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A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

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Abstract

Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin discretization can be performed using multiwavelets, which allow for higher-order vanishing moments, while maintaining local support. An implementation for scalar one-dimensional conservation laws has already been developed and tested. In the present paper we extend this strategy to systems of equations, in particular to the equations governing inviscid compressible flow.

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Acknowledgments

Financial support from the Deutsche Forschungsgemeinschaft (German Research Association) through grant GSC 111 and in the frameworks of the Collaborative Research Center SFB-TR-40 and the Research Unit FOR 1779, and by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under Grant number FA8655-08-1-3060, is gratefully acknowledged.

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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 , Aachen, Germany

    Nils Gerhard, Siegfried Müller & Roland Schäfer

  2. Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, Schinkelstraße 2, 52056 , Aachen, Germany

    Francesca Iacono & Georg May

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  1. Nils Gerhard
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  2. Francesca Iacono
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  3. Georg May
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  4. Siegfried Müller
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Correspondence to Siegfried Müller.

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Gerhard, N., Iacono, F., May, G. et al. A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows. J Sci Comput 62, 25–52 (2015). https://doi.org/10.1007/s10915-014-9846-9

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