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A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows

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Abstract

A coupled level set and moment of fluid method (CLSMOF) is described for computing solutions to incompressible two-phase flows. The local piecewise linear interface reconstruction (the CLSMOF reconstruction) uses information from the level set function, volume of fluid function, and reference centroid, in order to produce a slope and an intercept for the local reconstruction. The level set function is coupled to the volume-of-fluid function and reference centroid by being maintained as the signed distance to the CLSMOF piecewise linear reconstructed interface.

The nonlinear terms in the momentum equations are solved using the sharp interface approach recently developed by Raessi and Pitsch (Annual Research Brief, 2009). We have modified the algorithm of Raessi and Pitsch from a staggered grid method to a collocated grid method and we combine their treatment for the nonlinear terms with the variable density, collocated, pressure projection algorithm developed by Kwatra et al. (J. Comput. Phys. 228:4146–4161, 2009). A collocated grid method makes it convenient for using block structured adaptive mesh refinement (AMR) grids. Many 2D and 3D numerical simulations of bubbles, jets, drops, and waves on a block structured adaptive grid are presented in order to demonstrate the capabilities of our new method.

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References

  1. Ahn, H., Shashkov, M.: Geometric algorithms for 3D interface reconstruction. In: IMR’07, pp. 405–422 (2007)

    Google Scholar 

  2. Ahn, H., Shashkov, M.: Adaptive moment-of-fluid method. J. Comput. Phys. 228(8), 2792–2821 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahn, H., Shashkov, M., Christon, M.: The moment-of-fluid method in action. Commun. Numer. Methods Eng. 25(10), 1009–1018 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ahn, H.T., Shashkov, M.: Multi-material interface reconstruction on generalized polyhedral meshes. J. Comput. Phys. 226, 2096–2132 (2007). doi:10.1016/j.jcp.2007.06.033. http://dl.acm.org/citation.cfm?id=1290206.1290465

    Article  MathSciNet  MATH  Google Scholar 

  5. Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H., Welcome, M.: A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142, 1–46 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Anderson, W., Ryan, H., Santoro, J., Hewitt, R.: Combustion instability mechanism in liquid rocket engines using impinging jet injectors. In: 31st AIAA ASME SAE ASEE Joint Propulsion Conference, AIAA 95-2357 (1995)

    Google Scholar 

  7. Arcoumanis, C., Gavaises, J., Nouri, E.A.W., Horrocks, R.: Analysis of the flow in the nozzle of a vertical multi hole diesel engine injector. Tech. Rep. SAE Paper 980811 (1998)

  8. Bell, J.B., Colella, P., Glaz, H.M.: A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85, 257–283 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Berger, M.J., Rigoustsos, I.: An algorithm for point clustering and grid generation. Tech. Rep. NYU-501, New York University-CIMS (1991)

  10. Bhaga, D., Weber, M.: Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. 105, 61–85 (1981)

    Article  Google Scholar 

  11. Cervone, A., Manservisi, S., Scardovelli, R., Zaleski, S.: A geometrical predictor-corrector advection scheme and its application to the volume fraction function. J. Comput. Phys. 228(2), 406–419 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chang, Y., Hou, T., Merriman, B., Osher, S.: Eulerian capturing methods based on a level set formulation for incompressible fluid interfaces. J. Comput. Phys. 124, 449–464 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cummins, S., Francois, M., Kothe, D.: Estimating curvature from volume fractions. Comput. Struct. 83, 425–434 (2005)

    Article  Google Scholar 

  14. Dyadechko, V., Shashkov, M.: Moment-of-fluid interface reconstruction. Technical Report LA-UR 07-1537, Los Alamos National Laboratory (2007)

  15. Dyadechko, V., Shashkov, M.: Reconstruction of multi-material interfaces from moment data. J. Comput. Phys. 227(11), 5361–5384 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Enright, D., Nguyen, D., Gibou, F., Fedkiw, R.: Using the particle level set method and a second order accurate pressure boundary condition for free surface flows. In: Kawahashi, M., Ogut, A., Tsuji, Y. (eds.) Proc. of the 4th ASME-JSME Joint Fluids Eng. Conf., FEDSM2003-45144, Honolulu, HI (2003)

    Google Scholar 

  17. Fedkiw, R., Aslam, T., Xu, S.: The ghost fluid method for deflagration and detonation discontinuities. Technical Report CAM Report 98-36, University of California, Los Angeles (1998)

  18. Francois, M., Cummins, S., Dendy, E., Kothe, D., Sicilian, J., Williams, M.: A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213(1), 141–173 (2006)

