An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918518343073792 |
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| author | Baumann, Lena Einkemmer, Lukas Klingenberg, Christian Kusch, Jonas |
| author_facet | Baumann, Lena Einkemmer, Lukas Klingenberg, Christian Kusch, Jonas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem Baumann, Lena Einkemmer, Lukas Klingenberg, Christian Kusch, Jonas Numerical Analysis 35L65, 35Q49, 65M12, 65M22 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. |
| title | An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem |
| topic | Numerical Analysis 35L65, 35Q49, 65M12, 65M22 |
| url | https://arxiv.org/abs/2502.03008 |