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

Publication ,  Journal Article
Liu, JG; Shu, CW
Published in: Journal of Computational Physics
May 20, 2000

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.

## Published In

Journal of Computational Physics

0021-9991

May 20, 2000

160

2

## Start / End Page

577 / 596

• Applied Mathematics
• 51 Physical sciences
• 49 Mathematical sciences
• 40 Engineering
• 09 Engineering
• 02 Physical Sciences
• 01 Mathematical Sciences

### Citation

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Liu, J. G., & Shu, C. W. (2000). A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows. Journal of Computational Physics, 160(2), 577–596. https://doi.org/10.1006/jcph.2000.6475
Liu, J. G., and C. W. Shu. “A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows.” Journal of Computational Physics 160, no. 2 (May 20, 2000): 577–96. https://doi.org/10.1006/jcph.2000.6475.
Liu JG, Shu CW. A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows. Journal of Computational Physics. 2000 May 20;160(2):577–96.
Liu, J. G., and C. W. Shu. “A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows.” Journal of Computational Physics, vol. 160, no. 2, May 2000, pp. 577–96. Scopus, doi:10.1006/jcph.2000.6475.
Liu JG, Shu CW. A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows. Journal of Computational Physics. 2000 May 20;160(2):577–596.

## Published In

Journal of Computational Physics

0021-9991

May 20, 2000

160

2

577 / 596