A Voronoi Grid and a Particle Tracking Algorithm for DSMC

The DSMC method simulates a gas by three uncoupled steps: moving representative particles through a physical domain, performing probabilistic collisions and estimating the macroscopic state by ensemble averaging. In order to ease computational treatment of these three steps it is convenient to discretize the space with a grid that fits into the boundaries of the physical domain. For efficient particle tracking it is useful that the cells of this grid are convex polyhedra which preferably have no indirect neighbors. To reduce discretization errors in the collision step and to take reasonable averages the cells should be nearly isotropic, whereas their volume is primarily determined by the local flow gradients. Especially the latter condition requires the density of the grid to be continuously adaptable in space and time. We show that grids derived from Voronoi diagrams fulfill these requirements very well.