Efficient particle control in systems with large density gradients

Abstract

Simulations of large density gradients present a number of challenges for direct Monte Carlo methods, since they lead to too few particles in dilute regions and prohibitively many in the dense regions. We propose a particle control methodology that gives the user more control of the number of particles per cell by introducing a variable weight for each particle. The proposed scheme is based on the stochastic weighted particle method, requires only small modifications to DSMC, and exactly conserves mass, momentum, and energy. In validation tests of systems with density ratios of order 102-104, we observe 101-102 times less variance in the dilute region compared to a DSMC solution with the same number of system particles, while introducing a moderate additional computational cost.