Implicit Monte Carlo Diffusion—An Acceleration Method for Monte Carlo Time-Dependent Radiative Transfer Simulations

Abstract

Implicit Monte Carlo (IMC) is often employed to numerically simulate radiative transfer. In problems with regions that are characterized by a small mean free path, IMC can take a prohibitive amount of time, because many particle steps must be simulated to advance the particle through the time step. Problems containing regions with a small mean free path can frequently be accurately simulated much more quickly by employing the diffusion equation as an approximation. However, the diffusion approximation is not accurate in regions of the problem where the mean free path is large.We present a method for accelerating time-dependent Monte Carlo radiative transfer calculations by using a discretization of the diffusion equation to calculate probabilities that are used to advance particles in regions with small mean free paths. The method is demonstrated on problems with one-and two-dimensional orthogonal grids. It results in decreases in run time of more than an order of magnitude on these problems, while producing answers with accuracy comparable to pure IMC simulations. We call the method Implicit Monte Carlo Diffusion, which we abbreviate IMD.