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On limiting for higher order discontinuous Galerkin method for 2D Euler equations

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Abstract

We present an implementation of discontinuous Galerkin method for 2-D Euler equations on Cartesian meshes using tensor product Lagrange polynomials based on Gauss nodes. The scheme is stabilized by a version of the slope limiter which is adapted for tensor product basis functions together with a positivity preserving limiter. We also incorporate and test shock indicators to determine which cells need limiting. Several numerical results are presented to demonstrate that the proposed approach is capable of computing complex discontinuous flows in a stable and accurate fashion.

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Authors and Affiliations

  1. Dept. of Mathematics, Würzburg University, Würzburg, Germany

    Juan Pablo Gallego-Valencia & Christian Klingenberg

  2. TIFR Center for Applicable Mathematics, Bangalore, India

    Praveen Chandrashekar

Authors
  1. Juan Pablo Gallego-Valencia
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  2. Christian Klingenberg
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  3. Praveen Chandrashekar
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Correspondence to Juan Pablo Gallego-Valencia.

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Gallego-Valencia, J.P., Klingenberg, C. & Chandrashekar, P. On limiting for higher order discontinuous Galerkin method for 2D Euler equations. Bull Braz Math Soc, New Series 47, 335–345 (2016). https://doi.org/10.1007/s00574-016-0142-1

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  • DOI: https://doi.org/10.1007/s00574-016-0142-1

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