{
  "id": "2312.08280",
  "version": "v1",
  "published": "2023-12-13T16:53:32.000Z",
  "updated": "2023-12-13T16:53:32.000Z",
  "title": "New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties",
  "authors": [
    "Alina Chertock",
    "Michael Herty",
    "Arsen S. Iskhakov",
    "Safa Janajra",
    "Alexander Kurganov",
    "Maria Lukacova-Medvidova"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and it is based on fifth-order weighted essentially non-oscillatory (WENO) interpolations in (multidimensional) random space combined with second-order piecewise linear reconstruction in physical space. Compared with spectral approximations in the random space, the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving a high-order accuracy. The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations. In the latter case, the methods are also proven to be well-balanced and positivity-preserving.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-13T16:53:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-order numerical methods",
      "hyperbolic systems",
      "nonlinear pdes",
      "uncertainties",
      "random space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}