A Parallel, Energy-Stable Low-Rank Integrator for Nonlinear Multi-Scale Thermal Radiative Transfer

TL;DR

This paper introduces a parallel, energy-stable low-rank integrator for nonlinear multi-scale thermal radiative transfer, effectively handling complex interactions and multiple time scales in high-dimensional problems.

Contribution

It develops an asymptotic-preserving, mass conservative, rank-adaptive integrator that efficiently manages nonlinear effects and boundary conditions in thermal radiative transfer simulations.

Findings

The integrator is energy stable under hyperbolic and parabolic CFL conditions.

It efficiently captures nonlinear thermal radiation effects.

Numerical experiments demonstrate its effectiveness.

Abstract

Thermal radiative transfer models physical phenomena ranging from supernovas in astrophysics to radiation from a hohlraum striking a fusion target in plasma physics. Transport and absorption of particles in radiative transfer at different rates lead to a complex interaction between the material and particles that involves highly varying time scales. Resolving these effects can require prohibitively small step sizes, which, combined with nonlinear effects and the particle density's high-dimensional phase space, render conventional numerical methods computationally expensive. This work presents an asymptotic--preserving, mass conservative, rank-adaptive, and parallel integrator for a macro--micro decomposition-based dynamical low-rank approximation of the thermal radiative transfer equations. The proposed integrator efficiently incorporates reflection-transmission type boundary conditions in the low-rank factors. It captures the nonlinear effects of thermal radiation and is energy stable with the step size restriction capturing both hyperbolic and parabolic CFL conditions. The efficacy of the proposed integrator is demonstrated with numerical experiments.