A numerical method is developed for modeling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modeling the interface, where most of the numerical approximations are made. Novel features are that the reintialization procedure has been redefined in cells crossed by the interface; the density has been smoothed across the interface using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an essentially non-oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favorable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case.

1.
Harlow
,
F. H.
, and
Welch
,
J. E.
, 1965, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluids With Free Surface
,”
Phys. Fluids
0031-9171,
8
, pp.
2182
2189
.
2.
Colagrossi
,
A.
, and
Landrini
,
M.
, 2002, “
Numerical Simulation of 2-Phase Flows by Smoothed Particle Hydrodynamics
,” NuTTS, Pornichet (France).
3.
Shopov
,
P. J.
,
Minev
,
P. D.
,
Bazhelkov
,
I. B.
, and
Zapryanov
,
Z. D.
, 1990, “
Interaction of a Deformable Bubble With a Rigid Wall at Moderate Reynolds-Numbers
,”
J. Fluid Mech.
0022-1120,
129
, pp.
241
271
.
4.
Li
,
W. Z.
, and
Yan
,
Y. Y.
, 2002, “
Direct-Predictor Method for Solving Steady Terminal Shape of a Gas Bubble Rising Through a Quiescent Liquid
,”
Numer. Heat Transfer, Part B
1040-7790,
42
, pp.
55
71
.
5.
Hirt
,
C. W.
, and
Nichols
,
B. D.
, 1981, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
0021-9991,
39
, pp.
201
225
.
6.
Scardovelli
,
R.
, and
Zaleski
,
S.
, 1999, “
Direct Numerical Simulation of Free-Surface and Interfacial Flow
,”
Annu. Rev. Fluid Mech.
0066-4189,
31
, pp.
567
603
.
7.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S.
, 1994, “
A Level Set Approach for Computing Solutions to Incompressible Two Phase Flows
,”
J. Comput. Phys.
0021-9991,
114
, pp.
146
159
.
8.
Tryggvason
,
G.
,
Bunner
,
B.
,
Esmaeeli
,
A.
,
Juric
,
D.
,
Al-Rawahi
,
N.
,
Tauber
,
W.
,
Han
,
J.
,
Nas
,
S.
, and
Jan
,
J. Y.
, 2001, “
A Front-Tracking Method for the Computations of Multiphase Flow
,”
J. Comput. Phys.
0021-9991,
169
, pp.
798
859
.
9.
Lafaurie
,
B.
,
Nardone
,
C.
,
Scardovelli
,
R.
,
Zaleski
,
S.
, and
Zanetti
,
G.
, 1994, “
Modelling Merging and Fragmentation Multiphase Flows With SURFER
,”
J. Comput. Phys.
0021-9991,
113
, pp.
134
147
.
10.
Lawson
,
L. J.
,
Rudman
,
M.
,
Guerra
,
A.
, and
Liow
,
J. L.
, 1999, “
Experimental and Numerical Comparisons of the Break-up of a Large Bubble
,”
Exp. Fluids
0723-4864,
26
, pp.
524
534
.
11.
Zhao
,
Y.
,
Tan
,
H. H.
, and
Zhang
,
B.
, 2002, “
A High-Resolution Characteristics-Based Implicit Dual Time-Stepping VOF Method for Free Surface Flow Simulation on Unstructured Grids
,”
J. Comput. Phys.
0021-9991,
183
, pp.
233
273
.
12.
Sussman
,
M.
,
Almgren
,
A. S.
,
Bell
,
J. B.
,
Colella
,
P.
,
Howell
,
L. H.
, and
Welcome
,
M. L.
, 1999, “
An Adaptive Level Set Approach for Incompressible Two-Phase Flow
,”
J. Comput. Phys.
0021-9991,
148
, pp.
81
124
.
13.
Yabe
,
T.
,
Xiao
,
F.
, and
Utsumi
,
T.
, 2001, “
The Constrained Interpolation Profile Method for Multiphase Analysis
,”
J. Comput. Phys.
0021-9991,
169
, pp.
556
593
.
14.
Yabe
,
T.
,
Ogata
,
Y.
,
Takizawa
,
K.
,
Kawai
,
T.
,
Segawa
,
A.
, and
Sakurai
,
K.
, 2002, “
The Next Generation CIP as a Conservative Semi-Lagrangian Solver for Solid, Liquid and Gas
,”
J. Comput. Appl. Math.
0377-0427,
149
, pp.
267
277
.
15.
Tsai
,
W. T.
, and
Yue
,
D. K. P.
, 1993, “
Interaction Between a Free Surface and a Vortex Sheet Shed in the Wake of a Surface-Piercing Plate
,”
J. Fluid Mech.
0022-1120,
257
, pp.
691
721
.
16.
Wehausen
,
J. V.
, and
Laitone
,
E. V.
, 1960,
Handbuch der Physik
, pp.
446
778
.
17.
Fraigneau
,
Y.
,
Guermond
,
J. L.
, and
Quartapelle
,
L.
, 2001, “
Approximation of Variable Density Incompressible Flows by Means of Finite Elements and Finite Volumes
,”
Commun. Numer. Methods Eng.
1069-8299,
17
, pp.
893
902
.
18.
Colicchio
,
G.
, 2004, “
Violent Disturbances and Fragmentation of Free Surfaces
,” School of Civil Engineering and the Environment. Southampton,
University of Southampton
, p.
170
.
19.
Yue
,
W.
,
Lin
,
C. L.
, and
Patel
,
V. C.
, 2003, “
Numerical Simulation of Unsteady Multidimensional Free Surface Motions by Level Set Method
,”
Int. J. Numer. Methods Fluids
0271-2091,
42
, pp.
853
884
.
20.
Harten
,
A.
, and
Osher
,
S.
, 1987, “
Uniformly High-Order Accurate Nonoscillatory Schemes. 1
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429,
24
, pp.
279
309
.
21.
Russo
,
G.
, and
Smereka
,
P.
, 2000, “
A Remark on Computing Distance Functions
,”
J. Comput. Phys.
0021-9991,
163
, pp.
51
67
.
22.
Greco
,
M.
, 2001, “
,”
Marine Hydrodynamics
, Trondheim, NTNU.
23.
Brackbill
,
J. U.
,
Kothe
,
D. B.
, and
Zemach
,
C.
, 1992, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
0021-9991,
100
, pp.
335
354
.
24.
Liu
,
X.
,
Fedkiw
,
R. P.
, and
Kand
,
M.
, 2003, “
A Boundary Condition Capturing Methods for Poisson’s Equation on Irregular Domains
,”
J. Comput. Phys.
0021-9991,
160
, pp.
151
178
.
25.
Walters
,
J. K.
, and
Davidson
,
J. F.
, 1962, “
The Inital Motion of a Gas Bubble Formed in an Inviscid Liquid
,”
J. Fluid Mech.
0022-1120,
12
, pp.
408
416
.
26.
Ohring
,
S.
, and
Lugt
,
H. J.
, 1991, “
Interaction of a Viscous Vortex Pair With a Free-Surface
,”
J. Fluid Mech.
0022-1120,
227
, pp.
47
70
.
27.
Zalesak
,
S. T.
, 1979, “
Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids
,”
J. Comput. Phys.
0021-9991,
31
, pp.
335
362
.
28.
Sethian
,
J. A.
, 1999,
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science
,
Cambridge University Press
, Cambridge.