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


A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

Hong Luo 1*, Luqing Luo 1, Robert Nourgaliev 2

1 Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA.
2 Thermal Science and Safety Analysis Department, Idaho National Laboratory, Idaho Falls, ID, 83415, USA.

Received 25 September 2011; Accepted (in revised version) 3 February 2012
Available online 22 May 2012
doi:10.4208/cicp.250911.030212a

Abstract

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant 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.

AMS subject classifications: 65M60, 65M99, 76M25, 76M10

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Key words: Discontinuous Galerkin methods, least-squares reconstruction, compressible Euler equations.

*Corresponding author.
Email: hong_luo@ncsu.edu (H. Luo), lluo2@ncsu.edu (L. Luo), Robert.Nourgaliev@inl.gov (R. Nourgaliev)
 

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