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溃坝问题的间断有限元方法
引用本文:李宏,文宗川.溃坝问题的间断有限元方法[J].应用数学与计算数学学报,2003,17(2):40-48.
作者姓名:李宏  文宗川
作者单位:1. 内蒙古大学数学系,呼和浩特,010020
2. 内蒙古工业大学管理学院,呼和浩特,010020
基金项目:内蒙古大学青年科学基金(ND0107),博士科研启动项目的资助.
摘    要:本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法,给出该方法的精度分析,通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力,并将其推广到求解浅水问题.针对坝底无摩擦,无坡度的理想情形进行讨论,给出方溃坝和圆溃坝问题的数值模拟结果.

关 键 词:有限元方法  精度分析  方溃坝  圆溃坝  数值模拟
修稿时间:2002年10月20

Discontinuous Finite Element Method for Dam Break Problems
Li Hong Wen Zongchuan Dept. of Math. of Inner Mongolia University,Huhhot ,China Management insituite of Inner Mongolia Polytechnic University,Huhhot ,China.Discontinuous Finite Element Method for Dam Break Problems[J].Communication on Applied Mathematics and Computation,2003,17(2):40-48.
Authors:Li Hong Wen Zongchuan Dept of Math of Inner Mongolia University  Huhhot  China Management insituite of Inner Mongolia Polytechnic University  Huhhot  China
Institution:Li Hong Wen Zongchuan Dept. of Math. of Inner Mongolia University,Huhhot 010020,China Management insituite of Inner Mongolia Polytechnic University,Huhhot 010020,China
Abstract:In this paper we study the Runge-Kutta discontinuous Galerkin finite element method pro-posed at 1990's. We gave the accuracy analysis,proved the ability to capture the sharp wave in solving discontinuous problems. In the mean time,the method is generalized to solve shallow water equations.The ideal problems without friction and slope on bed are discussed.The simulations of square and circular dam problems are given.
Keywords:Runge-Kutta discontinuous Galerkin finite element method  shallow water equa-tions  numerical simulations  
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