The method of non-linear time transformation in boundary-value problems of potential theory with moving boundaries for the non-linear wave equation

1991 ◽  
Vol 55 (6) ◽  
pp. 944-948
Author(s):  
V.A. Pozdeyev
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Potential Theory ◽  
Linear Time ◽  
Boundary Value ◽  
Moving Boundaries ◽  
Time Transformation ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Non Linear

Non-Linear Wave Loads Acting on Obliquely Slowly Advancing Platform

2009 ◽  
Author(s):  
Yasunori Nihei ◽  
Sota Sugimoto ◽  
Takashi Tsubogo ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Boundary Value ◽  
The Body ◽  
Linear Wave ◽  
Wave Loads ◽  
Forward Speed ◽  
Wave Drift ◽  
Non Linear ◽  
Drift Force

It is necessary to evaluate wave drift force for ships advancing obliquely. There are some approaches, for instance the strip method, solving the Navier-Stokes equation directly in the fluid domain (CFD), potential theory and so on. In the present study, the non-linear wave loads acting on the ship with constant oblique forward speed is considered based on the potential theory. Consistent perturbation expansion based on two parameters, i.e. the incident wave slope and the ratio of the forward speed compared to the phase velocity of the waves, is performed on a moving frame (body-fixed) coordinate system to simplify the problem. So obtained boundary value problems for each order of potentials is solved by means of the hybrid method. The fluid domain is divided into two regions by an artificial circular cylinder surrounding the body. The potential in the inner region is expressed by an integral over the boundary surface with a Rankin source as its Green function while it is expressed in the eigen function expansion for the outer region. Consequently, the boundary value problems can be solved efficiently. In the present paper, the authors will discuss the effects of the obliquely advancing on the wave drift force in a diffraction wave field up to the order proportional to the advancing speed. An ellipsoid model is used in the calculation and the wave drift force is evaluated for various Froude number.

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