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Study on adjoint variational principles in ship hydrofynamics

船舶流体力学伴随变分原理研究

基本信息

批准号：
11450382
负责人：
MATSUMURA Kiyoshige
金额：
$ 3.01万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

A unified method of formulation for adjoint variational principles on the boundary value problem with unknown wetted surface is presented. This problem is reduced to solve a system of two integral equations. One is the equation on the hull boundary condition. The other is equality condition in height of the hull bottom to the water surface at the spray root line.Functional associated with the variational principles are formulated by integrating the weighted residuals of the kinematic condition on the water surface in addition to the one on the hull boundary. Both conditions are represented in the vortex line function set zero on the upstream water surface, and the adjoint generalized vortex line function, the one of the weight functions, is set zero on the downstream water surface. The other weight function is the integration factor found commonly in those two boundary conditions. Owing to the integration factor, the residual integration over the water surface is replaced with the bottom height of the hull at the spray root line, so that the equality condition in height is included smoothly in the functional.In 2D simple case, the adjoint variable is related to the natural one by coordinate reverse. As a result, the functional mentioned above is able to be reduced to the quadratic formula which does not include any more adjoint variable.

本文给出了湿表面未知边值问题伴随变分原理的统一列式方法。这个问题归结为求解一个两个积分方程组。一个是关于船体边界条件的方程。另一种是船体底部到水面高度相等的条件，通过对水面运动条件和船体边界运动条件的加权残量积分，建立了与变分原理相关的泛函。这两个条件都表示在涡线函数设置为零的上游水面上，和伴随的广义涡线函数，权函数之一，设置为零的下游水面上。另一个权重函数是这两个边界条件中常见的积分因子。由于引入了积分因子，将水面上的残差积分用船体在喷雾根部的底高代替，使高度相等条件平滑地包含在泛函中，在二维简单情况下，伴随变量通过坐标变换与自然变量相关联。其结果是，上述功能是能够减少到二次公式，其中不包括任何更多的伴随变量。