台阶形陆架上孤立波传播的数值模拟

为了研究孤立波在带有陡升台地的陆架上的传播,用MAC方法求解了二维纳维尔-斯托克斯方程。本文在以下几点,改进了东京大学提出的修正的网格标记法:1.给出交错网格的新的标号系统;2.推导出自由表面上非规则星的新的压力迭代公式;3.对流函数、压力和速度使用了三值悬旗;4.把一维Burgers方程的部分守恒形式扩展用于二维N-S方程。这些使得程序更简单和精确。计算结果证卖,物理上很好地解释了孤立波的传播,入射波分成了反射波和透射波,然后开始分裂、破碎。 本文计算结果与线性波理论的结果很一致,但后者不能给出波运动的过程。

Numerical Simulation of a Solitary Wave Propagation on a Shelf with a Flight of Steps

The two-dimensional Navier-Stokes equations are solved by the MAC method to study a solitary wave propagation on a shelf with a terrance risen up suddenly. The modified mark and cell method presented by the Tokyo University has been improved in this paper as following: A new notation system of a staggered grid is given; 2. A new pressure iterative formula for the irregular stars on free surface is derived; 3. Hanging flags with three values is used for the stream function, pressure and velocities; 4 . A partially conservation form for one dimensional Burgers equation is used extensively to two dimensional N-S equations. All of them make the procedure more simple and accurate. It is properly clarified from computed results that the soliton propagation is interpreted physically. A incident wave is divided into a reflective wave and a transmissive wave, then begins to split and break.The results given by the present method are in good agreement with results from the linear wave theory which can not give the history of wave motion.