Viscous and inviscid matching of three-dimensional free-surface flows utilizing shell functions
A methodology is presented for matching a solution to a three-dimensional free-surface viscous flow in an interior region to an inviscid free-surface flow in an outer region. The outer solution is solved in a general manner in terms of integrals in time and space of a time-dependent free-surface Green function. A cylindrical matching geometry and orthogonal basis functions are exploited to reduce the number of integrals required to characterize the general solution and to eliminate computational difficulties in evaluating singular and highly oscillatory integrals associated with the free-surface Green-function kernel. The resulting outer flow is matched to a solution of the Navier–Stokes equations in the interior region and the matching interface is demonstrated to be transparent to both incoming and outgoing free-surface waves.
KeywordsIntegral equations Open-boundary condition Pseudo-spectral solutions Time-dependent free-surface Green function Viscous-inviscid matching Wave-body interaction
R.W. Yeung acknowledges partial support for the preparation of this article under Office of Naval Research Grant No. N00014-09-1086 at UC Berkeley. J. A. Hamilton acknowledges support from the David and Lucille Packard foundation.
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