小振幅波有限差分方法数值模拟

摘要

The model of small-amplitude water wave has been developed based on potential flow theory. There are Numerical experiments of water wave motion undertaken in a two dimensional tank. Crank-Nicolson’s implicit scheme is adopted to discretize the equations about the linear potential flow. Firstly, coordinate transformation is introduced to map the time-dependent irregular physical domain to a time-independent fixed square calculation domain. Secondly, a staggered mesh system is applied to divide calculation domain. The numerical results agree well with analytic result and small-amplitude wave have standing wave linear features and node immobility.%　　文章研究了二维水槽下线性势流方程小振幅波的数值解，采用Crank-Nicolson隐式有限差分方法对线性势流方程组进行离散。通过坐标变换将随不规则物理区域变换成一个固定的正方形计算区域，运用交错网格对计算区域进行分割。数值模拟自由面小振幅波的波高，计算出自由面波高的误差值。数值结果表明数值解很好地吻合解析解以及小振幅波具有驻波的线性特征和波节不动性。