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

✍ Scribed by Jian-Guo Liu; Chi-Wang Shu

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
374 KB
Volume
160
Category
Article
ISSN
0021-9991

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✦ Synopsis

In this paper we introduce a high-order discontinuous Galerkin method for twodimensional 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.

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