Multi-domain boundary element method with dissipation

Abstract

The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method (MDBEM) is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.

Keywords

multi-domain boundary element method (MDBEM) / fairly perfect fluid / moonpool resonance / dissipation

References

[1] Guével P (1982). Le problème de diffraction-radiation-Première partie: Théorèmes fondamentaux. ENSM, Univ. Nantes.

[2] Chen XB (2004). Hydrodynamics in offshore and naval applications-Part I. Keynote Lecture of 6th Intl Conf HydroDynamics, Perth, Australia.

[3] Molin B. On the piston and sloshing modes in moonpools. Journal of Fluid Mechanics, 2001, 430(1): 27-50

[4] Newman J (2003). Low-frequency resonance of moonpools. Proc.18th IWWWFB, Carry-Le-Rouet, France.

[5] Sadó Garriga O, Falzarano JM (2004). Water waves and marine structure interaction. Proc. 23rd OMAE, Vancouver, Canada, 1155–1165.

[6] Dai Y.S., Duan W.Y. Potential flow theory of ship motions in waves, 2008, Beijing, China: The National Defense Industries Press

[7] Martin PA, Risso FJ (1993). Boundary integral equations for bodies of small, but finite, thickness. Proc. 8th IWWWFB, St John’s, Canada.