Strategies for efficient particle resolution in the direct simulation Monte Carlo method. (Q1971423)

This paper considers several issues of the so-called direct simulation Monte Carlo method (DSMC) as a statistical particle method for the computation of nonequilibrium gas flows. The gas flow is modeled by a large number of particles representing physical molecules and atoms on the microscopic level. The motion of these particles together with interactive collisions should reproduce the macroscopic behavior of the gas. The accuracy of this particle DSMC method has already been investigated by \textit{G. Chen} and \textit{I. D. Boyd} [ibid. 126, No. 2, 434--448 (1996, Zbl 0856.65003)] with respect to the numerical error in view of macroscopic properties. The present method is generally aiming at a numerically optimal calculation such that minimum number of particles per cell is needed to resolve the desired physics of the gas flow. The distribution of particles and the computational cost of simulations can be controlled by various computational parameters, varying particle weights and time steps, and by grid manipulation. The drawbacks and benefits of these methods are studied by the authors. A combination of time step variation and grid manipulation turns out to be the most effective simulation strategy to find a numerically efficient distribution of particles for a variety of gas flows. A model flow problem is presented, including both expansion and compression.