Journal of Engineering Mathematics

, Volume 70, Issue 1, pp 43–66

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

Open AccessArticle

DOI: 10.1007/s10665-010-9438-0

Cite this article as:
Hamilton, J.A. & Yeung, R.W. J Eng Math (2011) 70: 43. doi:10.1007/s10665-010-9438-0


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.


Integral equationsOpen-boundary conditionPseudo-spectral solutionsTime-dependent free-surface Green functionViscous-inviscid matchingWave-body interaction
Download to read the full article text

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