中文摘要：

开发了一种基于非均匀有理B样条（NURBS）的Rankine源高阶面元法用于求解浅水中下潜物体有航速辐射问题。基于势流理论,流场中的扰动速度势用物体表面和自由面上分布的Rankine源来表达,同时用映像法计及水底的影响;采用NURBS曲面精确表达物面和自由面,在求出边界面上的未知源强后,物体表面的速度势分布用B样条表示;采用配置方法对边界积分方程进行求解,采用高斯—勒让德公式计算方程中的积分,同时开发了一种解决数值积分中奇异性问题的方法。采用文中数值方法求解了浅水中下潜圆球的有航速辐射问题,计算得到了下潜圆球水动力系数和自由面波形,所得水动力系数计算结果和他人的计算结果进行了比较,其吻合程度良好,从而验证了文中开发方法的有效性。

英文摘要：

A high-order Rankine panel method based on Non-Uniform Rational B-Splines （NURBS） is developed for solving the radiation problem of a submerged body with forward speed in shallow water. Based on the potential flow theory, the disturbance velocity potential is expressed by Rankine source dis- tributions on the body surface and free surface, whereas the method of images is applied to account for the effect of the water bottom. A NURBS surface is used to precisely represent the body geometry and free sur- face. The velocity potential on the body surface is described by B-splines, after the source density distri- bution on the boundary surface is determined. A collocation approach is applied to solve the boundal~~ in- tegral equation and the integral is evaluated by applying Gauss-Legendre quadrature.A method is devel- oped to deal with the singularity in the numerical integral.The radiation problem of a submerged sphere with forward speed in shallow water is solved by the numerical method to obtain the hydrodynamic coeffi-cients and wave pattern. The numerical results of hydrodynamic coefficients are in good agreement with the calculation results obtained by others, which shows the validity of the proposed numerical method.