{
  "id": "2002.12740",
  "version": "v1",
  "published": "2020-02-28T14:30:19.000Z",
  "updated": "2020-02-28T14:30:19.000Z",
  "title": "The Moving Discontinuous Galerkin Finite Element Method with Interface Condition Enforcement for Compressible Viscous Flows",
  "authors": [
    "Andrew D. Kercher",
    "Andrew Corrigan",
    "David A. Kessler"
  ],
  "comment": "29 pages, 11 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "physics.comp-ph"
  ],
  "abstract": "The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive law, and the corresponding interface conditions in order to provide the means to detect interfaces or under-resolved flow features. To satisfy the resulting overdetermined weak formulation, the discrete domain geometry is introduced as a variable, so that the method implicitly fits a priori unknown interfaces and moves the grid to resolve sharp, but smooth, gradients, achieving a form of anisotropic curvilinear $r$-adaptivity. This approach avoids introducing low-order errors that arise using shock capturing, artificial dissipation, or limiting. The utility of this approach is demonstrated with its application to a series of test problems culminating with the compressible Navier-Stokes solution to a Mach 5 viscous bow shock for a Reynolds number of $10^{5}$ in two-dimensional space. Time accurate solutions of unsteady problems are obtained via a space-time formulation, in which the unsteady problem is formulated as a higher dimensional steady space-time problem. The method is shown to accurately resolve and transport viscous structures without relying on numerical dissipation for stabilization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-28T14:30:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discontinuous galerkin finite element method",
      "moving discontinuous galerkin finite element",
      "interface condition enforcement",
      "compressible viscous flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}