Considering the differences between the internal and external free surface conditions and the possibly thin-walled moonpool structure, the multi-region matching approach is introduced.

As shown in Figure 4.3: Fluid Regions of Floating Structures with Moonpools, a matching boundary surface below the m-th moonpool is added. The m-th moonpool internal fluid region is enclosed by , while the external fluid region is bound by alongside the free surface of , the seabed surface and the far field surface at infinity.

Denoting the diffraction wave and radiation wave potential component in the moonpool fluid region as and and the diffraction wave and radiation wave potential component in the external fluid region as and , the potential is determined by the source distribution approach:

(4–128)

where is the source strength over the integral surfaces and is the pulsating source Green function defined by Equation 4–18.

The potential of the m-th moonpool internal fluid regions is matched on with that of the external fluid region by the boundary conditions of

(4–129)