非线性波浪绕射问题的数值计算

Numerical Calculation of Nonlinear Wave Diffraction

本文给出非线性波浪绕射问题的计算模型,并用时间步进和边界元法求解。该模型能适用于严重非线性情形,且能满足初始条件和辐射条件。作为对该模型的检验,我们对孤立波绕过穿刺水面的直立圆柱的算例进行了计算,并同Isaacson的解析解、李宝元的差分解进行了比较,结果吻合很好。此外我们还用数值方法同时模拟造波机造波和求该波与直立圆柱的相互作用。结果表明,数值波浪水池能够以尽可能短的暂态过程,模拟波浪与物体的相互作用,提供良好的初始条件。数值波浪水池还能用于任意水深、任意水底形状下的相互作用问题。本文的计算模型和算法具有机时省,计算稳定的优点。

The calculatipnal model of nonlinear wave diffraction is presented. The diffraction problem is solved by boundary element method coupled with time marching scheme. This model is appropriate to the serious nonlinear case, and it is easy to satisfy the initial condition and radiation condition. As an examination, the interaction of a soliton and a fixed vertical circular cylinder is calculated. The numerical results show good agreement with Isaacson's analytical solution and Li's finite difference solution. The same works have been done for the diffraction of periodic waves with the wave front which is produced by a numerical wave tank upon a fixed circular cylinder. Besides, the method may be used for any water depth and any body shape.