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

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A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same ... continued below

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Luo, Hong; Luo, Luquing; Nourgaliev, Robert & Mousseau, Vincent June 1, 2009.

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A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.

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  • 19th AIAA CFD Conferencel ,San Antonio, TX, USA,06/22/2009,06/25/2009

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  • Report No.: INL/CON-09-16255
  • Grant Number: DE-AC07-99ID-13727
  • Office of Scientific & Technical Information Report Number: 963749
  • Archival Resource Key: ark:/67531/metadc935345

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  • June 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 1, 2016, 1:42 p.m.

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Luo, Hong; Luo, Luquing; Nourgaliev, Robert & Mousseau, Vincent. A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids, article, June 1, 2009; [Idaho]. (digital.library.unt.edu/ark:/67531/metadc935345/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.