COMPUTATION OF NONLINEAR FREE-SURFACE FLOWS

We review recent advances in computations of incompressible flows invo lving a fully nonlinear free surface. Our focus is on the treatment of the free surface and (large) nonlinearity. Both potential as well as rotational and viscous free-surface flows are considered. For the form er, we review mixed-Eulerian-Lagrangian boundary-integral methods and the recently developed high-order spectral methods. For the latter, th e focus is mainly on volume-discretization methods utilizing Eulerian or boundary-fitted grids. The importance and proper treatment of visco us free-surface conditions for these problems are emphasized. We concl ude that computations for nonlinear potential-flow wave problems are r easonably mature although further developments to improve efficiency a nd robustness are needed for large complex problems. Nonlinear viscous free-surface flow computations are relatively new. Many of the diffic ulties such as large Reynolds numbers computations are common to flows without a free surface. On the other hand, problems such as those ass ociated with the contact line, wave breaking, free-surface turbulence, and surfactants are unique to free-surface hydrodynamics and represen t some of the difficult remaining challenges in computational fluid dy namics.