摘要:
1956-1960年间由Turner[13],Clough[16]等引入有限元概念、方法以来,首先在结构分析领域内取得极大进展.与此同时,它也应用于固体力学的许多领域[2,4,7].在七十年代,有限元方法较广泛地应用于流体力学的许多领域[3,11,12].最近几年来,有限元方法也应用于物理海洋学中的一些问题中,例如湖泊与海洋环流问题[14,15,19],潮汐与风暴潮问题[17]等.本文从流体力学原理出发,应用有限元理论建立了黑潮的三维流场有限元方程组.采用了海流理论中常见的物理模式[1,5,18],考虑了压力梯度、柯氏力、重力、水平与垂直方向上的湍流摩擦效应,而不考虑惯性力的影响.本文对所应用的有限元几何形状——三角棱柱进行了插值误差分析,证明了三角形棱面不能出现较大的钝角,也证明了完备性的问题.并将动力计算和有限元二种方法计算的流速进行了比较.
Abstract:
In recent years,applications of finite element methods to some problems in physical oceanography have been reported.The present paper is devoted to application of finite element methods to the calculation of three-dimentional ocean current.We establish the equations of finite element approximation for three-dimensional ocean current.We start with the basic principle of fluid mechanics(the principle of virtual power)and incompres sibility of the seawater.Considering gravitational forces,coriolis forces,the forces due to gradients of pressure and lateral and vertical friction and neglecting forces due to accelerations,we can write equation(2.2).It may always be assumed in the theory of ocean currents that 1)as i=3,the vertical balance of forces are the vertical pressure gradient and gravitational force and 2) the vertical velocity component(U3m) may always be neglected except for(2.14).Then the global system of equations(Matrix forms) are given as(2.30)-(2.32).The finite element interpolation error is given as(3.14).The discussion of results and problems,see part 4.
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