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	Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws
	Tang, HZ ; Tang, T
	2003
关键词	adaptive mesh method hyperbolic conservation laws finite volume method SINGULAR PROBLEMS GAS-DYNAMICS MULTIPLE DIMENSIONS SPACE DIMENSIONS GRID GENERATION HARMONIC MAPS SCHEMES SYSTEMS PDES FLOW
英文摘要	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.; Mathematics, Applied; SCI(E); EI; 128; ARTICLE; 2; 487-515; 41
语种	英语
出处	SCI ; EI
出版者	siam journal on numerical analysis
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/315100]
专题	数学科学学院
推荐引用方式 GB/T 7714	Tang, HZ,Tang, T. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. 2003-01-01.

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