Stochastic Numerics for the Boltzmann Equation

Sergej Rjasanow, Wolfgang Wagner (auth.)9783540252689, 9783540276890, 3540252681

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Table of contents :
Kinetic theory….Pages 1-32
Related Markov processes….Pages 33-64
Stochastic weighted particle method….Pages 65-146
Numerical experiments….Pages 147-210