A Newton multigrid method for steady-state shallow water equations with topography and dry areas

doi:10.1007/s10483-016-2108-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (11): 1441-1466.doi: https://doi.org/10.1007/s10483-016-2108-6

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Kailiang WU¹, Huazhong TANG^2,3

1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;
2. HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;
3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China

收稿日期:2016-01-25 修回日期:2016-04-01 出版日期:2016-11-01 发布日期:2016-11-01
通讯作者: Huazhong TANG E-mail:hztang@pku.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.91330205 and 11421101) and the National Key Research and Development Program of China (No.2016YFB0200603)

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Kailiang WU¹, Huazhong TANG^2,3

1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;
2. HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;
3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, China

Received:2016-01-25 Revised:2016-04-01 Online:2016-11-01 Published:2016-11-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.91330205 and 11421101) and the National Key Research and Development Program of China (No.2016YFB0200603)

摘要/Abstract

摘要：

A Newton multigrid method is developed for one-dimensional (1D) and twodimensional (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 steadystate 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.

关键词: steady-state solution, block symmetric Gauss-Seidel, multigrid, Newton method, shallow water equation(SWE)

Abstract:

Key words: steady-state solution, multigrid, Newton method, block symmetric Gauss-Seidel, shallow water equation(SWE)

中图分类号:

Kailiang WU, Huazhong TANG. A Newton multigrid method for steady-state shallow water equations with topography and dry areas[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(11): 1441-1466.

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A Newton multigrid method for steady-state shallow water equations with topography and dry areas

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

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