Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators

  • Authors:

  • Mark H. Carpenter;Jan Nordström;David Gottlieb

  • Affiliations:

  • Computational Aerosciences Branch, NASA Langley Research Center, Hampton, USA 23681-2199;Computational Physics Department, FOI, Stockholm, Sweden 16490 and Department of Information Technology, Uppsala, Uppsala, Sweden 75105 and Department of Aeronautical and Vehicle Engineering, KTH- ...;Computational Physics Department, FOI, Stockholm, Sweden 16490 and Department of Information Technology, Uppsala, Uppsala, Sweden 75105 and Department of Aeronautical and Vehicle Engineering, KTH- ...

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2010

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Abstract

A general interface procedure is presented for multi-domain collocation methods satisfying the summation-by-parts (SBP) spatial discretization convention. Unlike more traditional operators (e.g. FEM) applied to the advection-diffusion equation, the new procedure penalizes the solution and the first p derivatives across the interface. The combined interior/interface operators are proven to be pointwise stable, and conservative, although accuracy deteriorates for p驴2. Penalties between two different sets of variables are compared (motivated by FEM primal and flux formulations), and are shown to be equivalent for certain choices of penalty parameters. Extensive validation studies are presented using two classes of high-order SBP operators: (1) central finite difference, and (2) Legendre spectral collocation.