Accelerated Simulation of a Heavy Particle in a Gas of Elastic Spheres

A new, accelerated algorithm for a system of elastic hard-spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. It is shown that, in the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of the colloid is given by a stochastic differential equation. The coefficients of the equation are calculated on the fly using a short-time event driven simulation. The trajectory of the colloid is simulated using Brownian dynamics with the parameters obtained in the micro, event driven one. The efficiency of the simulation is independent of the mass ratio. A few numerical examples, which serve as a proof of principle, are presented. The examples demonstrate that our results are consistent with analytical predictions in the ideal gas limit. A result of a simulation with a dense gas is also presented.