The capturing of free surfaces in incompressible multi-fluid flows

By treating it as a contact discontinuity in the density field, a free surface between two immiscible fluids can be automatically 'captured' by the enforcement of conservation laws. A surface-capturing method of this kind requires no special tracking or fitting treatment for the free surface, thereby offering the advantage of algorithm simplicity over the surface-tracking or the surface-fitting method. A surface-capturing method based on a new multi-fluid incompressible Navier-Stokes formulation is developed. It is applied to a variety of free-surface flows, including the Rayleigh-Taylor instability problem, the ship waves around a Wigley hull and a model bubble-rising problem to demonstrate the validity and versatility of the present method. Copyright (C) 2000 John Wiley and Sons, Ltd.