{
  "id": "1712.08218",
  "version": "v1",
  "published": "2017-12-21T21:27:22.000Z",
  "updated": "2017-12-21T21:27:22.000Z",
  "title": "Well-Balanced Schemes for the Euler Equations with Gravitation: Conservative Formulation Using Global Fluxes",
  "authors": [
    "Alina Chertock",
    "Shumo Cui",
    "Alexander Kurganov",
    "Şeyma Nur Özcan",
    "Eitan Tadmor"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-21T21:27:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76M12",
      "65M08",
      "35L65",
      "76N15",
      "86A05"
    ],
    "keywords": [
      "euler equations",
      "global fluxes",
      "well-balanced schemes",
      "conservative formulation",
      "preserving steady-state solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}