Volume 12, Issue 5
A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

Hong Luo, Luqing Luo & Robert Nourgaliev

Commun. Comput. Phys., 12 (2012), pp. 1495-1519.

Published online: 2012-12

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  • Abstract

A reconstruction-base ddiscontinuous Galerkin(RDG(P1P2))method, avariant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements. 

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