非線性造波水槽數值穩定性研究

Abstract

本研究主要為以邊界元素法模擬有限振幅(finite amplitude) Stokes wave及cnoidal wave(橢圓波簡稱cn wave)二種非線性數值水槽的造波模式，而造波方式分別採用虛擬直推式造波板及點源造波二種，當以直推式造波板模擬非線性波時，將會產生一因造波板有限位移所造成的高階自由波，而此自由波將使水槽內波形成非固定因此必需加以消除，在Stokes wave的情形中，可由解析解找出直推式造波板速度公式中的自由波成份並加以消除，然而在模擬cn wave的造波板公式由於是隱函式的緣故，目前並無解析解可以求得其自由波的函式，為了解決此問題，本研究另以點源造波的方式模擬數值水槽，點源造波不用造波板因此不會產生高階自由波。當以二種造波方式模擬Stokes wave時，所模擬的數值結果非常相近，但模擬cn wave時，數值結果有相當差異，因此本研究分別採用了四種速度公式來模擬cn wave，它們所模擬出來的結果有些不同，當以Wiegel水平速度公式為點源造波造波函數模擬cn wave時發生了平均水位下降的問題，本研究以試誤法找出了一個簡單的修正關係，改善了水位下降的問題，作法是在理論波谷高度加一修正高度，如此可以有效改善平均水位高度下降的情況。

In present study the fluid is assumed to be incompressible , inviscid and its motion irrotational. A fully nonlinear numerical wave tank (NWT) has been simulated by use of a boundary element method (BEM) in the time domain. The BEM is repeatedly solved at each time step and the fully nonlinear free surface boundary condition are integrated with time to update its position and boundary values. Two kinds of nonlinear waves, Stokes wave and cnoidal wave, are simulated in the NWT. The incident nonlinear waves are performed by simulating a piston motion wave maker at one end of the NWT and by aligning a series of internal point sources vertically in the middle of the NWT. In order to avoid the reflection of outgoing nonlinear waves, a numerical wave-absorption filter has been developed for open-boundary treatment by combining a so called sponge layer with a linearly distributed damping factor and a sommerfeld radiation condition. The numerical result show that the nonlinear Stokes wave NWT simulated by the present approaches agree favorably with the corresponding analytical solution. But, the agreement is less favorable for the simulation of cnoidal wave NWT.