×

Boundary conditions for free interfaces with the lattice Boltzmann method. (English) Zbl 1349.76665

Summary: We analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner et al. is shown to be first order accurate. The article presents a new free surface boundary scheme that is suitable for second order accurate simulations based on the LBM. The new method takes into account the free surface position and its orientation with respect to the computational lattice. Numerical experiments confirm the theoretical findings and illustrate the different behavior of the original method and the new method.

MSC:

76M28 Particle methods and lattice-gas methods

Software:

waLBerla
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Aidun, C. K.; Clausen, J. R., Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech., 42, 439-472 (2010) · Zbl 1345.76087
[2] Ammer, R.; Markl, M.; Ljungblad, U.; Körner, C.; Rüde, U., Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method, Comput. Math. Appl., 67, 318-330 (2014) · Zbl 1381.76273
[3] Anderl, D.; Bauer, M.; Rauh, C.; Rüde, U.; Delgado, A., Numerical simulation of adsorption and bubble interaction in protein foams using a lattice Boltzmann method, Food Funct., 5, 755-763 (2014)
[4] Attar, E.; Körner, C., Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition, Int. J. Heat Fluid Flow, 32, 1, 156-163 (2011)
[5] Benzi, R.; Succi, S.; Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222, 3, 145-197 (1992)
[6] Bogner, S.; Rüde, U., Simulation of floating bodies with the lattice Boltzmann method, Comput. Math. Appl., 65, 901-913 (2013) · Zbl 1319.76036
[7] Bouzidi, M.; Firdaouss, M.; Lallemand, P., Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids, 13, 11, 3452 (2001) · Zbl 1184.76068
[8] Buick, J. M.; Greated, C. A., Gravity in a lattice Boltzmann model, Phys. Rev. E, 61, 5, 5307 (2000)
[9] Chen, S.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329-364 (1998) · Zbl 1398.76180
[10] Do-Quang, M.; Aurell, E.; Vergassola, M., An inventory of lattice Boltzmann models of multiphase flows (2000), Royal Institute of Technology, report no. 00:03
[11] Donath, S.; Mecke, K.; Rabha, S.; Buwa, V.; Rüde, U., Verification of surface tension in the parallel free surface lattice Boltzmann method in walberla, Comput. Fluids, 45, 1, 177-186 (2010) · Zbl 1430.76009
[12] Feichtinger, C.; Donath, S.; Köstler, H.; Götz, J.; Rüde, U., WaLBerla: HPC software design for computational engineering simulations, J. Comput. Sci., 2, 2, 105-112 (2011)
[13] Fuster, Daniel; Agbaglah, Gilou; Josserand, Christophe; Popinet, Stéphane; Zaleski, Stéphane, Numerical simulation of droplets, bubbles and waves: state of the art, Fluid Dyn. Res., 41, 6, 065001 (2009) · Zbl 1423.76002
[14] Ginzbourg, I.; Adler, P. M., Boundary flow condition analysis for three-dimensional lattice Boltzmann model, J. Phys. II France, 4, 191-214 (1994)
[15] Ginzburg, I., Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Adv. Water Resour., 28, 1171-1195 (2005)
[16] Ginzburg, I.; d’Humieres, D., Multireflection boundary conditions for lattice Boltzmann models, Phys. Rev. E, 68, 066614 (2003), 29 pp
[17] Ginzburg, I.; Steiner, K., Lattice Boltzmann model for free-surface flow and its application to filling process in casting, J. Comput. Phys., 185, 61-99 (2003) · Zbl 1062.76554
[18] Ginzburg, I.; Verhaeghe, F.; d’Humieres, D., Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions, Commun. Comput. Phys., 3, 2, 427-478 (2008)
[19] Guo, Z.; Zheng, C.; Shi, B., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65, 046308 (2002), 6 pp · Zbl 1244.76102
[20] He, X.; Luo, L.-S., Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys., 88, 3/4, 927-944 (1997) · Zbl 0939.82042
[21] Hirt, C. W.; Nichols, B. D., Volume of fluid (vof) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201-225 (1981) · Zbl 0462.76020
[22] Hirt, C. W.; Shannon, J. P., Free-surface stress conditions for incompressible-flow calculations, J. Comput. Phys., 2: 403-411 (1968) · Zbl 0197.25901
