A general outer boundary condition for time-dependent wave-body interaction problems is developed. The technique is based on domain decomposition and the unsteady free-surface Green function solution of the flow in an outer region. The boundary condition results in a shell condition which may be applied to a variety of interior solution methods. When the interior solution method is a boundaryintegral method, an implicit matching can be done. When a volume-discretization method is used in the interior region, a newly developed explicit matching procedure is performed. Demonstrations of the transparent properties of this shell are made for several unsteady problems.

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