Numerical Simulation of the Stationary One{dimensional Boltzmann Equation by Particle Methods

The paper presents a numerical simulation technique { based on the well{known particle methods { for the stationary, one{dimensional Boltzmann equation for Maxwellian molecules. In contrast to the standard splitting methods, where one works with the instationary equation, the current approach simulates the direct solution of the stationary problem. The model problem investigated is the heat transfer between two parallel plates in the rareeed gas regime. An iteration process is introduced which leads to the stationary solution of the exact { space discretized { Boltzmann equation, in the sense of weak convergence.