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A refined volume-of-fluid algorithm for capturing sharp fluid interfaces on arbitrary meshes. (English) Zbl 1351.76198

Summary: This paper presents a new volume-of-fluid scheme (M-CICSAM), capable of capturing abrupt interfaces on meshes of arbitrary topology, which is a modification to the compressive interface capturing scheme for arbitrary meshes (CICSAM) proposed in the recent literature. Without resort to any explicit interface reconstruction, M-CICSAM is able to precisely model the complex free surface deformation, such as interface rupture and coalescence. By theoretical analysis, it is shown that the modified CICSAM overcomes three inherent drawbacks of the original CICSAM, concerning the basic differencing schemes, the switching strategy between the compressive downwind and diffusive high-resolution schemes, and the far-upwind reconstruction technique on arbitrary unstructured meshes. To evaluate the performance of the newly proposed scheme, several classic interface capturing methods developed in the past decades are compared with M-CICSAM in four test problems. The numerical results clearly demonstrate that M-CICSAM produces more accurate predictions on arbitrary meshes, especially at high Courant numbers, by reducing the numerical diffusion and preserving the interface shape.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Txx Multiphase and multicomponent flows

Software:

RIPPLE
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Full Text: DOI Link

References:

[1] Ubbink, O.; Issa, R. I., A method for capturing sharp fluid interfaces on arbitrary meshes, J. Comput. Phys., 153, 1, 26-50 (1999) · Zbl 0955.76058
[2] Pericleous, K. A.; Chan, K. S.; Cross, M., Free surface flow and heat transfer in cavities: the SEA algorithm, Numer. Heat Transf., 27, 4, 487-507 (1995)
[3] Heyns, J. A.; Malan, A. G.; Harms, T. M.; Oxtoby, O. F., Development of a compressive surface capturing formulation for modelling free-surface flow by using the volume-of-fluid approach, Int. J. Numer. Methods Fluids, 71, 6, 788-804 (2013) · Zbl 1430.76471
[4] Pan, D.; Chang, C. H., The capturing of free surfaces in incompressible multi-fluid flows, Int. J. Numer. Methods Fluids, 33, 2, 203-222 (2000) · Zbl 0972.76067
[5] Darwish, M.; Moukalled, F., Convective schemes for capturing interfaces of free-surface flows on unstructured grids, Numer. Heat Transf., 49, 1, 19-42 (2006)
[6] Kelecy, F. J.; Pletcher, R. H., The development of a free surface capturing approach for multidimensional free surface flows in closed containers, J. Comput. Phys., 138, 2, 939-980 (1997) · Zbl 0903.76058
[7] Jahanbakhsh, E.; Panahi, R.; Seif, M. S., Numerical simulation of three-dimensional interfacial flows, Int. J. Numer. Methods Heat Fluid Flow, 17, 4, 384-404 (2007) · Zbl 1231.76209
[8] Unverdi, S. O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multifluid flows, J. Comput. Phys., 100, 1, 25-37 (1992) · Zbl 0758.76047
[9] Okamoto, T.; Kawahara, M., Two-dimensional sloshing analysis by Lagrangian finite element method, Int. J. Numer. Methods Fluids, 11, 5, 453-477 (1990) · Zbl 0711.76008
[10] de Sousa, F. S.; Mangiavacchi, N.; Nonato, L. G.; Castelo, A.; Tomé, M. F.; Ferreira, V. G.; Cuminato, J. A.; McKee, S., A front-tracking/front-capturing method for the simulation of 3D multifluid flows with free surfaces, J. Comput. Phys., 198, 2, 469-499 (2004) · Zbl 1116.76412
[11] Kim, M. S.; Lee, W. I., A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface-tracking algorithm and its verification, Int. J. Numer. Methods Fluids, 42, 7, 765-790 (2003) · Zbl 1143.76536
[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] Tryggvason, G.; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y.-J., A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 2, 708-759 (2001) · Zbl 1047.76574
[14] Harlow, F. H.; Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8, 2182-2189 (1965) · Zbl 1180.76043
[15] Chan, R. K.C.; Street, R. L., A computer study of finite-amplitude water waves, J. Comput. Phys., 6, 1, 68-94 (1970) · Zbl 0207.27403
[16] Nakayama, T.; Mori, M., An Eulerian finite element method for time-dependent free surface problems in hydrodynamics, Int. J. Numer. Methods Fluids, 22, 3, 175-194 (1996) · Zbl 0874.76043
[17] Scardovelli, R.; Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., 31, 567-603 (1999)
[18] Pilliod, J. E.; Puckett, E. G., Second-order accurate volume-of-fluid algorithms for tracking material interfaces, J. Comput. Phys., 199, 2, 465-502 (2004) · Zbl 1126.76347
[19] Rudman, M., A volume-tracking method for incompressible multi-fluid flows with large density variations, Int. J. Numer. Methods Fluids, 28, 357-378 (1998) · Zbl 0915.76060
