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A characteristic space-time conservation element and solution element method for conservation laws
Shen H; Wen CY; Zhang DL(张德良); Wen, CY (reprint author), Hong Kong Polytech Univ, Dept Mech Engn, Kowloon, Hong Kong, Peoples R China.
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
2015-05-01
Volume288Pages:101-118
ISSN0021-9991
AbstractIn this paper, an upwind space-time conservation elementand solution element(CE/SE) method is developed to solve conservation laws. In the present method, the mesh quantity and spatial derivatives are the independent marching variables, which is consistent with the original CE/SE method proposed by Chang (1995) [5]. The staggered time marching strategy and the definition of conservation element (CE) also follow Chang's propositions. Nevertheless, the definition of solution element (SE) is modified from that of Chang. The numerical flux through the interface of two different conservation elements is not directly derived by a Taylor expansion in the reversed time direction as proposed by Chang, but determined by an upwind procedure. This modification does not change the local and global conservative features of the original method. Although, the time marching scheme of mesh variables is the same with the original method, the upwind fluxes are involved in the calculation of spatial derivatives, yielding a totally different approach from that of Chang's method. The upwind procedure breaks the space-time inversion invariance of the original scheme, so that the new scheme can be directly applied to capture discontinuities without spurious oscillations. In addition, the present method maintains low dissipation in a wide range of CFL number (from 10(-6) to 1). Furthermore, we extend the upwind CE/SE method to solve the Euler equations by adopting three different approximate Riemann solvers including Harten, Lax and van Leer (HLL) Riemann solver, contact discontinuity restoring HLLC Riemann solver and mathematically rigorous Roe Riemann solver. Extensive numerical examples are carried out to demonstrate the robustness of the present method. The numerical results show that the new CE/SE solvers perform improved resolutions. (C) 2015 Elsevier Inc. Allrightsreserved.
KeywordSpace-time Conservation Element And Solution Element (Ce/se) Method Upwind Scheme Characteristic-based Scheme Riemann Solver
Subject AreaComputer Science, Interdisciplinary Applications ; Physics, Mathematical
DOI10.1016/j.jcp.2015.02.018
URL查看原文
Indexed BySCI
Language英语
WOS IDWOS:000351079900006
WOS KeywordGODUNOV-TYPE METHODS ; DIFFERENCE SCHEME ; EULER EQUATIONS ; SYSTEMS ; FLOWS
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
Funding OrganizationResearch Grants Council, Hong Kong [GRF 526913] ; Department of Mechanical Engineering, The Hong Kong Polytechnic University under Departmental General Research Fund [4-ZZE8] ; National Natural Science Foundation of China [11372265]
DepartmentLHD激波与爆轰物理
Classification一类
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/49916
Collection高温气体动力学国家重点实验室
Corresponding AuthorWen, CY (reprint author), Hong Kong Polytech Univ, Dept Mech Engn, Kowloon, Hong Kong, Peoples R China.
Recommended Citation
GB/T 7714
Shen H,Wen CY,Zhang DL,et al. A characteristic space-time conservation element and solution element method for conservation laws[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2015,288:101-118.
APA Shen H,Wen CY,张德良,&Wen, CY .(2015).A characteristic space-time conservation element and solution element method for conservation laws.JOURNAL OF COMPUTATIONAL PHYSICS,288,101-118.
MLA Shen H,et al."A characteristic space-time conservation element and solution element method for conservation laws".JOURNAL OF COMPUTATIONAL PHYSICS 288(2015):101-118.
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