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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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)
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)
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)
Kang, M., Fedkiw, R., Liu, X.-D.: A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15 (2000)
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)
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)
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)
Hong, J.-M., Shinar, T., Kang, M., Fedkiw, R.: On boundary condition capturing for multiphase interfaces. J. Sci. Comput. 31, 99–125 (2007)
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
Yu, J.-D., Sakai, S., Sethian, J.A.: Two-phase viscoelastic jetting. J. Comput. Phys. 220(2), 568–585 (2007)
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)
Goktekin, T.G., Bargteil, A.W., O’Brien, J.F.: Method for animating viscoelastic fluids. ACM Trans. Graph. 23(3), 463–468 (2004)
Losasso, F., Shinar, T., Selle, A., Fedkiw, R.: Multiple interacting fluids. In: SIGGRAPH 2006. ACM TOG 25, pp. 812–819 (2006)
Irving, G.: Methods for the physically based simulation of solids and fluids. Department of Computer Science, Stanford, Palo Alto (2007)
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)
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)
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)
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)
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)
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)
Tatebe, O.: The multigrid preconditioned conjugate gradient method. In: 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, 1993
Briggs, W.L., Henson, V.E., McCormick, S.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000)
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)
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)
Sussman, M.: A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput. Struct. 83, 435–444 (2005)
Hadamard, J.: Movement permanent lent d’une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 1735–1738 (1911)
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)
Bhaga, D., Weber, M.E.: Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. Digit. Arch. 105(1), 61–85 (2006)
Bright, A.: Minimum drop volume in liquid jet breakup. Chem. Eng. Res. Des. 63, 59–66 (1985)
Richards, J.R., Lenhoff, A.M., Beris, A.N.: Dynamic breakup of liquid-liquid jets. Phys. Fluids 6, 2640–2655 (1994)
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)
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)
Johnson, J.R.E., Dettre, R.H.: The wettability of low-energy liquid surfaces. J. Colloid Interface Sci. 21(6), 610–622 (1966)
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)
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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