p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

  • Authors:

  • Krzysztof J. Fidkowski;Todd A. Oliver;James Lu;David L. Darmofal

  • Affiliations:

  • Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 37, Room 401, USA;Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 37, Room 401, USA;Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 37, Room 401, USA;Aerospace Computational Design Laboratory, Massachusetts Institute of Technology, Building 37, Room 401, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier-Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p=0 discretization of the scalar convection-diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal h^p^+^1 order of accuracy as well as p-independent multigrid convergence rates, at least up to p=3. In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.