Abu-Al-Saud, Moataz O.; Popinet, Stéphane; Tchelepi, Hamdi A. A conservative and well-balanced surface tension model. (English) Zbl 1415.76494 J. Comput. Phys. 371, 896-913 (2018). Summary: This article describes a new numerical scheme to model surface tension for an interface represented by a level-set function. In contrast with previous schemes, the method conserves fluid momentum and recovers Laplace’s equilibrium exactly. It is formally consistent and does not require the introduction of an arbitrary interface thickness, as is classically done when approximating surface-to-volume operators using Dirac functions. Variable surface tension is naturally taken into account by the scheme and accurate solutions are obtained for thermocapillary flows. Application to the Marangoni breakup of an axisymmetric droplet shows that the method is robust also in the case of changes in the interface topology. Cited in 13 Documents MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76D45 Capillarity (surface tension) for incompressible viscous fluids Keywords:surface tension; momentum conservation; well-balanced; levelset; Marangoni stresses; thermocapillarity Software:PROST; Gerris PDFBibTeX XMLCite \textit{M. O. Abu-Al-Saud} et al., J. Comput. Phys. 371, 896--913 (2018; Zbl 1415.76494) Full Text: DOI HAL References: [1] Abadie, T.; Aubin, J.; Legendre, D., On the combined effects of surface tension force calculation and interface advection on spurious currents within volume of fluid and level set frameworks, J. Comput. Phys., 297, 611-636 (2015) · Zbl 1349.76422 [2] Abu-Al-Saud, M. O.; Riaz, A.; Tchelepi, H. A., Multiscale level-set method for accurate modeling of immiscible two-phase flow with deposited thin films on solid surfaces, J. Comput. Phys., 333, 297-320 (2017) · Zbl 1375.76045 [3] Brackbill, J. U.; Kothe, D. B.; Zemach, C., A continuum method for modeling surface tension, J. Comput. Phys., 100, 2, 335-354 (1992) · Zbl 0775.76110 [4] Brady, P. T.; Herrmann, M.; Lopez, J. M., Confined thermocapillary motion of a three-dimensional deformable drop, Phys. Fluids, 23, 2, Article 22101 pp. (2011) [5] Chorin, A. J., A numerical method for solving incompressible viscous flow problems, J. Comput. Phys., 2, 1, 12-26 (1967) · Zbl 0149.44802 [6] Detrixhe, M.; Aslam, T. D., From level set to volume of fluid and back again at second-order accuracy, Int. J. Numer. Methods Fluids, 80, 4, 231-255 (2016) [7] du Chéné, A.; Min, C.; Gibou, F., Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes, J. Sci. Comput., 35, 2-3, 114-131 (2008) · Zbl 1203.65043 [8] Gorokhovski, M.; Herrmann, M., Modeling primary atomization, Annu. Rev. Fluid Mech., 40, 343-366 (2008) · Zbl 1232.76058 [9] Gueyffier, D.; Li, J.; Nadim, A.; Scardovelli, R.; Zaleski, S., Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows, J. Comput. Phys., 152, 2, 423-456 (1999) · Zbl 0954.76063 [10] Herrmann, M.; Lopez, J. M.; Brady, P.; Raessi, M., Thermocapillary motion of deformable drops and bubbles, (Proceedings of the Summer Program (2008)), 155 [11] Jiang, G.-S.; Shu, C.-W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126, 1, 202-228 (1996) · Zbl 0877.65065 [12] Kovscek, A. R.; Radke, C. J., Fundamentals of Foam Transport in Porous Media (1994), ACS Publications [13] Leveque, R. J.; Li, Z. L., The immersed interface method for elliptic-equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31, 1019 (1994) · Zbl 0811.65083 [14] Luddens, F.; Bergmann, M.; Weynans, L., Enablers for high-order level set methods in fluid mechanics, Int. J. Numer. Methods Fluids, 79, 12, 654-675 (2015), Fld. 4070 · Zbl 1455.76128 [15] Lake, L. W., Enhanced Oil Recovery (1989), Prentice Hall: Prentice Hall New Jersey [16] Lamb, H., Hydrodynamics (1916), University Press · JFM 26.0868.02 [17] Ma, C.; Bothe, D., Direct numerical simulation of thermocapillary flow based on the volume of fluid method, Int. J. Multiph. Flow, 37, 9, 1045-1058 (2011) [18] Min, C., On reinitializing level set functions, J. Comput. Phys., 229, 8, 2764-2772 (2010) · Zbl 1188.65122 [19] Miralles, V.; Huerre, A.; Williams, H.; Fournié, B.; Jullien, M.-C., A versatile technology for droplet-based microfluidics: thermomechanical actuation, Lab Chip, 15, 9, 2133-2139 (2015) [20] Muradoglu, M.; Tryggvason, G., A front-tracking method for computation of interfacial flows with soluble surfactants, J. Comput. Phys., 227, 4, 2238-2262 (2008) · Zbl 1329.76238 [21] Peskin, C. S., Flow patterns around heart valves: a numerical method, J. Comput. Phys., 10, 2, 252-271 (1972) · Zbl 0244.92002 [22] Popinet, S., An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys., 228, 16, 5838-5866 (2009) · Zbl 1280.76020 [23] Popinet, S., Numerical models of surface tension, Annu. Rev. Fluid Mech., 50, 1, 49-75 (2018) · Zbl 1384.76016 [24] Popinet, S.; Zaleski, S., A front-tracking algorithm for accurate representation of surface tension, Int. J. Numer. Methods Fluids, 30, 6, 775-793 (1999) · Zbl 0940.76047 [25] Renardy, Y.; Renardy, M., Prost: a parabolic reconstruction of surface tension for the volume-of-fluid method, J. Comput. Phys., 183, 2, 400-421 (2002) · Zbl 1057.76569 [26] Russo, G.; Smereka, P., A remark on computing distance functions, J. Comput. Phys., 163, 1, 51-67 (2000) · Zbl 0964.65089 [27] Seric, I.; Afkhami, S.; Kondic, L., Direct numerical simulation of variable surface tension flows using a volume-of-fluid method, J. Comput. Phys., 352, 615-636 (2018) · Zbl 1375.76051 [28] Young, N. O.; Goldstein, J. S.; Block, M. J., The motion of bubbles in a vertical temperature gradient, J. Fluid Mech., 6, 3, 350-356 (1959) · Zbl 0087.19902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.