采用Green-Naghdi方程和有限元法计算浅水船波

采用波动方程／有限元法求解Green-Naghdi(G-N)方程计算船舶在有限水深区域的兴波和波浪阻力。把行驶船舶对水面的扰动作为移动压力直接加在Green-Naghdi方程里，以描述运动船体和水面的相互作用，并经此来计算不面波动、船底水动压力和波浪阻力。G－N方程比浅水方程增加一个非线性的频散项，以补充有限水深对浅水船波的影响。采用随船运动网格的有限方法，以Series 60 CB=0.6船作为算例给出浅水船波的计算结果，并与浅水方程的结果进行了比较。计算结果表明，当船速小于临界速度时，由于频散的影响，G－N方程级出的船后尾波波高比浅水方程的结果大，同时波浪阻力也比浅水方程的结果有所提高。当船速大于临界速度时，G－N方程的计算结果与浅水方程基本相同，频率散射无明显影响。

Numerical Study of Ship Waves in Shallow Water based on Green-Naghdi Equation

This paper employs Green Naghdi (G N) equation to study ship waves in shallow water of finite depth. The ship body is considered as a moving pressure disturbance on free surface. The water depth volriation, nonlinearity, frequency dispersion, free surface disturbance, energy dissipation and boundary reflection may play important roles to ship waves. These problems are hardly studied together based on potential theory. Green Naghdi equation is a typical Boussinesq type equation, which involves nonlinearity and frequency dispersion. Furthermore, Green Naghdi equation does not require irrotational condition and the limitation of the ratio of wave height to water depth. The frequency dispersion term of G N equation accounts for the effects of finite eater depth on ship waves. In present work the moving pressure is added to Green Naghdi equation to investigate the interaction of the ship body and free surface. Wave equation model and finite element method (WE/FEM) with moving grids are used to solve Green Naghdi equation. The numerical examples of a Series 60 C B= 0.6 ship are presented. Three dimensional free surface elevations and wave resistance are given. A comparison between the results predicted by the G N equation and the shallow water equation is made. The numerical results indicate that the wave resistance predicted by G N equation is lager than that predicted by shallow water equation when the depth Froude number is less then one (F r=gh<1) , and the frequency dispersion is needed for ship waves in subcritical flows. In supercritical flows (F r=gh>1) , the G N equation and the shallow water equation give almost the same results, the frequency dispersion may be negligible.