A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations

被引:111
作者
Bunya, Shintaro [2 ]
Kubatko, Ethan J. [3 ]
Westerink, Joannes J. [4 ]
Dawson, Clint [1 ]
机构
[1] Univ Texas Austin, Austin, TX 78712 USA
[2] Univ Tokyo, Bunkyo Ku, Tokyo 1138656, Japan
[3] Ohio State Univ, Columbus, OH 43210 USA
[4] Univ Notre Dame, Notre Dame, IN 46556 USA
基金
日本学术振兴会; 美国国家科学基金会;
关键词
Shallow water equations; Wetting and drying; Moving boundary; Discontinuous Galerkin method; RKDG method; FINITE-ELEMENT-METHOD; WAVE-EQUATION; MODEL; ORDER; DISCRETIZATIONS; FLOWS;
D O I
10.1016/j.cma.2009.01.008
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper proposes a wetting and drying treatment for the piecewise linear Runge-Kutta discontinuous Galerkin approximation to the shallow water equations. The method takes a fixed mesh approach as opposed to mesh adaptation techniques and applies a post-processing operator to ensure the positivity of the mean water depth within each finite element. In addition, special treatments are applied in the numerical flux computation to prevent an instability due to excessive drying. The proposed wetting and drying treatment is verified through comparisons with exact solutions and convergence rates are examined. The obtained orders of convergence are close to or approximately equal to 1 for solutions with discontinuities and are improved for smooth solutions. The combination of the proposed wetting and drying treatment and a TVB slope limiter is also tested and is found to be applicable on condition that they are applied exclusively to an element at the same Runge-Kutta step. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:1548 / 1562
页数:15
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