A New Scheme for Solving High-Order DG Discretizations of Thermal Radiative Transfer using the Variable Eddington Factor Method

TL;DR

This paper introduces an efficient semi-implicit scheme for high-order thermal radiative transfer using the Variable Eddington Factor method, balancing accuracy and computational cost through iterative convergence strategies.

Contribution

It develops a novel iterative scheme combining outer and inner loops to solve TRT more efficiently with potential for reduced computational effort.

Findings

The semi-implicit scheme performs comparably to fully implicit methods.

One outer iteration per time step can yield sufficiently accurate results.

The method demonstrates robustness and efficiency in TRT simulations.

Abstract

We present a new approach for solving high-order thermal radiative transfer (TRT) using the Variable Eddington Factor (VEF) method (also known as quasidiffusion). Our approach leverages the VEF equations, which consist of the first and second moments of the $S_N$ transport equation, to more efficiently compute the TRT solution for each time step. The scheme consists of two loops - an outer loop to converge the Eddington tensor and an inner loop to converge the iteration between the temperature equation and the VEF system. By converging the outer iteration, one obtains the fully implicit TRT solution for the given time step with a relatively low number of transport sweeps. However, one could choose to perform exactly one outer iteration (and therefore exactly one sweep) per time step, resulting in a semi-implicit scheme that is both highly efficient and robust. Our results indicate that the error between the one-sweep and fully implicit variants of our scheme may be small enough for consideration in many problems of interest.