Numerical solutions of the Boltzmann equation: comparison of different algorithms

In the paper we compare different algorithms for numerical solutions of the Boltzmann equation. For this comparison we have taken the standard problem of the shock wave structure in a mono-atomic rarefied gas. Different parameters characterizing the shock structure have been calculated by a Monte Carlo simulation (DSMC), a second order time-relaxed Monte Carlo method (TRMC2), a fully deterministic discrete velocity method (DV), a discrete velocity method with Monte Carlo calculations of collision integral (DVMC) and a molecular dynamics method (MD). Results of these calculations have been compared with the shock wave structure obtained in experiments in a shock tube. The results of the comparison are not conclusive. We have observed general agreement between numerical and experimental results but there is no single numerical method which fits best to the experimental measurements. (c) 2007 Elsevier Masson SAS. All rights reserved.