{
  "id": "1912.09577",
  "version": "v1",
  "published": "2019-12-19T22:20:21.000Z",
  "updated": "2019-12-19T22:20:21.000Z",
  "title": "An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity",
  "authors": [
    "Andrea Thomann",
    "Gabriella Puppo",
    "Christian Klingenberg"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized equations on which we apply a pressure splitting and a Suliciu relaxation. On the resulting model, we apply a splitting of the flux into a linear implicit and an non-linear explicit part that leads to a scale independent time-step. The explicit step consists of a Godunov type method based on an approximative Riemann solver where the source term is included in the flux formulation. We develop the method for a first order scheme and give an extension to second order. Both schemes are designed to be well-balanced, preserve the positivity of density and internal energy and have a scale independent diffusion. We give the low Mach limit equations for well-prepared data and show that the scheme is asymptotic preserving. These properties are numerically validated by various test cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-19T22:20:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second order well-balanced imex relaxation",
      "order well-balanced imex relaxation scheme",
      "speed second order well-balanced imex",
      "euler equations",
      "well-balanced finite volume scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}