Study on adjoint variational principles in ship hydrofynamics

Research Project

Project/Area Number	11450382
Research Category	Grant-in-Aid for Scientific Research (B)
Allocation Type	Single-year Grants
Section	一般
Research Field	船舶工学
Research Institution	Osaka University
Principal Investigator	MATSUMURA Kiyoshige Osaka Univ. Fac. Eng., Assoc. Prof., 工学研究科, 助教授 (10135668)
Project Period (FY)	1999 – 2001
Project Status	Completed (Fiscal Year 2001)
Budget Amount *help	¥4,700,000 (Direct Cost: ¥4,700,000) Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000) Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000) Fiscal Year 1999: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywords	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
Research Abstract	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.