    Article  MATH  Google Scholar 

  19. Gross, S., Reusken, A.: An extended pressure finite element space for two-phase incompressible flows with surface tension. J. Comput. Phys. 224(1), 40–58 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Helmsen, J., Colella, P., Puckett, E.: Non-convex profile evolution in two dimensions using volume of fluids. LBNL Technical Report LBNL-40693, Lawrence Berkeley National Laboratory (1997)

  21. Kang, M., Fedkiw, R., Liu, X.D.: A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15, 323–360 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kwatra, N., Su, J., Grétarsson, J.T., Fedkiw, R.: A method for avoiding the acoustic time step restriction in compressible flow. J. Comput. Phys. 228, 4146–4161 (2009). doi:10.1016/j.jcp.2009.02.027. http://dl.acm.org/citation.cfm?id=1528939.1529237

    Article  MathSciNet  MATH  Google Scholar 

  23. Lamb, H.: Hydrodynamics. Dover, New York (1932)

    MATH  Google Scholar 

  24. van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136 (1979)

    Article  Google Scholar 

  25. Lin, S., Chen, J.: Role played by the interfacial shear in the instability mechanism of a viscous liquid jet surrounded by a viscous gas in a pipe. J. Fluid Mech. 376, 37–51 (1998)

    Article  MATH  Google Scholar 

  26. Marchandise, E., Remacle, J.: A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. J. Comput. Phys. 219(2), 780–800 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Martin, J., Moyce, W.J.: An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos. Trans. R. Soc. Lond. A 244, 312–324 (1952)

    Article  MathSciNet  Google Scholar 

  28. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  29. Pilliod, J., Puckett, E.: Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys. 199(2), 465–502 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Popinet, S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Raessi, M., Pitsch, H.: Modeling interfacial flows characterized by large density ratios with the level set method. Annual Research Brief (2009)

  32. Schofield, S., Christon, M.: Effects of element order and interface reconstruction in fem/volume-of-fluid incompressible flow simulation. Int. J. Numer. Methods Fluids (2012). doi:10.1002/fld.3657

    MathSciNet  MATH  Google Scholar 

  33. Stewart, P., Lay, N., Sussman, M., Ohta, M.: An improved sharp interface method for viscoelastic and viscous two-phase flows. J. Sci. Comput. 35(1), 43–61 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  34. Strang, G.: On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5, 506–517 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sussman, M.: A second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles. J. Comput. Phys. 187, 110–136 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  36. Sussman, M.: A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput. Struct. 83, 435–444 (2005)

    Article  Google Scholar 

  37. Sussman, M., Almgren, A., Bell, J., Colella, P., Howell, L., Welcome, M.: An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148, 81–124 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  38. Sussman, M., Ohta, M.: A stable and efficient method for treating surface tension in incompressible two-phase flow. SIAM J. Sci. Comput. 31(4), 2447–2471 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Sussman, M., Puckett, E.: A coupled level set and volume of fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162, 301–337 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  40. Sussman, M., Smith, K., Hussaini, M., Ohta, M., Zhi-Wei, R.: A sharp interface method for incompressible two-phase flows. J. Comput. Phys. 221(2), 469–505 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wang, Y.: Numerical methods for two-phase jet flow. Ph.D. Thesis, Dept. of Mathematics, Florida State University (2010)

  42. Wang, Y., Simakhina, S., Sussman, M.: A hybrid level set-volume constraint method for incompressible two phase flows. J. Comput. Phys. (2012, in review)

  43. Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31, 335–362 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Work supported in part by the National Science Foundation under contracts DMS 0713256, DMS 1016381. M. Sussman also acknowledges the support by United Technologies Research Center and Sandia National Labs. M. Arienti acknowledges the support by Sandia National Laboratories via the Early Career LDRD program. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The work of M. Shashkov was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 and partially supported by the DOE Advanced Simulation and Computing (ASC) program and the DOE Office of Science ASCR Program.

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Authors and Affiliations

  1. Department of Applied & Computational Mathematics, Florida State University, Tallahassee, USA

    Matthew Jemison & Mark Sussman

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany

    Eva Loch

  3. X-Computational Physics Division, Los Alamos National Laboratory, Los Alamos, USA

    Mikhail Shashkov

  4. Thermal/Fluid Science and Engineering, Sandia National Labs, Livermore, USA

    Marco Arienti

  5. Department of Energy System, Institute of Technology and Science, Department of Mechanical Engineering, Faculty of Engineering, The University of Tokushima, Tokushima, Japan

    Mitsuhiro Ohta

  6. Department of Mathematics, University of California, Santa Barbara, USA

    Yaohong Wang

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  1. Matthew Jemison
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Correspondence to Mark Sussman.

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Jemison, M., Loch, E., Sussman, M. et al. A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows. J Sci Comput 54, 454–491 (2013). https://doi.org/10.1007/s10915-012-9614-7

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