Particle Monte Carlo Algorithms with Small Number of Particles in Grid Cells

Abstract

The Direct Simulation Monte Carlo (DSMC) analysis of two- and three-dimensional rarefied gas flows requires computational resources of very large proportions. One of the major causes for this is that, along with the multidimensional computational mesh, the standard DSMC approach also requires a large number of particles in each cell of the mesh in order to obtain sufficiently accurate results. In this paper we present two modified simulation procedures which allow more accurate calculations with a smaller mean number of particles ($\left\langle{N}\right\rangle \sim 1$) in the grid cells. In the general DSMC scheme, the standard DSMC collision algorithm is replaced by a new collision procedure based on ”Bernoulli trials” scheme or its simplified version. The modified algorithms use a symmetric Strang splitting scheme that improves the accuracy of the splitting method to O(τ ²) with respect to the time step τ making the modified DSMC method a more effective numerical tool for both steady and unsteady gas flow calculations on fine multidimensional grids. Here the considered modifications are validated on the one-dimensional unsteady-state problem of strong shock wave formation.