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High order level contour reconstruction method

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Abstract

Complex interfacial physics arising from geometric curvature associated with surface tension as well as phase transformation make it a formidable task to design an accurate, reliable, and yet simple method for direct computation of multiphase flows. Hybrid methods mixing conventional, Volume-of-Fluid, Level Set, Phase Field, and Front Tracking methods have recently become popular in an attempt to overcome the shortcomings of each method alone. We developed the Level Contour Reconstruction Method (LCRM) as part of a hybrid method for treating the complex interface geometry associated with general three-dimensional multiphase flows. The main idea in that work focused on a simple and robust algorithm especially suited for dynamic interfaces in the three-dimensional case by combining characteristics of both Front Tracking and Level Set methods. In this article we describe a modification to the LCRM which introduces a high order interpolation kernel during the course of the interface reconstruction along with a new hybrid surface tension formulation. With this we can essentially eliminate any mass redistribution between regions of differing curvature and reconstruct the interface accurately and smoothly. The improvement with high order reconstruction is also noticeable vis a vis spurious currents which are further decreased by two orders of magnitude over the previous linear reconstruction method. Moreover, there is no disturbance concurrent with reconstruction and the solution fidelity is not influenced by the reconstruction time step. This High Order Level Contour Reconstruction Method retains the simplicity of the original LCRM and avoids complicated interface smoothing procedures.

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Abbreviations

u:

Velocity vector

U max :

Magnitude of the maximum velocity

V:

Interface velocity vector

P:

Pressure

g:

Gravitational acceleration

F:

Local surface tension force vector

Δ x , Δ y , Δ z :

Grid spacing in eachx, y, andz direction

N p :

Number of interface elements

N x, Ny, Nz :

Number of grid in eachx, y, andz direction

σ:

Surface tension coefficient

μ:

Viscosity

ρ:

Density

κL :

Twice the mean interface curvature

I:

Indicator function

n f :

Unit normal to the interface

δ f :

Dirac delta function

La=σρD/μ2 :

Laplace number

Ca=U max μ/σ:

Capillary number

1:

Fluid 1

2:

Fluid 2

References

  • Aulisa, E., Manservisi, S. and Scardovelli, R., 2003, “A Mixed Markers and Volume-of-fluid Method for the Reconstruction and Advection of Interfaces in Two-phase and Free-boundary Flows,”J. Comput. Phys., Vol. 188, pp. 611–639.

    Article  Google Scholar 

  • Brackbill, J. U., Kothe, D. B. and Zemach, C., 2002, “A Continuum Method for Modeling Surface Tension,”J. Comput. Phys., Vol. 100, pp. 335–354.

    Article  MathSciNet  Google Scholar 

  • Chorin, J., 1968, “Numerical Solution of the Navier-Stokes Equations,”Math. Comput, Vol. 22, pp. 745–762.

    Article  MathSciNet  Google Scholar 

  • Enright, D., Fedkiw, R., Ferziger, J. and Mitchell, I., 2002, “A Hybrid Particle Level set Method for Improved Interface Capturing,”J. Comput. Phys., Vol. 183, pp. 83–116.

    Article  MathSciNet  Google Scholar 

  • Harlow, F. H. and Welch, J. E., 1965, “Numerical Calculation of Time Dependent Viscous Incompressible Flow of Fluid with Free Surface,”Phys. Fluids, Vol. 8, pp. 2182–2189.

    Article  Google Scholar 

  • Jamet, D., Lebaigue, O., Coutris, N., and Delhaye, J. M., 2001, “The Second Gradient Method for the Direct Numerical Simulation of Liquid-Vapor Flows with Phase-change,”J. Comput. Phys., Vol. 169, pp. 624–651.

    Article  MathSciNet  Google Scholar 

  • Juric, D. and Tryggvason, G., 1998, “Computations of Boiling Flows,”Int. J. Multiphase Flow, Vol. 24, pp. 387–410.

    Article  Google Scholar 

  • Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. and Zanetti, G., 1994, “Modeling Merging and Fragmentation in Multiphase Flows with SURFER,”J. Comput. Phys., Vol. 113, pp. 134–147.

    Article  MathSciNet  Google Scholar 

  • Monaghan, J., 1985, “Particle Methods for Hydrodynamics,”Comput. Phys. Rep., Vol. 3, pp. 71–124.

    Article  Google Scholar 

  • Osher, S. and Fedkiw, R. P., 2001, “Level Set Methods: An Overview and Some Recent Results,”J. Comput. Phys., Vol. 169, pp. 463–502.

