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Journal of Scientific Computing

, Volume 62, Issue 1, pp 25–52 | Cite as

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

  • Nils Gerhard
  • Francesca Iacono
  • Georg May
  • Siegfried Müller
  • Roland Schäfer
Article

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.

Keywords

Grid adaptivity Multiresolution analysis High-order methods Multiwavelet Discontinuous Galerkin  Conservation laws 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Nils Gerhard
    • 1
  • Francesca Iacono
    • 2
  • Georg May
    • 2
  • Siegfried Müller
    • 1
  • Roland Schäfer
    • 1
  1. 1.Institut für Geometrie und Praktische MathematikRWTH Aachen UniversityAachenGermany
  2. 2.Aachen Institute for Advanced Study in Computational Engineering ScienceRWTH Aachen UniversityAachenGermany

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