浅水环流问题的有限元分析

吕玉麟; 赖国璋

浅水环流问题的有限元分析

大连工学院工程力学研究所

计量
- 文章访问数: 1788
- HTML全文浏览量: 85
- PDF下载量: 422
- 被引次数: 0
出版历程
- 收稿日期: 1982-12-27
- 刊出日期: 1984-10-15

The Mathematical Modelling of Near Coast Shallow Water Circulation

Dalian Institute of Technology, Dalian

摘要

摘要: 考虑涡流粘性,底部摩擦,Coriolis力和重力作用,以单层模型的竖直向积分建立二维流动的环流控制方程.用Galerkin加权余量法建立环流边值问题的弱形式.用有限元法和分裂时间法分别离散空间和时间进行数值近似计算.采用线性内插的“人工光滑”处理以消除短波长噪音干扰,而避免已有的大阻尼系数方法等缺陷.为节省计算内存容量,程序中建立稀疏矩阵的一维紧凑存贮格式,排除了全部“零”元素的容量要求.

Abstract: This paper presents a finite element method to solve the shallow water circulation problem numerically.Considering the Coriolis effect,bottom friction and eddy viscosity,the continuity equation and momentum equation are integrated vertically. Using Galerkin weighted residual method,the weak variational formulation is derived for the finite element analysis. The split-time method is applied for the numerical integration instead of iteration for nonlinear terms. Moreover,an artificial smooth approach is proposed to suppress the short wavelength noise.In order to save computer storage units,a densed storage scheme is set up,where all the zero elements in large scaled and sparse matrices are excluded.

HTML全文

参考文献(11)

[1]	Leendertse,J.J.,Aspects of a Computational model for long period water wave propagation,Rand Corp.RM-5294-PR,(1967).
[2]	金子史雄、崛江毅、村上和男.ADI法による潮流污染掂散の数值酬算—大阪湾に遭用した场合につひこ.港湾技衔研究所银告,14,1(1975).
[3]	Liggett,J.A.and D.A.Woolhiser,DifFerence solutions of the shallow water equation,Jour.Engng.Mech.Division,ASME,EM2,April,(1967).
[4]	Taylor,C.and J.Davis,Tidal and long water propagation-A finite element approach,Computers and Fluids,Vol.3,(1975).
[5]	Connor,J.J.and J.D.Wang,Mathematical models of the Massachusetts Bay,Part I,MIT Sea Grant Technical Report,MITSG 74-4,(1973).
[6]	Easton,A.K.and H.R.Milner,Comparison of two tidal model for Cario Bay,Victoria Finite Element Methods is Engineering,Dec.(1976).
[7]	Kawahare,M.,A.Takeuchi and T.Yoshida,Two step explicit finite element method for Tsunami wave propagation analysis,Int.J.Num.Meth.Engng.Vol.12,No.2,(1978).
[8]	Gray,W.G.and D.R.Lynch,On the control of noise in finite element tidal computations,Computers and Fluids,Vol.7,No.3.March,(1979).
[9]	Grotkop,G.,Finite element analysis of long-period water waves,Comp.Math.in Appl.Mech.and Engng.,Vol 2,(1973).
[10]	Norton,W.R.,I.P.King and G.T.Orlob,A finite element model for lower granite reservoir,Water Resources,Engineers Inc.,Walnut Creek,(1973).
[11]	Withum,D.,K.P.Holz and U.Meissner,Finite element formulations for tidal wave analysis,Computer Methods in Applied Mechanics and Engineering,17/18(1979).