The influence of cell geometry on the Godunov scheme applied to the linear wave equation

  • Authors:

  • Stéphane Dellacherie;Pascal Omnes;Felix Rieper

  • Affiliations:

  • Commissariat í l' ínergie Atomique, CEA, DEN, DM2S-SFME, F-91191 Gif-sur-Yvette, France;Commissariat í l' ínergie Atomique, CEA, DEN, DM2S-SFME, F-91191 Gif-sur-Yvette, France and Université Paris 13, LAGA, CNRS UMR 7539, Institut Galilée, 99 Avenue J.-B. Clé ...;Goethe-Universität Frankfurt, Institut für Atmosphäre und Umwelt, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier-Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.