Abstract:Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide variety of kinetic partial differential equations is the concept of dynamical low-rank approximation (DLRA). In this paper, we consider the thermal radiative transfer equations with Su-Olson closure, leading to a linearized kinetic model. For the conducted theoretical and practical considerations we use a multiplicative splitting of the distribution function that poses additional challenges in finding an energy stable discretization and deriving a hyperbolic Courant-Friedrichs-Lewy (CFL) condition. We propose such an energy stable DLRA scheme that makes use of the augmented basis update & Galerkin integrator. This integrator allows for additional basis augmentations, enabling us to give a mathematically rigorous proof of energy stability and local mass conservation. Numerical examples confirm the derived properties and show the computational advantages of the DLRA scheme compared to a numerical solution of the full system of equations.
| Subjects: | Numerical Analysis (math.NA) |
| MSC classes: | 35L65, 35Q49, 65M12, 65M22 |
| Cite as: | arXiv:2502.03008 [math.NA] |
| (or arXiv:2502.03008v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2502.03008 arXiv-issued DOI via DataCite |
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| Related DOI: | https://doi.org/10.1016/j.cam.2026.117671
DOI(s) linking to related resources |
From: Lena Baumann [view email]
[v1]
Wed, 5 Feb 2025 09:05:38 UTC (845 KB)
[v2]
Fri, 22 May 2026 17:18:43 UTC (1,299 KB)
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