包含泥沙冲淤的浅水方程的混合有限元法(Ⅱ)——时间沿特征方向离散的全离散情形

罗振东; 朱江; 曾庆存; 谢正辉

包含泥沙冲淤的浅水方程的混合有限元法(Ⅱ)——时间沿特征方向离散的全离散情形

基金项目: 国家自然科学基金资助项目(10071052;49776283);中国科学院"百人计划"资助项目;国家杰出青年科学基金资助项目(40225015);北京市优秀人才专项经费资助项目;北京市自然科学基金资助项目

详细信息

作者简介:
罗振东(1958- ),男,广西桂平人,教授,博士,博士生导师,研究方向:有限元法及其应用(联系人.Tel:86-10-68902352;Fax:86-10-68902785;E-mail:luozhd@mail.cnu.edu.cn);曾庆存(1935- ),男,广东人,研究员,中科院院士,博士,博士生导师,从事地球流体力学、大气环流、数值天气预报理论、气侯动力学和气侯数值模拟、环境生态动力学、自然控制论、大气遥感等方面的研究.

中图分类号: O241.4
计量
- 文章访问数: 2847
- HTML全文浏览量: 150
- PDF下载量: 502
- 被引次数: 0
出版历程
- 收稿日期: 2000-08-30
- 修回日期: 2003-06-28
- 刊出日期: 2004-02-15

Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics

摘要

摘要: 进一步研究由水动力学方程、泥沙输运方程和河床变化方程组成的浅水方程混合有限元法，给出时间沿特征方向离散的一种全离散格式，并证明全离散的水流速度、床底高度、水体厚度、水中泥沙含量的混合有限元解的存在性和收敛性(误差估计)．
- 混合有限元法 /
- 浅水方程 /
- 误差估计 /
- 水流和泥沙淤积 /
- 特征方法
Abstract: The mixed finite element(MFE)methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.
- mixed finite element method /
- shallow water equation /
- error estimate /
- current and silt sedimentation /
- characteristics method

HTML全文

参考文献(12)

[1]	Boris J P,Book D L.Flux corrected transport[J].SHASTA J Comput Phys,1973,2(1):36—69.
[2]	Pironneau O.On the transport-diffusion algorithm and its applications to the Navier-Stokes equations[J].Numer Math,1982,38(2):309—332. doi: 10.1007/BF01396435
[3]	Bermúdez A,Rodriguez′ C,Vilar M A.Solving shallow water equations by a mixed implicit finite element method[J].IMA J Numer Anal,1991,11(1):79—97. doi: 10.1093/imanum/11.1.79
[4]	罗振东，朱江，曾庆存，等.包含泥沙冲淤的浅水方程的混合有限元法(Ⅰ)——时间连续的情形[J].应用数学和力学，2004，25(1)：74—84.
[5]	忻孝康，刘儒勋，蒋伯诚.计算流体动力学[M].长沙：国防科技大学出版社，1989.
[6]	ZENG Qing-cun.Silt sedimentation and relevant engineering problem—an example of natural cybernetics[A].In:Proceeding of the Third International Congress on Industrial and Applied Mathematics[C].ICIAM95 held in Hamburg,Academic Verlag,1995,463—487.
[7]	Chipada S,Dawson C N,Martinez M L,et al.Finite element approximations to the system of shallow water equations—Ⅰ:Continuous-time a priori error estimates[J].SIAM J Numer Anal,1998,35(2):692—711. doi: 10.1137/S0036142995296515
[8]	Adams R A.Sobolev Spaces[M].New York:Academic Press,1975.
[9]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam:North-Holland,1978.
[10]	罗振东.有限元混合法理论基础及其应用[M].济南：山东教育出版社，1996.
[11]	Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].Berlin,Heidelberg,New York:Springer-Verlag,1991.
[12]	Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations[M].Berlin Beidelberg, New York:Springer-Verlag,1979.