Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws

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	Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws
	Tang, HZ ; Tang, T
	2003
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	41 期号:2 页码:487-515
摘要	We develop efficient moving mesh algorithms for one- and two-dimensional hyperbolic systems of conservation laws. The algorithms are formed by two independent parts: PDE evolution and mesh-redistribution. The first part can be any appropriate high-resolution scheme, and the second part is based on an iterative procedure. In each iteration, meshes are first redistributed by an equidistribution principle, and then on the resulting new grids the underlying numerical solutions are updated by a conservative-interpolation formula proposed in this work. The iteration for the mesh-redistribution at a given time step is complete when the meshes governed by a nonlinear equation reach the equilibrium state. The main idea of the proposed method is to keep the mass-conservation of the underlying numerical solution at each redistribution step. In one dimension, we can show that the underlying numerical approximation obtained in the mesh-redistribution part satisfies the desired TVD property, which guarantees that the numerical solution at any time level is TVD, provided that the PDE solver in the first part satisfies such a property. Several test problems in one and two dimensions are computed using the proposed moving mesh algorithm. The computations demonstrate that our methods are efficient for solving problems with shock discontinuities, obtaining the same resolution with a much smaller number of grid points than the uniform mesh approach.
关键词	adaptive mesh method hyperbolic conservation laws finite volume method
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000183233500004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18065
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, HZ
作者单位	1.Chinese Acad Sci, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Tang, HZ,Tang, T. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2003,41(2):487-515.
APA	Tang, HZ,&Tang, T.(2003).Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws.SIAM JOURNAL ON NUMERICAL ANALYSIS,41(2),487-515.
MLA	Tang, HZ,et al."Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws".SIAM JOURNAL ON NUMERICAL ANALYSIS 41.2(2003):487-515.