A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids

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A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need ... continued below

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Luo, Hong; Xia, Yidong; Nourgaliev, Robert & Cai, Chunpei June 1, 2011.

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A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.

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  • AiAA CFD Conference,Honolulu, Hawaii,06/26/2011,07/01/2011

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  • Report No.: INL/CON-11-22526
  • Grant Number: DE-AC07-05ID14517
  • Office of Scientific & Technical Information Report Number: 1027910
  • Archival Resource Key: ark:/67531/metadc831504

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  • June 1, 2011

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  • May 19, 2016, 3:16 p.m.

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  • Dec. 1, 2016, 1:42 p.m.

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Luo, Hong; Xia, Yidong; Nourgaliev, Robert & Cai, Chunpei. A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids, article, June 1, 2011; Idaho Falls, Idaho. (digital.library.unt.edu/ark:/67531/metadc831504/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.