Temporal-Stability-Enhanced and Energy-Stable Dynamical Low-Rank Approximation for Multiscale Linear Kinetic Transport Equations

TL;DR

This paper introduces an energy-stable, asymptotic-preserving low-rank numerical method for multiscale linear kinetic transport equations, improving computational efficiency and stability across regimes.

Contribution

It develops a novel low-rank scheme that is unconditionally stable in the diffusive regime and preserves asymptotic behavior, with proven energy stability.

Findings

The method is energy stable under discrete ordinates discretization.

Numerical experiments confirm efficiency and accuracy across regimes.

The scheme captures correct asymptotic limits.

Abstract

In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic behavior, and can achieve significant reductions in computational cost through a low-rank representation and large time step stability. A low-rank formulation consistent with the discrete energy is introduced under the discrete ordinates discretization, and energy stability of the resulting scheme is established. Numerical experiments confirm the energy stability and demonstrate that the method is efficient while maintaining accuracy across different regimes and capturing the correct asymptotic limits.