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A discontinuous Galerkin method with Hancock-type time integration for hyperbolic systems with stiff relaxation source terms

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Computational Fluid Dynamics 2006

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Abstract

A new discretization method for hyperbolic systems with stiff relaxation source terms (hyperbolic-relaxation equations) is introduced. The method is based on Huynh’s “upwind moment scheme” for hyperbolic conservation laws with implicit treatment of the source term. A Von Neumann analysis shows superiority in both stability and accuracy of the resulting fully discrete scheme over the method-of-line based semi-discrete schemes, and numerical experiments confirm the analysis. Our goal is developing a unified numerical method for simulating a continuum and transitional flow.

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References

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Author information

Authors and Affiliations

  1. The University of Michigan, Ann Arbor, MI 48109, USA

    Yoshifumi Suzuki

  2. The University of Michigan, Ann Arbor, MI 48109, USA

    Bram van Leer

Authors
  1. Yoshifumi Suzuki
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  2. Bram van Leer
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Corresponding author

Correspondence to Yoshifumi Suzuki .

Editor information

Editors and Affiliations

  1. Dynamique des Fluides, Institut von Karman de, Chaussee de Waterloo 72, Rhode-St.-Genese, 1640, Belgium

    Herman Deconinck

  2. Fac. Engineering, University of Ghent, Sint-Pietersnieuwstraat 41, Gent, 9000, Belgium

    E. Dick

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© 2009 Springer-Verlag Berlin Heidelberg

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Suzuki, Y., van Leer, B. (2009). A discontinuous Galerkin method with Hancock-type time integration for hyperbolic systems with stiff relaxation source terms. In: Deconinck, H., Dick, E. (eds) Computational Fluid Dynamics 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92779-2_6

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  • DOI: https://doi.org/10.1007/978-3-540-92779-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92778-5

  • Online ISBN: 978-3-540-92779-2

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