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High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields
Qian, Shouguo1; Liu, Yu1; Li, Gang1; Yuan, Li2,3
2018-07-15
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume329Pages:23-37
AbstractEuler equations under gravitational fields often appear in some interesting astrophysical and atmospheric applications. The Euler equations are coupled with gravitational source term due to the gravity and admit hydrostatic equilibrium state where the flux produced by the pressure gradient is exactly balanced by the gravitational source term. In this paper, we construct high order discontinuous Galerkin methods for the Euler equations under gravitational fields, which are well-balanced for the isentropic type hydrostatic equilibrium state. To maintain the well-balanced property, we first reformulate the governing equations in an equivalent form. Then we propose a novel source term approximation based on a splitting algorithm as well as well-balanced numerical fluxes. Rigorous theoretical analysis and extensive numerical examples all suggest that the proposed methods maintain the hydrostatic equilibrium state up to the machine precision. Moreover, one-and two-dimensional simulations are performed to test the ability of the current methods to capture small perturbation of such equilibrium state, and the genuine high order accuracy in smooth regions. (C) 2018 Elsevier Inc. All rights reserved.
KeywordEuler equations Isentropic equilibrium state Discontinuous Galerkin methods Well-balanced property Gravitational fields
DOI10.1016/j.amc.2018.01.059
Language英语
Funding ProjectNatural Science Foundation of PR China[11771228] ; Natural Science Foundation of PR China[11321061] ; Natural Science Foundation of PR China[11261160486] ; Natural Science Foundation of PR China[91641107]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000427813700004
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30085
Collection计算数学与科学工程计算研究所
Affiliation1.Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Qian, Shouguo,Liu, Yu,Li, Gang,et al. High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields[J]. APPLIED MATHEMATICS AND COMPUTATION,2018,329:23-37.
APA Qian, Shouguo,Liu, Yu,Li, Gang,&Yuan, Li.(2018).High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields.APPLIED MATHEMATICS AND COMPUTATION,329,23-37.
MLA Qian, Shouguo,et al."High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields".APPLIED MATHEMATICS AND COMPUTATION 329(2018):23-37.
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