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

Published online by Cambridge University Press:  20 August 2015

Hong Luo ,
Luqing Luo  and
Robert Nourgaliev
Hong Luo*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
Luqing Luo*
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
Robert Nourgaliev*
Affiliation:
Thermal Science and Safety Analysis Department, Idaho National Laboratory, Idaho Falls, ID, 83415, USA
*
Corresponding author.Email address:hong_luo@ncsu.edu
Email address:lluo2@ncsu.edu
Email address:Robert.Nourgaliev@inl.gov
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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.

Keywords

65M6065M9976M2576M10Discontinuous Galerkin methodsleast-squares reconstructioncompressible Euler equations
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1495 - 1519
Copyright
Copyright © Global Science Press Limited 2012

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