A high-order / low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations

TL;DR

This paper introduces the HOLO algorithm that combines high-order solutions with low-order equations to preserve conservation laws in time-dependent low-rank transport calculations, improving accuracy without increasing computational cost.

Contribution

The paper presents a novel HOLO algorithm that ensures conservation in dynamical low-rank methods for transport problems by coupling high- and low-order solutions.

Findings

HOLO algorithm conserves quantities effectively.

Maintains computational efficiency and accuracy.

Demonstrated through numerical experiments.

Abstract

Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits the applicability of the method. Here we address this conservation issue by solving a low-order equation with closure terms computed via a high-order solution calculated with DLR. We observe that the high-order solution well approximates the closure term, and the low-order solution can be used to correct the conservation bias in the DLR evolution. We also apply the linear discontinuous Galerkin method for the spatial discretization to obtain the asymptotic limit. We then demonstrate with the numerical results that this so-called high-order / low-order (HOLO) algorithm is conservative without sacrificing computational efficiency and accuracy.