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An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows

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Abstract

We introduce a robust method for computing viscous and viscoelastic two-phase bubble and drop motions. Our method utilizes a coupled level-set and volume-of-fluid technique for updating and representing the air-water interface. Our method introduces a novel approach for treating the viscous coupling terms at the air-water interface; these improvements result in improved stability for computing two-phase bubble formation solutions. We also present an improved, “positive-preserving” discretization technique for updating the configuration tensor for viscoelastic flows, in the context of computing two-phase bubble and drop motion.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Jimenez, E., Sussman, M., Ohta, M.: A computational study of bubble motion in Newtonian and viscoelastic fluids. Fluid Dyn. Mater. Process. 1(2), 97–108 (2005)

    MathSciNet  Google Scholar 

  3. Sussman, M., Ohta, M.: Improvements for calculating two-phase bubble and drop motion using an adaptive sharp interface method. Fluid Dyn. Mater. Process. 3(1), 21–36 (2007)

    MathSciNet  Google Scholar 

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

  5. Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost fluid method). J. Comput. Phys. 152(2), 457–492 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Liu, X.-D., Fedkiw, R.P., Kang, M.: A boundary condition capturing method for Poisson’s equation on irregular domains. J. Comput. Phys. 160(1), 151–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Li, J., Renardy, Y.Y., Renardy, M.: Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Phys. Fluids 12(2), 269–282 (2000)

    Article  Google Scholar 

  8. Hong, J.-M., Shinar, T., Kang, M., Fedkiw, R.: On boundary condition capturing for multiphase interfaces. J. Sci. Comput. 31, 99–125 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., Fedkiw, R.: Directable photorealistic liquids. In: Eurographics/ACM SIGGRAPH Symposium on Computer Animation, 2004

  10. Yu, J.-D., Sakai, S., Sethian, J.A.: Two-phase viscoelastic jetting. J. Comput. Phys. 220(2), 568–585 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pillapakkam, S.B., Singh, P.: A level-set method for computing solutions to viscoelastic two-phase flow. J. Comput. Phys. 174(2), 552–578 (2001)

    Article  MATH  Google Scholar 

  12. Goktekin, T.G., Bargteil, A.W., O’Brien, J.F.: Method for animating viscoelastic fluids. ACM Trans. Graph. 23(3), 463–468 (2004)

    Article  Google Scholar 

  13. Losasso, F., Shinar, T., Selle, A., Fedkiw, R.: Multiple interacting fluids. In: SIGGRAPH 2006. ACM TOG 25, pp. 812–819 (2006)

  14. Irving, G.: Methods for the physically based simulation of solids and fluids. Department of Computer Science, Stanford, Palo Alto (2007)

  15. Chilcott, M.D., Rallison, J.M.: Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newton. Fluid Mech. 29, 381–432 (1988)

    Article  Google Scholar 

  16. Singh, P., Leal, L.G.: Finite-element simulation of the start-up problem for a viscoelastic fluid in an eccentric rotating cylinder geometry using a third-order upwind scheme. Theor. Comput. Fluid Dyn. V5(2), 107–137 (1993)

    Article  Google Scholar 

  17. Khismatullin, D., Renardy, Y., Renardy, M.: Development and implementation of VOF-PROST for 3D viscoelastic liquid-liquid simulations. J. Non-Newton. Fluid Mech. 140(1-3), 120–131 (2006)

    Article  MATH  Google Scholar 

  18. Trebotich, D., Colella, P., Miller, G.H.: A stable and convergent scheme for viscoelastic flow in contraction channels. J. Comput. Phys. 205(1), 315–342 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. 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  MATH  MathSciNet  Google Scholar 

  20. Sussman, M., Puckett, E.G.: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301–337 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  21. Tatebe, O.: The multigrid preconditioned conjugate gradient method. In: 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, 1993

  22. Briggs, W.L., Henson, V.E., McCormick, S.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000)

    Google Scholar 

  23. van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 100, 25–37 (1979)

    Google Scholar 

  24. Sussman, M.: A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J. Comput. Phys. 187(1), 110–136 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  26. Hadamard, J.: Movement permanent lent d’une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 1735–1738 (1911)

    Google Scholar 

  27. Rybczynski, W.: Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium. Bull. Int. Acad. Sci. Cracovia Cl. Sci. Math. Natur, 40–46 (1911)

  28. Bhaga, D., Weber, M.E.: Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. Digit. Arch. 105(1), 61–85 (2006)

    Google Scholar 

  29. Bright, A.: Minimum drop volume in liquid jet breakup. Chem. Eng. Res. Des. 63, 59–66 (1985)

    Google Scholar 

  30. Richards, J.R., Lenhoff, A.M., Beris, A.N.: Dynamic breakup of liquid-liquid jets. Phys. Fluids 6, 2640–2655 (1994)

    Article  MATH  Google Scholar 

  31. Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)

    Article  MATH  Google Scholar 

  32. Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  33. Johnson, J.R.E., Dettre, R.H.: The wettability of low-energy liquid surfaces. J. Colloid Interface Sci. 21(6), 610–622 (1966)

    Article  Google Scholar 

  34. Noh, D.S., Kang, I.S., Leal, L.G.: Numerical solutions for the deformation of a bubble rising in dilute polymeric fluids. Phys. Fluids A 5, 1315 (1993)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    P. A. Stewart, N. Lay & M. Sussman

  2. Department of Applied Chemistry, Muroran Institute of Technology, 27-1, Mizumotocho, Muroran-shi, Hokkaido, 050-8585, Japan

    M. Ohta

Authors
  1. P. A. Stewart
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  2. N. Lay
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  3. M. Sussman
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  4. M. Ohta
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Correspondence to M. Sussman.

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Stewart, P.A., Lay, N., Sussman, M. et al. An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows. J Sci Comput 35, 43–61 (2008). https://doi.org/10.1007/s10915-007-9173-5

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  • DOI: https://doi.org/10.1007/s10915-007-9173-5

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