浅水波的位移法求解

Solving shallow water waves with the displacement method

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.