{
  "id": "2110.13509",
  "version": "v2",
  "published": "2021-10-26T09:08:05.000Z",
  "updated": "2022-08-08T11:14:20.000Z",
  "title": "An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations",
  "authors": [
    "Mirco Ciallella",
    "Lorenzo Micalizzi",
    "Philipp Öffner",
    "Davide Torlo"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration method for the shallow water equations. Due to the positivity-preserving property of mPDeC, the resulting scheme is unconditionally positivity preserving for the water height. To apply the mPDeC approach, we have to interpret the spatial semi-discretization in terms of production-destruction systems. Only small modifications inside the classical WENO implementation are necessary and we explain how it can be done. In numerical simulations, focusing on a fifth order method, we demonstrate the good performance of the new method and verify the theoretical properties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-08T11:14:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary high order",
      "shallow water equations",
      "positivity preserving method",
      "finite volume weno method",
      "high order well-balanced finite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}