非线性船尾波的数值模拟

Numerical Simulation of Non-linear Stern Waves

本文对二维平底船无粘不可压非线性船尾波进行数值模拟。自由表面上采用全非线性的动力边界条件及运动边界条件,利用时间相关流函数法逼近恒定解。借助动边界坐标拟合法,在一固定的矩形转换区域上建立问题的差分解,解决了自由面数值计算所特有的一些困难,此外,在出流边界上引用了辐射条件,有效地缩短了计算域。最后,通过物理模型试验的实测结果来验证计算结果的合理理。

Stern waves are one of the important hydraulic phenomena in the fluid dynamics of ship. Investigation of the formation and hydraulic character of the stern waves by numerical method has theoretical and practical significance. There are some results having been reported by several researcher in recent years. This problem is still been studying now. This paper deals with the simulation of vertically 2-D stern waves by solving the Laplace equation of stream function with time dependent boundary fitted coordinate's method.The mapping and governing equations are descritized with explicite finite-difference scheme and solved with point-SOR method. The boundary conditions on free surface are descritized with weighted implicite finite difference scheme. To reduce the computational domain, efforts are particularly focused on treatment of outflow boundary. Two types of finite-difference schemes, Forward in ti me-centered in space and upwind in space scheme, are applied.In order to verify the varidity of the method a simplified expreriment is performed. The schematized ship model is shown in Fig 3-The time-dependent boundary fitted coordinates used in this computation is shown in Fig 6. Theresults for short and long computational domains are compared in Fig,.:,5. There-are, almost no difference between them in the region behind stern in which one is interested.' That means that the treatment of outflow boundary is good. The ^calculated waves are, 'also compared with Vanden-Broeck's results and experimental data, Fig 1, Fig 8. The agreements between them are satisfactory. The difference in amplitude between calculated wave and experimental data is due partly to the experimental condition, measuring error and due partly to the influence of viscosity. .