Simulating Radiative Transfer with Filtered Spherical Harmonics

Abstract

This letter presents a novel application of filters to the spherical harmonics ($P_N$) expansion for radiative transfer problems in the high-energy-density regime. The filter, which is based on non-oscillatory spherical splines, preserves both the equilibrium diffusion limit and formal converges properties of the unfiltered expansion. Results demonstrate that solutions to the filtered $P_N$ equations are (i) more robust and less oscillatory than standard Pn solutions and (ii) more accurate than discrete ordinates solutions of comparable order. The filtered $P_7$ solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem. Given the benefits of this method we believe it will enable more routine use of high-fidelity radiation-hydrodynamics calculations in the simulation of physical systems.