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Journal of Engineering Mathematics

, Volume 70, Issue 1–3, pp 43–66 | Cite as

Viscous and inviscid matching of three-dimensional free-surface flows utilizing shell functions

  • J. Andrew Hamilton
  • Ronald W. Yeung
Open Access
Article

Abstract

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.

Keywords

Integral equations Open-boundary condition Pseudo-spectral solutions Time-dependent free-surface Green function Viscous-inviscid matching Wave-body interaction 

Notes

Acknowledgment

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.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Research and Development DivisionMonterey Bay Aquarium Research InstituteMoss LandingUSA
  2. 2.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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