    Article  MathSciNet  Google Scholar 

  • Popinet, S. and Zaleski, S., 1999, “A Front-Tracking Algorithm for Accurate Representation of Surface Tension,”Int. J. Num. Meth. Fluids, Vol. 30, pp. 493–500.

    Article  Google Scholar 

  • Renardy, Y. and Renardy, M., 2002, “PROST: A Parabolic Reconstruction of Surface Tension for the Volume-of-fluid Method,”J. Comput. Phys., Vol. 183, pp. 400–421.

    Article  MathSciNet  Google Scholar 

  • Ryskin, G. and Leal, L. G., 1984, “Numerical Solution of Free-Boundary Problems in Fluid Mechanics. Part 1. The Finite-Difference Technique,”J. Fluid Mech., Vol. 148, pp. 1–17.

    Article  Google Scholar 

  • Ryskin, G. and Leal, L. G., 1984, “Numerical Solution of Free-Boundary Problems in Fluid mechanics. Part 2. Buoyancy-Driven Motion of a Gas Bubble Through a Quiescent Liquid,”J. Fluid Mech., Vol. 148, pp. 19–35.

    Article  Google Scholar 

  • Scardovelli, R. and Zaleski, S., 1999, “Direct Numerical Simulation of Free-Surface and Interfacial Flow,”Ann. Rev. Fluid Mech., Vol. 31, pp. 567–603.

    Article  MathSciNet  Google Scholar 

  • Shin, S. and Juric, D., 2002, “Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking Without Connectivity,”J. Comput. Phys., Vol. 180, pp. 427–470.

    Article  Google Scholar 

  • Shin, S., 2002, “A Level Contour Reconstruction Method for Three-Dimensional Multiphase Flows and its Application,”Ph.D. Thesis, Georgia Institute of Technology.

  • Shin, S., Abdel-Khalik, S. I., Daru, V. and Juric, D., 2005, “Accurate Representaion of Surface Tension Using the Level Contour Reconstruction Method,”J. Comput. Phys., Vol. 203, pp. 493–516.

    Article  Google Scholar 

  • Shirani, E., Ashgriz, N. and Mostaghimi, J., 2005, “Interface Pressure Caluclation Based on Conservation of Momentum for Front Capturing Methods,”J. Comput. Phys., Vol. 203, pp. 154–175.

    Article  Google Scholar 

  • Shu, C. W. and Osher, S., 1989, “Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes II,”J. Comput. Phys., Vol. 83, pp. 32–78.

    Article  MathSciNet  Google Scholar 

  • Son, G., 2001, “Numerical Study on a Sliding Bubble During Nucleate Boiling,”KSME International Journal, Vol. 15, pp. 931–940.

    Google Scholar 

  • Sussman, M. and Puckett, E. G., 2000, “A Coupled Level Set and Volume-of-fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows,”J. Comput. Phys., Vol. 162, pp. 301–337.

    Article  MathSciNet  Google Scholar 

  • Sussman, M., Fatemi, E., Smereka, P. and Osher, S., 1998, “An Improved Level Set Method for Incompressible Two-Phase Flows,”Computers and Fluids, Vol. 27, pp. 663–680.

    Article  Google Scholar 

  • Torres, D. J. and Brackbill, J. U., 2000, “The Point-Set Method: Front-Tracking Without Connectivity,”J. Comput. Phys., Vol. 165, pp. 620–644.

    Article  Google Scholar 

  • Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. and Jan, Y. -J., 2001, “A Front Tracking method for the Computations of Multiphase Flow,”J. Comput. Phys., Vol. 169, pp. 708–759.

    Article  Google Scholar 

  • Unverdi, S. O. and Tryggvason, G., 1992a, “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows,”J. Comput. Phys., Vol. 100, pp. 25–37.

    Article  Google Scholar 

  • Unverdi, S. O. and Tryggvason, G., 1992b, “Computations of Multi-Fluid Flows,”Physica D., Vol. 60, pp. 70–83.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and System Design Engineering, Hongik University, 72-1, Sangsu-dong, Mapo-gu, 121-791, Seoul, Korea

    Seungwon Shin

  2. Laboratoire d’Informatique pour la Mecanique et les Sciences de l’Ingenieur (LIMSI), CNRS-UPR 3251, BP133, 91403, Orsay, France

    Damir Juric

Authors
  1. Seungwon Shin
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  2. Damir Juric
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Correspondence to Seungwon Shin.

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Shin, S., Juric, D. High order level contour reconstruction method. J Mech Sci Technol 21, 311–326 (2007). https://doi.org/10.1007/BF02916292

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  • DOI: https://doi.org/10.1007/BF02916292

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