Mitigating Teleportation Error in Frequency-Dependent Hybrid Implicit Monte Carlo Diffusion Methods

Abstract

This work investigates teleportation error in frequency-dependent Hybrid Implicit Monte Carlo Diffusion (HIMCD). HIMCD dynamically applies Implicit Monte Carlo Diffusion (Gentile, 2001; Cleveland et al., 2010) to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) (Fleck and Cummings, 1971) to regions where the diffusion approximation is invalid. Teleportation error arises in Monte Carlo simulations when a source is represented with the wrong spatial distribution causing radiation energy to propagate unphysically fast through a material (McKinley et al., 2003). Both frequency-dependent HIMCD and Hybrid IMC/Discrete Diffusion Monte Carlo (Densmore et al., 2012) suffer from a new source of teleportation error that is intrinsic to these methods. This teleportation error arises from sampling a new spatial location of a Monte Carlo particle when it scatters from a diffusive opaque group to a moderately opaque transport group. In this work we show that sampling these “up-scatter” locations with a flat spatial distribution in the cell, as was done in previous work (Densmore et al., 2012; Wollaeger et al., 2013), creates significant teleportation error in optically thick cells. We then show that source tilting can improve these results for moderately opaque cells, but is not accurate enough to significantly improve the teleportation error in extremely opaque cells. Finally we present a new set of criteria that can be used to define which opacity groups are diffusive, in conjunction with source tilting, to significantly reduce teleportation regardless of the cell’s opacity. We refer to this new set of diffusion criteria as “over-lumping” because it includes moderately opaque frequency groups, which were previously excluded by other criteria (Densmore et al., 2012), into the diffusion domain. The over-lumping criterion is tested using two test cases: a Marshak wave moving through stationary optically thick iron, and a frequency-dependent radiation hydrodynamic ablation test case.