The capturing of free surfaces in incompressible multi-fluid flows

Abstract

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 © 2000 John Wiley & Sons, Ltd.

An essential solution of water entry problems and its engineering applications

“…In this paper, by using free surface capturing method (Qian et al, 2006;Kelecy and Pletcher, 1997;Pan and Chang, 2000;Wang and Wang, 2009), the incompressible Euler equations for a variable density fluid are adopted as governing equations and the free surface is captured as a contact discontinuity in the density field. Owing to its advantage of conveniently updating a few cells locally near solid boundary rather than re-meshing the whole flow domain, Cartesian cut cell mesh system (Yang et al, 1997a(Yang et al, , 2007bCauson et al, 2001) is applied in the treatment of the moving body.…”

An investigation of interface-sharpening schemes for multi-phase mixture flows

“…Following the modeling of Daly [31] and Pan and Chang [15], the interface position is fixed and an initial velocity is assigned to the two fluids as After an initial transient, the exponential growth rate becomes linear and is the slope of the curve of a log of the amplitude versus time plot, where the amplitude of the instability is defined as the average absolute displacement at the bounding edge and line of symmetry at the center of the wave. Numerical results for the three Reynolds numbers using the THINC-EM method are presented in Fig.…”

“…Our attention focuses on algebraic interface-capturing schemes [15][16][17], which are similar to MUSCL-type reconstruction techniques in that an assumed form for the property variation of the volume fraction within a mesh cell is chosen. These typically do not use geometric reconstruction of the interface within a mesh cell, as is done in classical VOF methods, and as such, they are easier to implement.…”

“…As pointed out in [15], the abrupt change in the fluid properties across a sharp interface can lead to a loss of diagonal dominance in this system and to numerical instability. To mitigate this effect, we follow [15] and use instead the linearization…”

“…Ghost-fluid strategies [12][13][14] have been shown to provide extremely sharp-interface-capturing when used with level-set techniques. More recently, there has been a trend to simplify VOF procedures by introducing smooth basis functions that better represent a discontinuity on the mesh-scale but do not require geometric reconstruction [15][16][17]. These techniques appear suitable for incorporation into codes that adopt conventional dimension-by-dimension upwinding methods.…”