Implicit Filtered PN for High-Energy Density Thermal Radiation Transport using Discontinuous Galerkin Finite Elements

TL;DR

This paper introduces a fully-implicit filtered spherical harmonics method for thermal radiative transfer, demonstrating improved solver convergence and analyzing error estimates through numerical simulations and comparisons with Monte Carlo methods.

Contribution

It presents a novel fully-implicit filtered spherical harmonics approach for non-linear thermal radiative transfer, including local filtering strategies and convergence analysis.

Findings

Filtering improves iterative solver convergence.

Error estimates from linear theory largely hold in non-linear cases.

The method performs well on unstructured mesh test problems.

Abstract

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte-Carlo (IMC) calculations.