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	A Newton multigrid method for steady-state shallow water equations with topography and dry areas
	Wu, Kailiang ; Tang, Huazhong
	2016
关键词	Newton method multigrid block symmetric Gauss-Seidel shallow water equation (SWE) steady-state solution DISCONTINUOUS GALERKIN METHOD GAS-KINETIC SCHEME SOURCE TERMS WENO SCHEMES FLOWS ACCURACY MESHES GRIDS
英文摘要	A Newton multigrid method is developed for one-dimensional (1D) and two-dimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady-state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.; National Natural Science Foundation of China [91330205, 11421101]; National Key Research and Development Program of China [2016YFB0200603]; SCI(E); 中国科学引文数据库(CSCD); ARTICLE; hztang@pku.edu.cn; 11; 1441-1466; 37
语种	英语
出处	CSCD ; SCI ; 万方 ; 知网 ; http://d.g.wanfangdata.com.cn/Periodical_yysxhlx-e201611004.aspx
出版者	APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/458612]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wu, Kailiang,Tang, Huazhong. A Newton multigrid method for steady-state shallow water equations with topography and dry areas. 2016-01-01.

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