连续分段运动下势流方程的数值模拟

Numerical Simulation of Potential Flow Equation under Continuous Segmental Motion

为研究二维水槽内无旋、无粘流体在分段激励下的自由面波高和非线性,本文运用势流方程的 Crank-Nicolson有限差分方法,通过改变激励参数,画出不同激励条件下自由面的波高.数值结果表明,在单一水平激励下,不同激励频率下的波高表现出规律的周期拍的现象.在分段激励下,当水平激励消失时,自由面波高拍的现象亦消失.当自由面波高为小振幅时,自由面以驻波形式作自由振动.当自由面波高为大振幅时,波峰与波谷衰减,非线性现象出现,并且波高的振幅越大,非线性现象越明显.

In order to investigate the wave elevation on the free surface and the nonlinearity of a two dimensional tank with irrotational and inviscid fluid under segmented excitation, we utilize the Crank-Nicolson finite difference method for the potential flow equation. By changing the excitation parameters, we draw the wave height of the free surface under different excitation conditions. As shown in the numerical results, the wave elevation demonstrates the regular periodic beating phenomenon under the single horizontal excitation with different excited frequencies. Under the segmented excitation, the phenomenon of free surface wave beating disappears immediately when the horizontal excitation disappears. When the wave elevation of the free surface is small, the wave on the free surface exhibits the form of standing wave. When the free surface wave elevation is large, the wave crest and trough decrease, and the nonlinear phenomenon occurs. In addition, when the amplitude of the wave becomes larger, the nonlinear phenomenon is more obvious.