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

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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≥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.

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Authors and Affiliations

  1. Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA, 23681-2199, USA

    Mark H. Carpenter

  2. Computational Physics Department, FOI, 16490, Stockholm, Sweden

    Jan Nordström

  3. Department of Information Technology, Uppsala, 75105, Uppsala, Sweden

    Jan Nordström

  4. Department of Aeronautical and Vehicle Engineering, KTH—The Royal Institute of Technology, 10044, Stockholm, Sweden

    Jan Nordström

Authors
  1. Mark H. Carpenter
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  2. Jan Nordström
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  3. David Gottlieb
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Corresponding author

Correspondence to Mark H. Carpenter.

Additional information

Work performed in part, while M.H. Carpenter in residence at TU Delft, Delft, The Netherlands.

David Gottlieb passed away during the final revision of this paper. He left an indelible mark on our lives, and will be greatly missed. D. Gottlieb was formerly in Division of Applied Mathematics, Brown University, Providence, RI 02912.

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Carpenter, M.H., Nordström, J. & Gottlieb, D. Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators. J Sci Comput 45, 118–150 (2010). https://doi.org/10.1007/s10915-009-9301-5

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  • DOI: https://doi.org/10.1007/s10915-009-9301-5

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