Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem

TL;DR

This paper develops a stable, mass-conserving dynamical low-rank approximation method for the Su-Olson radiative transfer problem, significantly reducing computational costs while maintaining accuracy.

Contribution

It introduces a novel stable discretization and a rank-adaptive strategy for DLRA applied to the Su-Olson model, ensuring mass conservation and efficiency.

Findings

The proposed method achieves high accuracy compared to full system solutions.

It significantly reduces computational and memory costs.

Numerical results demonstrate stability and efficiency of the approach.

Abstract

Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is dynamical low-rank approximation (DLRA), which represents and evolves the solution on a low-rank manifold, thereby significantly decreasing computational and memory requirements. Efficient discretizations for the DLRA evolution equations need to be carefully constructed to guarantee stability while enabling mass conservation. In this work, we focus on the Su-Olson closure leading to a linearized internal energy model and derive a stable discretization through an implicit coupling of internal energy and particle density. Moreover, we propose a rank-adaptive strategy to preserve local mass conservation. Numerical results are presented which showcase the accuracy and efficiency of the proposed low-rank method compared to the solution of the full system.