[23] Janßen, C., Kinetic approaches for the simulation of non-linear free surface flow problems in civil and environmental engineering (2010), Technische Universität Braunschweig, PhD thesis
[24] Janssen, C.; Grilli, S. T.; Krafczyk, M., Modelling of wave breaking and wave-structure interactions by coupling of fully nonlinear potential flow and lattice-Boltzmann models, (The International Society of Offshore and Polar Engineers (ISOPE), Proceedings of the Twentieth International Offshore and Polar Engineering Conference. The International Society of Offshore and Polar Engineers (ISOPE), Proceedings of the Twentieth International Offshore and Polar Engineering Conference, Beijing, China, June 20-25, 2010 (2010)), 686-693
[25] Junk, M.; Yang, Z., Asymptotic analysis of lattice Boltzmann boundary conditions, J. Stat. Phys., 121, 1/2, 3-35 (2005) · Zbl 1107.82049
[26] Junk, M.; Yang, Z., One-point boundary condition for the lattice Boltzmann method, Phys. Rev. E, 72, 066701 (Dec 2005)
[27] Körner, C.; Thies, M.; Hofmann, T.; Thürey, N.; Rüde, U., Lattice Boltzmann model for free surface flow for modeling foaming, J. Stat. Phys., 121, 1/2, 179-196 (2005) · Zbl 1108.76059
[28] Ladd, A.-J.-C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, J. Fluid Mech., 271, 285-309 (July 1994)
[29] McKibben, J. F.; Aidun, C. K., Extension of the volume-of-fluid method for analysis of free surface viscous flow in an ideal gas, Int. J. Numer. Methods Fluids, 21, 1153-1170 (1995) · Zbl 0893.76059
[30] Rüde, U.; Thürey, N., Free surface lattice-Boltzmann fluid simulations with and without level sets, (Proceedings of Vision, Modeling and Visualization (2004)), 199-208
[31] Rüde, U.; Thürey, N.; Iglberger, K., Free surface flows with moving and deforming objects for LBM, (Proceedings of Vision, Modeling and Visualization (2006)), 193-200
[32] Nichols, B. D.; Hirt, C. W., Improved free surface boundary conditions for numerical incompressible-flow calculations, J. Comput. Phys., 8, 434-448 (1971) · Zbl 0227.76048
[33] Nourgaliev, R. R.; Dinh, T. N.; Theofanous, T. G.; Joseph, D., The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiph. Flow, 29, 117-169 (2003) · Zbl 1136.76594
[34] Osher, S.; Fedkiw, R. P., Level set methods: an overview and some recent results, J. Comput. Phys., 169, 463-502 (2001) · Zbl 0988.65093
[35] Qian, Y. H.; d’Humieres, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equations, Europhysical Lett., 17, 6, 479-484 (1992) · Zbl 1116.76419
[36] Scardovelli, R.; Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., 31, 567-603 (1999)
[37] Sethian, J. A.; Smereka, P., Level set methods for fluid interfaces, Annu. Rev. Fluid Mech., 35, 341-372 (2003) · Zbl 1041.76057
[38] Svec, O.; Skocek, J.; Stang, H.; Geiker, M. R.; Roussel, N., Free surface flow of a suspension of rigid particles in a non-Newtonian fluid, J. Non-Newton. Fluid Mech., 179-180, 32-42 (2012)
[39] Thürey, N.; Pohl, T.; Rüde, U.; Öchsner, M.; Körner, C., Optimization and stabilization of LBM free surface flow simulations using adaptive parameterization, Proceedings of the First International Conference for Mesoscopic Methods in Engineering and Science. Proceedings of the First International Conference for Mesoscopic Methods in Engineering and Science, Comput. Fluids, 35, 8-9, 934-939 (2006) · Zbl 1177.76331
[40] Xing, X. Q.; Butler, D. L.; Ng, S. H.; Wang, Z.; Danyluk, S.; Yang, C., Simulation of droplet formation and coalesce using lattice Boltzmann-based single-phase model, J. Colloid Interface Sci., 311, 609-618 (2007)
[41] Xing, X. Q.; Butler, D. L.; Yang, C., Lattice Boltzmann-based single-phase method for free surface tracking of droplet motions, Int. J. Numer. Methods Fluids, 53, 333-351 (2007) · Zbl 1105.76048
[42] Yin, X.; Koch, D. L.; Verberg, R., Lattice-Boltzmann method for simulating spherical bubbles with no tangential stress boundary conditions, Phys. Rev. E, 73, 026301 (2006), 13 pp
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.