Study on adjoint variational principles in ship hydrofynamics

船舶流体力学伴随变分原理研究

• 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
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11450382/
• 关键词: adjoint variational principle; reversed flow; integration factor; self-adjoint; adjoint integral equation; non-linear eigen-value problem; 未定境界問題; 変分原理; 滑走艇; 非定常性; クッタの条件; 随伴問題; 未定浸水面; 摂動法; 成層流

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.

提出了未知润湿表面边值问题伴随变分原理的统一表述方法。这个问题被简化为求解两个积分方程组。一是船体边界条件方程。另一种是喷射根线处船体底部距水面高度相等的条件。通过对水面运动条件的加权残差和船体上的残差进行积分，制定了与变分原理相关的函数。边界。这两种情况都在上游水面上设置为零的涡线函数中表示，并且伴随广义涡线函数（权重函数之一）在下游水面上设置为零。另一个权重函数是这两个边界条件中常见的积分因子。由于积分因子的存在，水面上的残差积分被喷水根线处的船体底部高度所代替，从而使高度相等的条件顺利地包含在泛函中。在二维简单情况下，伴随变量通过坐标反转与自然相关。因此，上述泛函可以简化为不包含任何伴随变量的二次公式。

项目成果

Kiyoshige Matsumura: "Variational Principle for Determining the Unknown Wetted Surface of a Planning Ship in Periodic Motion"J. Kansai Soc. Nova. Arch. Japan. Vol.237. (2002)

Kiyoshige Matsumura：“确定规划船周期性运动未知润湿表面的变分原理”J。

松村 清重: "上下動揺する2次元滑走板の未定浸水長問題に関する変分原理について"関西造船協会誌. 237. (2002)

Kiyoshige Matsumura：“关于上下振荡的二维滑动板的未定洪水长度问题的变分原理”，关西造船协会杂志 237。（2002）

松村清重: "上下動揺する2次元滑走板の未定浸水長問題に関する積分原理について"関西造船協会誌. 237. (2002)

松村清重：“关于上下移动的二维滑动板的未定洪水长度问题的积分原理”，关西造船协会杂志 237。（2002）