[20] Meier, M.; Yadigaroglu, G.; Smith, B. L., A novel technique for including surface tension in PLIC-VOF methods, Eur. J. Mech. B, Fluids, 21, 1, 61-73 (2002) · Zbl 1064.76084
[21] Rider, W. J.; Kothe, D. B., Reconstructing volume tracking, J. Comput. Phys., 141, 2, 112-152 (1998) · Zbl 0933.76069
[22] Qian, L.; Causon, D. M.; Mingham, C. G.; Ingram, D. M., A free-surface capturing method for two fluid flows with moving bodies, Proc. R. Soc. A, 462, 2065, 21-42 (2006) · Zbl 1149.76642
[23] 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) · Zbl 0977.76071
[24] van der Pijl, S. P.; Segal, A.; Vuik, C.; Wesseling, P., A mass-conserving level-set method for modeling of multi-phase flows, Int. J. Numer. Methods Fluids, 47, 4, 339-361 (2005) · Zbl 1065.76160
[25] LeVeque, R. J., High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 33, 2, 627-665 (1996) · Zbl 0852.76057
[26] Bonometti, T.; Magnaudet, J., An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics, Int. J. Multiph. Flow, 33, 2, 109-133 (2007)
[27] Zalesak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 31, 3, 335-362 (1979) · Zbl 0416.76002
[28] Gopala, V. R.; van Wachem, B. G.M., Volume of fluid methods for immiscible-fluid and free-surface flows, Chem. Eng. J., 141, 1-3, 204-221 (2008)
[29] Rusche, H., Computational fluid dynamics of dispersed two-phase flows at high phase fractions (2002), Imperial College of Science, Technology and Medicine, PhD thesis
[30] Walters, D. K.; Wolgemuth, N. M., A new interface-capturing discretization scheme for numerical solution of the volume fraction equation in two-phase flows, Int. J. Numer. Methods Fluids, 60, 8, 893-918 (2009) · Zbl 1419.76466
[31] Thuburn, J., Multidimensional flux-limited advection schemes, J. Comput. Phys., 123, 1, 74-83 (1996) · Zbl 0840.76063
[32] Dendy, E. D.; Padial-Collins, N. T.; VanderHeyden, W. B., A general-purpose finite-volume advection scheme for continuous and discontinuous fields on unstructured grids, J. Comput. Phys., 180, 2, 559-583 (2002) · Zbl 1143.76499
[33] Xiao, F.; Ikebata, A., An efficient method for capturing free boundaries in multi-fluid simulations, Int. J. Numer. Methods Fluids, 42, 2, 187-210 (2003) · Zbl 1143.76547
[34] Yokoi, K., Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm, J. Comput. Phys., 226, 2, 1985-2002 (2007) · Zbl 1388.76281
[35] Lafaurie, B.; Nardone, C.; Scardovelli, R.; Zaleski, S.; Zanetti, G., Modelling merging and fragmentation in multiphase flows with SURFER, J. Comput. Phys., 113, 1, 134-147 (1994) · Zbl 0809.76064
[36] Muzaferija, S.; Peric, M.; Sames, P.; Schellin, T., A two-fluid Navier-Stokes solver to simulate water entry, (Proceedings of the Twenty-Second Symposium on Naval Hydrodynamics (1999)), 638-649
[37] Tsui, Y. Y.; Lin, S. W.; Cheng, T. T.; Wu, T. C., Flux-blending schemes for interface capture in two-fluid flows, Int. J. Heat Mass Transf., 52, 23-24, 5547-5556 (2009) · Zbl 1388.76432
[38] Hogg, P. W.; Gu, X. J.; Emerson, D. R., An implicit algorithm for capturing sharp fluid interfaces in the volume of fluid advection method (2006), Council for the Central Laboratory of the Research Councils
[39] Brackbill, J. U.; Kothe, D. B.; Zemach, C., A continuum method for modelling surface tension, J. Comput. Phys., 100, 2, 335-354 (1992) · Zbl 0775.76110
[40] Issa, R. I., Solution of the implicitly discretised fluid flow equations by operator-splitting, J. Comput. Phys., 62, 1, 40-65 (1986) · Zbl 0619.76024
[41] Panahi, R.; Jahanbakhsh, E.; Seif, M. S., Comparison of interface capturing methods in two phase flow, Iran. J. Sci. Technol., 539-548 (2005) · Zbl 1112.76483
[42] Leonard, B. P., The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection, Comput. Methods Appl. Mech. Eng., 88, 1, 17-74 (1991) · Zbl 0746.76067
[43] Leonard, B. P.; Mokhtari, S., Beyond first-order upwinding: the ultra-sharp alternative for non-oscillatory steady-state simulation of convection, Int. J. Numer. Methods Eng., 30, 4, 729-766 (1990)
[44] Roe, P. L., Characteristic-based schemes for the Euler equations, Annu. Rev. Fluid Mech., 18, 337-365 (1986) · Zbl 0624.76093
[45] Darwish, M. S.; Moukalled, F. H., Normalized variable and space formulation methodology for high-resolution schemes, Numer. Heat Transf., 26, 1, 79-96 (1994)
[46] van Leer, B., Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. Comput. Phys., 32, 1, 101-136 (1979) · Zbl 1364.65223
[47] Jasak, H.; Weller, H. G.; Gosman, A. D., High resolution NVD differencing scheme for arbitrarily unstructured meshes, Int. J. Numer. Methods Fluids, 31, 2, 431-449 (1999) · Zbl 0952.76057
[48] Zhang, D.; Jiang, C.; Yang, C.; Yang, Y., Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes, Int. J. Numer. Methods Fluids, 74, 3, 189-221 (2014) · Zbl 1455.65160
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