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A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids
Luo H; Xia YD; Spiegel S; Nourgaliev R; Jiang ZL(姜宗林); Luo, H (reprint author), N Carolina State Univ, Dept Mech & Aerosp Engn, Raleigh, NC 27695 USA.
2013-03-01
发表期刊JOURNAL OF COMPUTATIONAL PHYSICS
卷号236页码:477-492
ISSN0021-9991
摘要A reconstructed discontinuous Galerkin (RDG) method based on a hierarchical WENO reconstruction, termed HWENO (P1P2) in this paper, designed not only to enhance the accuracy of discontinuous Galerkin methods but also to ensure the nonlinear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this HWENO (P1P2) method, a quadratic polynomial solution (P-2) is first reconstructed using a Hermite WENO reconstruction from the underlying linear polynomial (P-1) discontinuous Galerkin solution to ensure the linear stability of the RDG method and to improve the efficiency of the underlying DG method. By taking advantage of handily available and yet invaluable information, namely the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the nonlinear stability of the RDG method. The developed HWENO (P1P2) method is used to compute a variety of flow problems on tetrahedral meshes to demonstrate its accuracy, robustness, and non-oscillatory property. The numerical experiments indicate that the HWENO (P1P2) method is able to capture shock waves within one cell without any spurious oscillations, and achieve the designed third-order of accuracy: one order accuracy higher than the underlying DG method.
关键词Discontinuous Galerkin Method Weno Reconstruction Unstructured Grids
学科领域计算流体力学
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收录类别SCI
语种英语
WOS记录号WOS:000314801500029
项目资助者DOE Office of Nuclear Energy's Nuclear Engineering University Program; fundamental research program of DTRA [HDTR1-10-1-0.123]
课题组名称LHD激波与爆轰物理
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被引频次:32[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://dspace.imech.ac.cn/handle/311007/47104
专题高温气体动力学国家重点实验室
通讯作者Luo, H (reprint author), N Carolina State Univ, Dept Mech & Aerosp Engn, Raleigh, NC 27695 USA.
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Luo H,Xia YD,Spiegel S,et al. A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2013,236:477-492.
APA Luo H,Xia YD,Spiegel S,Nourgaliev R,Jiang ZL,&Luo, H .(2013).A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids.JOURNAL OF COMPUTATIONAL PHYSICS,236,477-492.
MLA Luo H,et al."A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids".JOURNAL OF COMPUTATIONAL PHYSICS 236(2013):477-492.
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