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Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations

被引：36
|
作者：
Li, Gang [2 ,3 ]
Lu, Changna [4 ]
Qiu, Jianxian [1 ,2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
[3] Qingdao Univ, Sch Math Sci, Qingdao 266071, Shandong, Peoples R China
[4] Nanjing Univ Informat Sci & Technol, Coll Math & Phys, Nanjing 210044, Jiangsu, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2012年 / 51卷 / 03期
关键词：
WENO approximation; Up-wind linear approximation; Troubled-cell indicator; Shallow water equations; Hybrid schemes; Source term; DISCONTINUOUS GALERKIN METHODS; EXACT CONSERVATION PROPERTY; SOURCE TERMS; EFFICIENT IMPLEMENTATION; HYPERBOLIC SYSTEMS; ENO; GRADIENT; LAWS;
D O I：
10.1007/s10915-011-9520-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In (J. Comput. Phys. 229: 8105-8129, 2010), Li and Qiu investigated the hybrid weighted essentially non-oscillatory (WENO) schemes with different indicators for Euler equations of gas dynamics. In this continuation paper, we extend the method to solve the one- and two-dimensional shallow water equations with source term due to the non-flat bottom topography, with a goal of obtaining the same advantages of the schemes for the Euler equations, such as the saving computational cost, essentially non-oscillatory property for general solution with discontinuities, and the sharp shock transition. Extensive simulations in one- and two-dimensions are provided to illustrate the behavior of this procedure.
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页码：527 / 559
页数：33
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