论文标题
渐近 - 保利和能量稳定的动力学低级近似
Asymptotic--preserving and energy stable dynamical low-rank approximation
论文作者
论文摘要
辐射传输问题是在高维相空间中构成的，限制了精确解析的数值模拟的使用。在这种设置中有效降低计算成本和内存足迹的新兴工具是动态的低级近似（DLRA）。尽管具有效率，但仍需要仔细构建用于DLRA的数值方法，以确保稳定性，同时保留原始问题的关键特性。人们喜欢使用DLRA保留的重要物理效应包括捕获高冰片的扩散极限以及消散能量。在这项工作中，我们提出和分析了一种基于“非常规”的基础级别和Galerkin步骤积分器的动态低级方法。我们表明，该方法是渐近保护的，即它在CFL条件下捕获了扩散极限和能量稳定。衍生的CFL条件在接近扩散极限时捕获了从双曲线到抛物线状态的过渡。
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is dynamical low-rank approximation (DLRA). Despite its efficiency, numerical methods for DLRA need to be carefully constructed to guarantee stability while preserving crucial properties of the original problem. Important physical effects that one likes to preserve with DLRA include capturing the diffusion limit in the high-scattering regimes as well as dissipating energy. In this work we propose and analyze a dynamical low-rank method based on the "unconventional" basis-update & Galerkin step integrator. We show that this method is asymptotic-preserving, i.e., it captures the diffusion limit, and energy stable under a CFL condition. The derived CFL condition captures the transition from the hyperbolic to the parabolic regime when approaching the diffusion limit.
