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TECHNICAL PAPERS

Transport Coordinate (TC) Method for the Dynamics of Multiple Materials

[+] Author and Article Information
Wei Jia

Department of Mechanical Systems Engineering, Yamagata University, Yonezawa 9928510, Japane-mail: th107@dip.yz.yamagata-u.ac.jp

J. Fluids Eng 122(1), 125-133 (Dec 06, 1999) (9 pages) doi:10.1115/1.483234 History: Received August 24, 1998; Revised December 06, 1999
Copyright © 2000 by ASME
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References

Hirt,  C. W., and Nicholls,  B. D., 1981, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39, pp. 201–225.
Osher,  S., and Sethian,  J. A., 1988, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Comput. Phys., 79, pp. 12–49.
Sethian, J. A., 1996, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Science, Cambridge University Press.
Brackbill,  J. U., Kothe,  D. B., and Zemach,  C., 1992, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., 100, pp. 335–354.
Aleinov, I., et al., 1995, “Computing Surface Tension with High-Order Kernels,” Proceedings of the 6th International Symposium on Computational Fluid Dynamics, pp. 13–18.
Puckett,  E. G., Almgren,  A. S., Bell,  J. B., Marcus,  D. L., and Rider,  W. J., 1997, “A Second-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows,” J. Comput. Phys., 130, pp. 269–282.
Rudman,  M., 1997, “Volume Tracking Methods for Interfacial Flow Calculations,” IJNMF, 24, pp. 671–691.
Rider,  W. J., and Kothe,  D. B., 1998, “Reconstructing Volume Tracking,” J. Comput. Phys., 141, pp. 112–152.
Jia,  W., 1998, “An Accurate Semi-Lagrangian Scheme Designed for Incompressible Navier-Stokes Equations Written in Generalized Coordinates,” Trans. Japan Soc. Aero. Space Sci., 41, No. 133, pp. 105–117.
Staniforth,  A., and Cote,  J., 1991, “Semi-Lagrangian Integration Schemes for Atmospheric Models—A Review,” Mon. Weather Rev., 119, pp. 2206–2223.
Hirt,  C. W., Amsden,  A. A., and Cook,  J. L., 1974, “An Arbitrary Lagrangian Eulerian Computing Method for all Flow Speeds,” J. Comput. Phys., 14, pp. 227–253.
Rider, W. J., et al., 1995, “Stretching and Tearing Interfaces Tracking Methods,” LANL Preprint.
Lafaurie,  B., Nardone,  C., Scardovelli,  R., Zaleski,  S., and Zanetti,  G., 1994, “Modelling Merging and Fragmentation in Multiphase Flows with SURFER,” J. Comput. Phys., 113, pp. 134–147.

Figures

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Conceptions of VOF, LS, and transport coordinate methods
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Comparison of fluid interface and pressure contours of a moving droplet (a) without and (b) with restriction operation
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Contours of ρ (bold line), and ρ̄ of a circle object
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Conception of semi-Lagrangian method applied to solve advection equation
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Evolution of (a) contours of x0, (b) circle object, (c) needle object by TC method, and (d) needle object by VOF method. t=0, maximum deformation, and recovery instants from the left to the right.
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Fluid interface and pressure contours, and deformed base coordinates at t=5 from the left to the right. Re=200,σ=0,ρball=1,ρwall=0.5,ρair=0.1,ν=1/ρ. The results are calculated (a) without, and (b) with remeshing operation.
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Mass center velocity uMC of the ball against time
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Time series of deformations of fluid interface where there exists large density differences. Re=200,σ=0,ρball=1,ρwall=0.1,ρair=0.001,νballwall=1, and νair=10.
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Plots of (a) density, (b) smoothed density, (c) curvature, and (d) pressure along the midline of a rod. ρair=0.001,ρrod=1,σ=1. The computation is done on a 41×41 uniform grid.
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Kinetic energy of an oscillating droplet against time. ρair=0.001,ρdrop=1,νair=10,νdrop=1,σ=0.1, and Redrop=500.
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Velocity vectors and droplet shape of an oscillating droplet at typical time instants. ρair=0.001,ρdrop=1,νair=10,νdrop=1,σ=0.1, and Redrop=500.
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A 2D air bubble of diameter 5 mm rising in water
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Computation on dam breaking process in a 10 cm square box

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