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

  • Jian-Guo Liu
  • Chi-Wang Shu
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)


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.


Discontinuous Galerkin Method Finite Element Space Optimal Error Estimate Continuous Finite Element Total Energy Conservation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jian-Guo Liu
    • 1
  • Chi-Wang Shu
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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