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 convergence properties of the unfiltered expansion. While the method requires further mathematical justification and computational studies, preliminary results demonstrate that solutions to the filtered P N equations are (1) more robust and less oscillatory than standard P N solutions and (2) 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.