A particle simulation method for the BGK equation

A particle simulation method, the "relaxation time" simulation method (RTSM), is described. In RTSM the collision phase in standard DSMC is replaced by a procedure whereby some of the particle velocities in each cell at each time step are selected from an equilibrium distribution, while conserving the total energy and momentum in the cell. The remaining velocities in each cell are not changed. The number of velocities to be changed is determined from the local relaxation time, which can be derived from the cell density and temperature and any desired viscosity law. The relaxation time method is a simulation method to solve the BGK equation. RTSM is efficient compared to DSMC, and becomes more so as the collision rate increases, so RTSM appears to be a natural candidate for near continuum flows