
method to the numerical solution of the spatially two-dimensional
Boltzmann equation. The numerical solution of the Boltzmann
equation using naive deterministic methods leads to the amount of
numerical work of the order , where denotes the number
of discrete velocities in one direction. In the next part of the
talk we give an overview on deterministic numerical methods applied
to the Boltzmann equation by a number of authors. Then, in the
final part of the talk, we present the results of our numerical
experiments obtained by a new deterministic approximation of the
Boltzmann equation using Fast Fourier Transform.