Robust and accurate filtered spherical harmonics expansions for radiative transfer

Abstract

We present a novel application of filters to the spherical harmonics (PN) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme. The method is readily applied to existing codes that solve the PN equations. Numerical results demonstrate that the solution to the filtered PN equations are (i) more robust and less oscillatory than standard PN solutions and (ii) more accurate than discrete ordinates solutions of comparable order. In particular, the filtered P7 solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem in 2D Cartesian geometry.