On the Accuracy and Efficiency of the Direct Simulation Monte Carlo Method.

Abstract

The direct simulation Monte Carlo (DSMC) method is today by far the most popular simulation technique to solve the Boltzmann equation for rarefied flows. The first part of the thesis aims to characterize both the convergence and the accuracy of the DSMC method. The particular test case used for this investigation consists of an axisymmetric argon jet. Sampled flow quantities are found to be highly time-correlated, but the rate of convergence of their sampled averages is found to be well-predicted by a Central Limit Theorem taking that correlation into account. The influence of the number of particles and the time step on the accuracy of the simulation is then assessed. Their influence on the convergence and time correlation of sampled flow quantities is also studied. The second part of the thesis addresses one of the major shortcomings inherent to the DSMC method, the fact that the number of computational particles in any one cell is directly proportional to its density. For flows with large density disparities or multiple species, this often results in some cells containing excessive numbers of particles and others too few. A possible solution is thus to use both cell weights and species weights that vary in space. As each particular flow is different, optimum weight fields also differ between simulations. In this thesis, a novel adaptive procedure for the weights and time step is proposed. Both are automatically varied as the simulation progresses to steady state. The performance of the adaptive procedure is then assessed for a test case consisting of two counterflowing jets. Significant performance improvements are observed. These are mostly due to an improved distribution of computational particles throughout the domain for each individual species. In the last part of this thesis, a hybrid DSMC/Fluid method is applied to the simulation of a weakly ionized rarefied flow. Electrons are modeled via the use of an electron fluid model while DSMC is used to model the dynamics of all non-electron particles. Satisfactory results are obtained for both plasma parameters and gas properties.