Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910848772997120 |
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| author | Patwardhan, Chinmay Frank, Martin Kusch, Jonas |
| author_facet | Patwardhan, Chinmay Frank, Martin Kusch, Jonas |
| contents | The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type equation called the Rosseland approximation. The main challenges for constructing numerical schemes that exhibit the correct limiting behavior are posed by the solution's high-dimensional phase space and multi-scale effects. In this work, we propose an asymptotic-preserving and rank-adaptive dynamical low-rank approximation scheme based on the macro-micro decomposition of the particle density and a modified augmented basis-update \& Galerkin integrator. We show that this scheme, for linear particle emission by the material, dissipates energy over time under a step size restriction that captures the hyperbolic and parabolic CFL conditions. We demonstrate the efficacy of the proposed method in a series of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations Patwardhan, Chinmay Frank, Martin Kusch, Jonas Numerical Analysis 35L65, 35Q49, 65M12, 35B40 The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type equation called the Rosseland approximation. The main challenges for constructing numerical schemes that exhibit the correct limiting behavior are posed by the solution's high-dimensional phase space and multi-scale effects. In this work, we propose an asymptotic-preserving and rank-adaptive dynamical low-rank approximation scheme based on the macro-micro decomposition of the particle density and a modified augmented basis-update \& Galerkin integrator. We show that this scheme, for linear particle emission by the material, dissipates energy over time under a step size restriction that captures the hyperbolic and parabolic CFL conditions. We demonstrate the efficacy of the proposed method in a series of numerical experiments. |
| title | Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations |
| topic | Numerical Analysis 35L65, 35Q49, 65M12, 35B40 |
| url | https://arxiv.org/abs/2402.16746 |