一种基于数值保角变换的计算限制水域中船舶水动力的方法

A Method of Computing Ship Hydrodynamics in Restricted Waterways Based on Numerical Conformal Mapping

本文是在细长体理论的基础上，利用匹配渐近展开的方法，导出了反映船舶在限制水域中运动的横流积分方程。并利用数值保角变换的方法，求解了包括非对称多边形边界在内的复杂边界限制水域中的障碍格林函数。特别是重点研究了针对不同特点多边形边界而采用的保角变换处理方法，给出了能避免数值奇异性产生的保角变换过程和计算公式。最后，算例得到与其它算法（面源法）和试验相一致的结果。

In this paper, the lateral flow integral equation about the movement of ship in restricted waterways is obtained by the matched asymptotics technique based on slender body theory. Numerical conformal mapping method is employed to determine obstarcle Green function in restricted waterways with complicated boundary, including asymmetric polygon boundary. In particular, different applyings of conformal mapping methods are investigated in detail according to the character of polygon boundary I conformal transformations and its formulas to avoid numerical irregularity are also presented. In the end, two examples are given,the results are agreement with the test and the other computational method(panel method).