FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

  • Authors:

  • Eleuterio F. Toro;Arturo Hidalgo;Michael Dumbser

  • Affiliations:

  • Laboratory of Applied Mathematics, University of Trento, Via Mesiano 77, I-38100 Trento, Italy;ETSI Minas, Universidad Politécnica de Madrid, Calle Ríos Rosas 21, E-28003 Madrid, Spain;Laboratory of Applied Mathematics, University of Trento, Via Mesiano 77, I-38100 Trento, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

This paper is about the construction of numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple space dimensions on structured and unstructured meshes. The work is a multi-dimensional extension of the one-dimensional FORCE flux and is closely related to the work of Nessyahu-Tadmor and Arminjon. The resulting basic flux is first-order accurate and monotone; it is then extended to arbitrary order of accuracy in space and time on unstructured meshes in the framework of finite volume and discontinuous Galerkin methods. The performance of the schemes is assessed on a suite of test problems for the multi-dimensional Euler and Magnetohydrodynamics equations on unstructured meshes.