{
  "id": "2502.03008",
  "version": "v1",
  "published": "2025-02-05T09:05:38.000Z",
  "updated": "2025-02-05T09:05:38.000Z",
  "title": "An energy stable and conservative multiplicative dynamical low-rank discretization for the Su-Olson problem",
  "authors": [
    "Lena Baumann",
    "Lukas Einkemmer",
    "Christian Klingenberg",
    "Jonas Kusch"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-05T09:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35Q49",
      "65M12",
      "65M22"
    ],
    "keywords": [
      "conservative multiplicative dynamical low-rank discretization",
      "energy stable",
      "su-olson problem",
      "thermal radiative transfer equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}