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A Numerical Example on the Performance of High Order Discontinuous Galerkin Method for 2D Incompressible Flows

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Discontinuous Galerkin Methods

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 11))

Abstract

In this presentation we explore a recently introduced high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation [8]. In this method, the momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method. The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability. The method is suitable for inviscid or high Reynolds number flows. In our previous work, optimal error estimates are proven and verified by numerical experiments. In this presentation we present one numerical example, the shear layer problem, in detail and from different angles to illustrate the resolution performance of the method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, Maryland, 20742, USA

    Jian-Guo Liu

  2. Department of Mathematics, Brown University, Providence, Rhode Island, 02912, USA

    Chi-Wang Shu

Authors
  1. Jian-Guo Liu
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  2. Chi-Wang Shu
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George E. Karniadakis  & Chi-Wang Shu  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Liu, JG., Shu, CW. (2000). A Numerical Example on the Performance of High Order Discontinuous Galerkin Method for 2D Incompressible Flows. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_35

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64098-8

  • Online ISBN: 978-3-642-59721-3

  • eBook Packages: Springer Book Archive

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