Direct Simulation Monte Carlo Algorithms for Simulation of Non-equilibrium Gas Flows

The paper deals with some basic problems of the DSMC method concerning the generation of new collision algorithms with improved stochastic properties, allowing simulation of non-equilibrium gas flows with a smaller number of particles in cells compared to the traditional collision schemes. The modified algorithms avoid the events of repeated collisions, which are ones of the basic sources of bias from the theoretical Boltzmann collision frequency. The considered modifications are validated on the one-dimensional unsteady-state problem of strong shock wave formation and the macroscopic characteristics of the shock wave obtained by traditional and new collision algorithms are compared. The efficiency of the modified DSMC method is illustrated by numerical results obtained from the simulation of three-dimensional Rayleigh-Benard convection of a rarefied gas.