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Efficient Parallelization of a Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Sub-cells

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Abstract

We present a shock capturing procedure for high order Discontinuous Galerkin methods, by which shock regions are refined in sub-cells and treated by finite volume techniques. Hence, our approach combines the good properties of the Discontinuous Galerkin method in smooth parts of the flow with the perfect properties of a total variation diminishing finite volume method for resolving shocks without spurious oscillations. Due to the sub-cell approach the interior resolution on the Discontinuous Galerkin grid cell is nearly preserved and the number of degrees of freedom remains the same. This structure allows the interpretation of the data either as DG solution or as finite volume solution on the subgrid. In this paper we explain the efficient implementation of this coupled method on massively parallel computers and show some numerical results.

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  1. Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569, Stuttgart, Germany

    Matthias Sonntag & Claus-Dieter Munz

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  1. Matthias Sonntag
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  2. Claus-Dieter Munz
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Correspondence to Matthias Sonntag.

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Sonntag, M., Munz, CD. Efficient Parallelization of a Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Sub-cells. J Sci Comput 70, 1262–1289 (2017). https://doi.org/10.1007/s10915-016-0287-5

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