Polymorphic nodal elements and their application in discontinuous Galerkin methods

  • Authors:

  • Gregor J. Gassner;Frieder Lörcher;Claus-Dieter Munz;Jan S. Hesthaven

  • Affiliations:

  • Institute for Aerodynamics and Gasdynamics, University of Stuttgart, Pfaffenwaldring 21, 70550 Stuttgart, Germany;Institute for Aerodynamics and Gasdynamics, University of Stuttgart, Pfaffenwaldring 21, 70550 Stuttgart, Germany;Institute for Aerodynamics and Gasdynamics, University of Stuttgart, Pfaffenwaldring 21, 70550 Stuttgart, Germany;Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912, USA

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

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Abstract

In this work, we discuss two different but related aspects of the development of efficient discontinuous Galerkin methods on hybrid element grids for the computational modeling of gas dynamics in complex geometries or with adapted grids. In the first part, a recursive construction of different nodal sets for hp finite elements is presented. They share the property that the nodes along the sides of the two-dimensional elements and along the edges of the three-dimensional elements are the Legendre-Gauss-Lobatto points. The different nodal elements are evaluated by computing the Lebesgue constants of the corresponding Vandermonde matrix. In the second part, these nodal elements are applied within the modal discontinuous Galerkin framework. We still use a modal based formulation, but introduce a nodal based integration technique to reduce computational cost in the spirit of pseudospectral methods. We illustrate the performance of the scheme on several large scale applications and discuss its use in a recently developed space-time expansion discontinuous Galerkin scheme.