Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations
<|reference_start|>Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations: 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.<|reference_end|>
@article{patwardhan2024asymptotic-preserving,
    title={Asymptotic-preserving and energy stable dynamical low-rank approximation
  for thermal radiative transfer equations},
    author={Chinmay Patwardhan, Martin Frank and Jonas Kusch},
    journal={arXiv preprint arXiv:2402.16746},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.16746},
    primaryClass={math.NA cs.NA}
}