A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows


Journal Article

In this paper we introduce a high-order discontinuous Galerkin method for two-dimensional incompressible flow in the vorticity stream-function formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method. The stream function 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 efficient for inviscid or high Reynolds number flows. Optimal error estimates are proved and verified by numerical experiments. © 2000 Academic Press.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Shu, CW

Published Date

  • May 20, 2000

Published In

Volume / Issue

  • 160 / 2

Start / End Page

  • 577 - 596

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1006/jcph.2000.6475

Citation Source

  • Scopus