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. 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 whose drift and diffusion coefficients are not known explicitly. It is shown that these coefficients can be calculated on the fly using short-time event-driven simulations, thereby allowing us to simulate the stochastic differential equation for the colloid. The efficiency of the resulting scheme 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.