Volume of fluid interface reconstruction methods are used to resolve the interfaces between different materials in Eulerian and arbitrary Lagrangian Eulerian calculations. Their accuracy is critical to the overall accuracy of the calculation since the interfaces define the interactions between adjacent materials. The methods have evolved since the early 1960s, and the early criticisms of them no longer hold. In this review article, the differences between the methods and their relative strengths are reviewed, and 38 reference sources are used.
Issue Section:
Review Articles
1.
Youngs DL (1982), Time dependent multi-material flow with large fluid distortion, Numerical Methods for Fluid Dynamics, KW Morton and MJ Baines (eds), Academic Press, 273–285.
2.
Youngs DL (1987), An interface tracking method for a 3D eulerian hydrodynamics code, Tech Report AWRE/44/92/35, AWRE Design Math Div,
3.
Hyman
JM
(1984
), Numerical methods for tracking interfaces
, Physica D
, 12D
, 396
–407
.4.
Oran ES and Boris JP (1987), Numerical Simulation of Reactive Flow, Elsevier Sciences Publ.
5.
Benson
DJ
(1992
), Computational methods in Lagrangian and Eulerian hydrocodes
, Comput. Methods Appl. Mech. Eng.
, 99
, 235
–394
.6.
Rider WJ and Kothe DB (year?), Stretching and tearing interface tracking methods. Tech Report AIAA 95-1717, AIAA.
7.
Rider
WJ
and Kothe
DB
(1998
), Reconstructing volume tracking
, J. Comput. Phys.
, 141
, 112
–152
.8.
Scardovelli
R
and Zaleski
S
(1999
), Direct numerical simulation of free-surface and interfacial flow
, Annu. Rev. Fluid Mech.
, 31
, 567
–603
.9.
Chorin
A
, Hughes
TJR
, McCracken
MF
, and Marsden
JE
(1978
), Product formulas and numerical algorithms
, Commun. Pure Appl. Math.
, 31
, 205
–256
.10.
Johnson N (1990), personal communication, Los Alamos National Laboratory.
11.
van Leer B (1984), Multidimensional explicit difference schemes for hyperbolic conservation laws, Computing Methods in Applied Sciences and Engineering VI, R Glowinski and JL Lions, (eds), 493.
12.
Colella
P
(1990
), Multidimensional upwind methods for hyperbolic conservation laws
, J. Comput. Phys.
, 87
, 171
–209
(previously published as LBL-17023, May, 1984, Lawrence Berkeley Laboratory).13.
Saltzman
J
(1994
), An unsplit 3D upwind method for hyperbolic conservation laws
, J. Comput. Phys.
, 115
, 153
–168
.14.
Noh WF and Woodward P (1976), SLIC (Simple Line Interface Calculation), Volume 59, Springer-Verlag, Berlin.
15.
Hirt
CW
and Nichols
BD
(1981
), Volume of fluid (VOF) method for the dynamics of free boundaries
, J. Comput. Phys.
, 39
, 201
–225
.16.
DeBar RB (1974), Fundamentals of the KRAKEN code, Tech Report UCIR-760, Lawrence Livermore Laboratory.
17.
McMaster WH (1984), Computer codes for fluid-structure interactions, Tech Report UCRL-89724, Lawrence Livermore National Laboratory.
18.
Rudman
M
(1997
), Volume tracking methods for interfacial flow calculations
, Int. J. Numer. Methods Fluids
, 24
, 671
–691
.19.
Kothe DB, Rider WJ, Mosso SJ, and Brock JS (1996), Volume tracking of interfaces having surface tension in two and three dimensions. Tech Report AIAA 96-0859, AIAA.
20.
Zemach C (1993), Notes on the volume of a ruled hexahedron behind a truncating plane, Los Alamos National Laboratory.
21.
Gueyffier
D
, Li
J
, Nadim
A
, Scardovelli
R
, and Zaleski
S
(1999
), Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
, J. Comput. Phys.
, 152
, 423
–456
.22.
Addessio FL, Baumgardner JR, Dukowicz JK, Johnson NL, Kashiwa BA, Rauenzahn RM, and Zemach C (1990), CAVEAT: A Computer Code for Fluid Dynamics Problems with Large Distortion and Internal Slip, (revised edition), Los Alamos National Laboratory.
23.
Rowse DP (1987), Comments on the proposed ‘generalization of an interface tracking method’: A little understanding, STH/DPR/0387/1.
24.
Pilliod JE (1992), An analysis of piecewise linear interface reconstruction algorithms for volume-of-fluid methods, Master’s thesis, Univ of California, Davis.
25.
Pilliod JE and Puckett EG (1999), Second-order volume-of-fluid algorithms for tracking material interfaces, J. Comput. Phys., 99.
26.
Chorin
AJ
(1985
), Curvature and solidification
, J. Comput. Phys.
, 58
, 472
–490
.27.
Williams MW, Kothe DB, and Puckett EG (1999), Approximating interface topologies with applications to interface tracking algorithms, Tech Report 99–1076, AIAA, Reno, Nevada, presented at the 37th Aerospace Sciences Meeting.
28.
Barth TJ (1995), Aspects of unstructured grids and finite-volume solvers for euler and navier-stokes equations, VKI/NASA/AGARD Special Course on Unstructured Grid Methods for Advection Dominated Flows AGARD Publication R-787.
29.
Swartz
B
(1989
), The second-order sharpening of blurred smooth borders
, Math. Comput.
, 52
, 675
675
.30.
Nordmark
HO
(1991
), Rezoning for higher order vortex methods
, J. Comput. Phys.
, 97
, 366
–397
.31.
Williams MW (2000), Numerical Methods for Tracking Interfaces with Surface Tension in 3-D Mold-Filling Processes, PhD thesis, Univ of California, Davis.
32.
McGlaun JM, Thompson SL, and Elrick MG (1989), CTH: A three-dimensional shock wave physics code, Proc of 1989 Hypervelocity Impact Symp.
33.
Price GR, Reader GT, Rowe RD, and Bugg JD (1998), A piecewise parabolic interface calculation for volume tracking, Proc of 6th Annual Conf of the Computational Fluid Dynamics Society of Canada, Univ of Victoria, Victoria, British Columbia.
34.
Price GR and Rowe RD (1997), An extended piecewise linear volume-of-fluid algorithm for reconstruction of thin interfaces, Proc of 5th Annual Conf of the Computational Fluid Dynamics Society of Canada, 11(9)–11(14), Univ of Victoria, Victoria, British Columbia.
35.
More J, Garbow B, and Hillstrom K (1980), Minpack library, software library.
36.
Benson
DJ
(1998
), Eulerian finite element methods for the micromechanics of heterogeneous materials: dynamic prioritization of material interfaces
, Comput. Methods Appl. Mech. Eng.
, 151
, 343
–360
.37.
Bell RL and Hertel ES (1992), An improved material interface reconstruction algorithm for Eulerian codes, Tech Report SAND 92-1716, Sandia National Laboratories, Albuquerque NM.
38.
Mosso S and Clancy S (1994), Geometrically derived priority system for Youngs’ interface reconstruction, Tech report, Los Alamos National Laboratory.
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