article

A conservative level set method for two phase flow

Authors:

Elin Olsson,

Gunilla KreissAuthors Info & Claims

Journal of Computational Physics, Volume 210, Issue 1

Pages 225 - 246

https://doi.org/10.1016/j.jcp.2005.04.007

Published: 20 November 2005 Publication History

Abstract

A conservative method of level set type for moving interfaces in divergence free velocity fields is presented. The interface is represented implicitly by the 0.5 level set of a function @F being a smeared out Heaviside function, i.e., a function being zero on one side of the interface and one on the other. In a transition layer of finite, constant thickness @F goes smoothly from zero to one. The interface is moved implicitly by the advection of @F, which is split into two steps. First @F is advected using a standard numerical method. Then an intermediate step is performed to make sure that the smooth profile of @F and the thickness of the transition layer is preserved. Both these steps are performed using conservative second order approximations and thus conserving @!@F. In this way good conservation of the area bounded by the 0.5 contour of @F is obtained. Numerical tests shows up to second order accuracy and very good conservation of the area bounded by the interface. The method was also coupled to a Navier-Stokes solver for incompressible two phase flow with surface tension. Results with and without topological changes are presented.

References

[1]

W. Noh, P. Woodward, SLIC (simple line interface calculation), in: A. van de Vooren, P. Zandbergen (Eds.), Proceedings of the 5th International Conference on Fluid Dynamics, vol. 59 of Lecture Notes in Physics, 1976, pp. 330-340.

Google Scholar

[2]

Scardovelli, R. and Zaleski, S., Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech. v31. 567-603.

Crossref

Google Scholar

[3]

Unverdi, S. and Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. v100. 25-37.

Digital Library

Google Scholar

[4]

Osher, S. and Fedkiw, R., Level set methods and dynamic implicit surfaces. 2003. Springer-Verlag, Berlin.

Google Scholar

[5]

Sethian, J., Level set methods and fast marching methods. 1999. Cambridge University Press, Cambridge.

Google Scholar

[6]

Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. v114. 146-159.

Digital Library

Google Scholar

[7]

Sussman, M., Fatemi, E., Smereka, P. and Osher, S., An improved level set method for incompressible two-phase flows. Comp. Fluid. v27. 663-680.

Crossref

Google Scholar

[8]

Tornberg, A.-K. and Enhquist, B., A finite element based level set method for multiphase flow applications. Comput. Visual. Sci. v3. 93-101.

Digital Library

Google Scholar

[9]

Sussman, M. and Puckett, E., A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. J. Comput. Phys. v162. 301-337.

Digital Library

Google Scholar

[10]

Enright, D., Fedkiw, R., Ferziger, J. and Mitchell, I., A hybrid particle level set method for improved interface capturing. J. Comput. Phys. v183. 83-116.

Digital Library

Google Scholar

[11]

Leveque, R., Finite volume methods for hyperbolic problems. 2002. Cambridge University Press, Cambridge.

Google Scholar

[12]

Harten, A., The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws. Comm. Pure Appl. Math. 611-638.

Google Scholar

[13]

Brackbill, J.U., Kothe, D. and Zemach, C., A continuum method for modeling surface tension. J. Comput. Phys. v100. 335-353.

Digital Library

Google Scholar

[14]

Harlow, F. and Welch, E., Numerical calculation of time-dependent viscous incompressible flow of fluids with free surface. Phys. Fluids. v8. 2182

Google Scholar

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Index Terms

A conservative level set method for two phase flow
1. Applied computing
  1. Physical sciences and engineering
    1. Physics
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 210, Issue 1

20 November 2005

402 pages

ISSN:0021-9991

Issue’s Table of Contents

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 20 November 2005

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Zhao LDi YMao J(2024)A coupled FDEM-IBM-level set method for water entry of multiple flexible objectsJournal of Computational Physics10.1016/j.jcp.2024.113290516:COnline publication date: 18-Nov-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.113290
Jain S(2024)A model for transport of interface-confined scalars and insoluble surfactants in two-phase flowsJournal of Computational Physics10.1016/j.jcp.2024.113277515:COnline publication date: 15-Oct-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.113277
He ZTan S(2024)On immiscibility preservation conditions of material interfaces in the generic five-equation modelJournal of Computational Physics10.1016/j.jcp.2024.113192513:COnline publication date: 15-Sep-2024
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