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 2-D Cartesian geometry.
