ν-DSMC: A Fast Simulation Method for Rarefied Flow

A new approximate simulation method for rarefied flows, ν-DSMC, is described and tested by comparison with results from Birdʹs direct simulation Monte–Carlo (DSMC) method, and with a previously proposed ‘relaxation time’ simulation method (RTSM) which solves the BGK equation. Both ν-DSMC and RTSM execute about twice (or more) as fast as DSMC. In ν-DSMC all collision pairs (amongst near neighbours) are equally likely so the collision loops are suitable for parallel execution. In order to reproduce any desired viscosity law μ=μ(T) the collision rate must be altered by making the total collision cross-section a function of the local kinetic temperature. The approximate methods have been compared to DSMC in three test cases: (1) simple relaxation calculations, (2) high speed Couette flow, and (3) the plane normal shock problem. Both approximate methods produce the same relaxation rate as DSMC, but only the new method produces a nonequilibrium distribution function similar to that for DSMC. For the Couette flow, ν-DSMC produces profiles of flow velocity, density, and temperature which agree with DSMC results to within 3–5%, while the BGK solution produces temperatures which are up to 18% greater. Similar results were found for the normal shock wave. ν-DSMC predicts the location and size of the peak Tx temperature more accurately than does RTSM. The deviation of the temperature profiles from the DSMC results are 2–3 times greater for RTSM than for ν-DSMC. The conclusion from all test cases is clear: the incorrect Prandtl number predicted by the BGK equation detracts from the usefulness of the BGK equation as a model for rarefied flow; the new approximate simulation method is just as fast as solving the BGK equation and gives results which are in much better agreement with DSMC.