A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

  • Authors:

  • Georg May;Francesca Iacono;Antony Jameson

  • Affiliations:

  • Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany;Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany;Department of Aeronautics and Astronautics, Stanford University, Durand Building, 496 Lomita Mall, Stanford, CA 94305-4035, USA

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

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Abstract

Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to highly tuned lower order methods, such as finite-volume schemes. In this paper we investigate solution algorithms in conjunction with high-order Spectral Difference discretization for the Euler equations, using such techniques as multigrid and matrix-free implicit relaxation methods. In particular we present a novel hybrid multilevel relaxation method that combines (optionally matrix-free) implicit relaxation techniques with explicit multistage smoothing using geometric multigrid. Furthermore, we discuss efficient implementation of these concepts using such tools as automatic differentiation.