A direct simulation Monte Carlo method for rarefied gas flows in the limit of small Mach number

Abstract

Standard methods of simulating the mean velocity and mean force in a rarefied gas flow suffer from statistical errors associated with the random thermal motion of the gas molecules. The ratio of the statistical error to the mean velocity or force diverges in the limit of small Mach number, which is relevant to applications in aerosol science and microdevices. We present a novel extension of the direct-simulation Monte Carlo method in which the deviation from equilibrium is captured by noninteger weightings of the simulation gas particles, so that the mean velocity and force associated with the deviation from equilibrium can be computed without contamination by the thermal noise in the equilibrium state. The collision rules between simulation particles reproduce the changes in the gas velocity distribution function that would result from hard sphere intermolecular collisions. Because the collision rules produce new particles, particle splitting and recombination steps, which do not alter the velocity distribution function, must be introduced to maintain a finite number of particles and a finite maximum weighting per particle. The method is validated by comparing simulation results for pressure-driven flow in a channel and flow past a single sphere to corresponding solutions of the linearized Boltzmann equation. The method is then applied to obtain new results for the resistance to the relative motion of two spherical particles along their line of centers.