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

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.

Authors:
; ;
Publication Date:
Research Org.:
Idaho National Laboratory (INL)
Sponsoring Org.:
USDOE
OSTI Identifier:
1062197
Report Number(s):
INL/JOU-13-28296
DOE Contract Number:  
DE-AC07-05ID14517
Resource Type:
Journal Article
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 12; Journal Issue: 5
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; least-squares reconstruction; compressible Euler equations; Discontinuous Galerkin methods

Citation Formats

Hong Luo, Luqing Luo, and Robert Nourgaliev. A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids. United States: N. p., 2012. Web.
Hong Luo, Luqing Luo, & Robert Nourgaliev. A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids. United States.
Hong Luo, Luqing Luo, and Robert Nourgaliev. Thu . "A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids". United States.
@article{osti_1062197,
title = {A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids},
author = {Hong Luo and Luqing Luo and Robert Nourgaliev},
abstractNote = {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.},
doi = {},
journal = {Communications in Computational Physics},
number = 5,
volume = 12,
place = {United States},
year = {2012},
month = {11}
}