中文摘要：

针对潜艇在近水面航行难以定深控制问题,利用一阶泰勒展开边界元方法求解切向诱导速度精度高的优势对其垂向二阶波浪力（矩）研究。该方法对边界积分方程中的偶极强度进行泰勒展开并保留至一阶导数项,同时在格林第三公式中关于场点沿边界取切向导数封闭方程组,直接求解出速度势及其沿物面的切向速度。计算迎浪状态下椭球体的垂向二阶波浪力（矩）,与现有成果吻合度较高;进而计算迎浪状态下潜艇模型的垂向二阶波浪力（矩）。数值计算结果表明：该方法有较高的计算精度且收敛速度快。

英文摘要：

A submarine traveling near the free water surface experiences difficulty in depth control. Thus,the verti-cal second-order mean force and moment acting on the submarine were studied. One-order Taylor expansion bound-ary element method （ TEBEM） is used to improve the solution accuracy of the tangential induced velocity. This method keeps the first-order derivative for the dipole strength of the border integral equation and then takes the two tangential derivatives with respect to the field points on the boundary to form the closed equations in the third formu-la of the Green function. The velocity potential and the tangential induced velocity along object surface can be solved directly. This method was applied to calculate the vertical second-order drift loads of a submerged spheroid in head seas. The results show good agreement with previous numerical solutions. The vertical second-order drift loads of a submarine model were also calculated. TEBEM was found to achieve higher accuracy and quick convergence.