浅水波的位移法求解  

Solving shallow water waves with the displacement method

作　　者：钟万勰[1] 陈晓辉[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室工程力学系,大连116023

出　　处：《水动力学研究与进展（A辑）》2006年第4期486-493,共8页Chinese Journal of Hydrodynamics

基　　金：自然科学基金(10421002;10372019;10272026)

摘　　要：浅水波的速度分布与水深无关,位移也与水深无关,相当于杆件的刚性横截面假定。文中采用物质坐标,用水平位移作为基本未知量,将浅水波分析按固体力学中杆件非线性大位移问题处理。于是,分析力学的变分原理都可运用了。可采用正则变换,近似解的保辛积分等有效手段进行数值求解。以三峡升船机船厢中水波为例的计算,说明所论方法的有效性。The horizontal velocity distribution of shallow water wave theory is independent on the vertical coordinate , it implies that the horizontal displacement is independent on too, which corresponds to the rigid transverse cross section assumption of the rod theory in structural mechanics. Using the material coordinate as in analytical mechanics, the horizontal displacement is selected as the fundamental function to solve, therefore the shallow water wave analysis becomes the large displacement non-linear problem in structural mechanics. Analytical mechanics and the corresponding variational principles can be applied now. The powerful methodology, such as canonical transformation and symplectic conservative approximate FEM discretization and so on, is quite beneficial to numerical solution. The water waves in the pool of three-gorge ship-lift are used as numerical examples, and the symplectic conservative time integration gives satisfactory result.

关 键 词：浅水波 位移法 混合能密度 保辛 

分 类 号：TV131.2[水利工程—水力学及河流动力学] TB301[一般工业技术—材料科学与工程]