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.
