High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields

doi:10.1016/j.amc.2018.01.059

	High order well-balanced discontinuous Galerkin methods for Euler equations at isentropic equilibrium state under gravitational fields
	Qian, Shouguo 1; Liu, Yu 1; Li, Gang 1; Yuan, Li2,3
	2018-07-15
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	329 页码:23-37
摘要	Euler 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.
关键词	Euler equations Isentropic equilibrium state Discontinuous Galerkin methods Well-balanced property Gravitational fields
DOI	10.1016/j.amc.2018.01.059
语种	英语
资助项目	Natural 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000427813700004
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30085
专题	计算数学与科学工程计算研究所
通讯作者	Li, Gang
作者单位	1.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
推荐引用方式 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.