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Stable Boundary Treatment for the Wave Equation on Second-Order Form

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Abstract

A stable and accurate boundary treatment is derived for the second-order wave equation. The domain is discretized using narrow-diagonal summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, P.O. Box 337, 751 05, Uppsala, Sweden

    Ken Mattsson

  2. Mechanical Engineering—Center for Integrated Turbulence Simulations, Stanford University, Stanford, USA

    Frank Ham

  3. Mechanical Engineering—Flow Physics and Computation, Stanford University, Stanford, USA

    Gianluca Iaccarino

Authors
  1. Ken Mattsson
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  2. Frank Ham
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  3. Gianluca Iaccarino
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Correspondence to Ken Mattsson.

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Mattsson, K., Ham, F. & Iaccarino, G. Stable Boundary Treatment for the Wave Equation on Second-Order Form. J Sci Comput 41, 366–383 (2009). https://doi.org/10.1007/s10915-009-9305-1

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  • DOI: https://doi.org/10.1007/s10915-009-9305-1

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