A novel technique for including surface tension in PLIC-VOF methods.

*(English)*Zbl 1064.76084Summary: Various versions of volume-of-fluid (VOF) methods have been used successfully for numerical simulation of gas-liquid flows with an explicit tracking of the phase interface. Of these, piecewise-linear interface construction (PLIC-VOF) appears as a fairly accurate, although somewhat more involved variant. Including effects due to surface tension remains a problem, however. The most prominent methods, continuum surface force of J. U. Brackbill et al. [J. Comput. Phys. 100, No. 2, 335–354 (1992; Zbl 0775.76110)] and the method of S. Zaleski and co-workers [Proceedings of the 2nd International Conference on Multiphase Flows, Kyoto, Apr. 3–7, Vol. 2, PT2-1-PT2-12 (1995)], both induce spurious or ‘parasitic’ currents, and only moderate accuracy in regards to determining the curvature. We present here a new method to determine curvature accurately using an estimator function, which is tuned with a least-squares-fit against reference data. Furthermore, we show how spurious currents may be drastically reduced using the reconstructed interfaces from the PLIC-VOF method.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76T10 | Liquid-gas two-phase flows, bubbly flows |

76D45 | Capillarity (surface tension) for incompressible viscous fluids |

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\textit{M. Meier} et al., Eur. J. Mech., B, Fluids 21, No. 1, 61--73 (2002; Zbl 1064.76084)

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##### References:

[1] | Youngs, D.L, Time-dependent multi-material flow with large fluid distortion, (), 273-285 · Zbl 0537.76071 |

[2] | Rider, W.J; Kothe, D.B, Reconstructing volume tracking, J. comput. phys., 141, 112-152, (1998) · Zbl 0933.76069 |

[3] | Li, J, Calcul d’interface affine par morceaux (piecewise linear interface calculation), C. R. acad. sci. II B, 320, 391-396, (1995) · Zbl 0826.76065 |

[4] | Scardovelli, R; Zaleski, S, Direct numerical simulation of free-surface and interfacial flow, Annu. rev. fluid mech., 31, 567-603, (1999) |

[5] | M. Meier, Numerical and experimental study of large steam-air bubbles injected in a water pool, Dissertation no. 13091, Swiss Federal Institute of Technology, Zurich, Switzerland, 142 pages, 1999, http://www.lkt.iet.ethz.ch/ meier/ |

[6] | Carey, V.P, Liquid – vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment, (1992), Hemisphere Publishing Corporation |

[7] | Lafaurie, B; Nardone, C; Sardovelli, R; Zaleski, S; Zanetti, G, Modelling merging and fragmentation in multiphase flows with SURFER, J. comput. phys., 113, 134-147, (1994) · Zbl 0809.76064 |

[8] | Zaleski, S; Li, J; Succi, S; Scardovelli, R; Zanetti, G, Direct numerical simulation of flows with interfaces, (), PT2-1-PT2-12 |

[9] | Bird, R.B; Stewart, W.E; Lightfoot, E.N, Transport phenomena, (1960), Wiley New York |

[10] | Kataoka, I, Local instant formulation of two-phase flow, Int. J. multiphase flow, 12, 745-758, (1986) · Zbl 0613.76114 |

[11] | Brackbill, J.U; Kothe, D.B; Zemach, C, A continuum method for modelling surface tension, J. comput. phys., 100, 335-354, (1992) · Zbl 0775.76110 |

[12] | Kothe, D.B; Mjolsness, R.C, RIPPLE: a new model for incompressible flows with free surfaces, Aiaa j., 30, 11, 2694-2700, (1992) · Zbl 0762.76074 |

[13] | Sasmal, G.P; Hochstein, J.I, Marangoni convection with a curved and deforming free surface in a cavity, (), 199-207 |

[14] | Richards, J.R; Beris, A.N; Lenhoff, A.M, Drop formation in liquid – liquid systems before and after jetting, Phys. fluids, 7, 2617-2630, (1995) · Zbl 1026.76563 |

[15] | Wu, J; Yu, S.-T; Jiang, B.-N, Simulation of two-fluid flows by the least-squares finite element method using a continuum surface tension model, Int. J. num. meth. eng., 42, 583-600, (1998) · Zbl 0912.76035 |

[16] | AEA Technology, Engineering Software, CFX Computational Fluid Engineering, http://www.aeat.co.uk/cfx/ |

[17] | Computational Dynamics Ltd., CFD software products, Star-CD, http://www.cd.co.uk/ |

[18] | Rudman, M, A volume-tracking method for incompressible multifluid flows with large density variations, Internat. J. numer. methods in fluids, 28, 357-378, (1998) · Zbl 0915.76060 |

[19] | Williams, M.W; Kothe, D.B; Puckett, E.G, Convergence and accuracy of kernel-based continuum surface tension models, (), 347-356 |

[20] | Bussmann, M; Jostaghimi, J; Chandra, S, On a three-dimensional volume tracking model of droplet impact, Phys. fluids, 11, 1406-1417, (1999) · Zbl 1147.76344 |

[21] | D.B. Kothe, W.J. Rider, S.J. Mosso, J.S. Brock, J.I. Hochstein, Volume tracking of interfaces having surface tension in two and three dimensions, AIAA Paper 96-0859, Presented at the 34th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 15-18, 1996 (LANL Report LA-UR-96-88, http://www.lanl.gov/home/Telluride), 1-24 |

[22] | De Boor, C, A practical guide to splines, (1978), Springer New York · Zbl 0406.41003 |

[23] | Clift, R; Grace, J.R; Weber, M.E, Bubbles, drops and particles, (1978), Academic Press New York |

[24] | Sussman, M; Smereka, P, Axisymmetric free boundary problems, J. fluid mech., 341, 269-294, (1997) · Zbl 0892.76090 |

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