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Applied Mathematics and Mechanics

, Volume 37, Issue 11, pp 1441–1466 | Cite as

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

  • Kailiang Wu
  • Huazhong TangEmail author
Article

Abstract

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.

Key words

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

Chinese Library Classification

O241.82 O352 

2010 Mathematics Subject Classification

65N22 65N08 65N55 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingChina
  2. 2.HEDPS, CAPT & LMAM, School of Mathematical SciencesPeking UniversityBeijingChina
  3. 3.School of Mathematics and Computational ScienceXiangtan UniversityHunan ProvinceChina

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