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Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales

Published online by Cambridge University Press:  20 August 2015

Giacomo Falcucci ,
Stefano Ubertini ,
Chiara Biscarini ,
Silvia Di Francesco ,
Daniele Chiappini ,
Silvia Palpacelli ,
Alessandro De Maio  and
Sauro Succi
Giacomo Falcucci*
Affiliation:
Department of Technologies, University of Naples “Parthenope”, Centro Direzionale-Isola C4, 80143 Naples, Italy
Stefano Ubertini*
Affiliation:
Department of Technologies, University of Naples “Parthenope”, Centro Direzionale-Isola C4, 80143 Naples, Italy
Chiara Biscarini*
Affiliation:
H2CU, Honors Center of Italian Universities-University of Rome “La Sapienza”, Rome, Italy Water Resources Research and Documentation Centre, University for Foreigners, Villa La Colombella, Perugia, Italy
Silvia Di Francesco*
Affiliation:
H2CU, Honors Center of Italian Universities-University of Rome “La Sapienza”, Rome, Italy Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, Perugia, Italy
Daniele Chiappini*
Affiliation:
Department of Mechanical Engineering, University of Rome “Tor Vergata”, Viale Politecnico, Rome, Italy
Silvia Palpacelli
Affiliation:
Nu.M.I.D.I.A. srl, Via Berna 31, 00184 Roma, Italy
Alessandro De Maio*
Affiliation:
Nu.M.I.D.I.A. srl, Via Berna 31, 00184 Roma, Italy
Sauro Succi*
Affiliation:
Istituto Applicazioni Calcolo, CNR, Via dei Taurini 9, 00185 Rome, Italy
*
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Corresponding author.Email:[email protected]
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Abstract

The simulation of multiphase flows is an outstanding challenge, due to the inherent complexity of the underlying physical phenomena and to the fact that multiphase flows are very diverse in nature, and so are the laws governing their dynamics. In the last two decades, a new class of mesoscopic methods, based on minimal lattice formulation of Boltzmann kinetic equation, has gained significant interest as an efficient alternative to continuum methods based on the discretisation of the NS equations for non ideal fluids. In this paper, three different multiphase models based on the lattice Boltzmann method (LBM) are discussed, in order to assess the capability of the method to deal with multiphase flows on a wide spectrum of operating conditions and multiphase phenomena. In particular, the range of application of each method is highlighted and its effectiveness is qualitatively assessed through comparison with numerical and experimental literature data.

Keywords

47.11.-j47.65.CbLattice Boltzmannmultiphase flows
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 2 , February 2011 , pp. 269 - 296
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Prosperetti, A. and Tryggvason, G., Computational Methods for Multiphase Flow, Cambridge University Press, 2005.Google Scholar
[2]Grunau, D., Chen, S. and Eggert, K., A lattice Boltzmann model for multiphase fluid flows, Phys. Fluids. A., 5 (1993), 2557–2562.CrossRefGoogle Scholar
[3]Eggers, J., Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys., 69 (1997), 865–927.CrossRefGoogle Scholar
[4]Gunstensen, A. K., Rothman, D. H., Zaleski, S. and Zanetti, G., Lattice Boltzmann model of immiscible fluids, Phys. Rev. A., 43 (1991), 4320–4327.Google Scholar
[5]Gunstensen, A. K. and Rothman, D. H., Microscopic modeling of immiscible fluids in three dimensions by a lattice Boltzmann method, EPL., 18 (1992), 157–161.Google Scholar
[6]Rothman, D. H. and Keller, J. M., Immiscible cellular-automaton fluids, J. Stat. Phys., 52 (1988), 1119–1127.Google Scholar
[7]Succi, S., Filippova, O., Smith, G. and Kaxiras, E., Applying the Lattice Boltzmann equation to multiscale fluid problems, Computing in Science and Engineering, 3 (2001), 26–37.Google Scholar
[8]D’Humieres, D., Qian, Y. H. and Lallemand, P., Lattice BGK Models for Navier-Stokes equation, EPL., 17(6) (1992), 479–484.Google Scholar
[9]Succi, S., The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Series Numerical Mathematics and Scientific Computation, Oxford University Press, 2001.Google Scholar
[10]X., Shan. and H, Chen., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E., 47 (1993), 1815–1820.Google Scholar
[11]X., Shan. and H, Chen., Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Phys. Rev. E., 49 (1994), 2941–2948.Google Scholar
[12]Diotallevi, F., Biferale, L., Chibbaro, S. and Succi, S., Lattice Boltzmann simulation of capillary filling: finite vapour density effects, Euro. Phys. J. Spec. Top., 171 (2009), 237–243.CrossRefGoogle Scholar
[13]Biscarini, C., Di, S. Francesco and Menciola, P., CFD modelling approach for dam break flow studies, Hydrol. Earth. Syst. Sci. Discuss., 6 (2009), 6759–6793. Lattice Boltzmann Modeling: An Introduction for Scientists and Engineers, Springer Verlag, New-York, 2006.Google Scholar
[14]Biscarini, C., Di Francesco, S., Mencattini, M. and Pizzuto, L., Free surface lattice Boltzmann method for hydraulic problems, Acta of the First International Conference on Computational Methods for Thermal Problems, 129–132, ThermaComp2009, Naples, Italy.Google Scholar
[15]Falcucci, G., Bella, G., Chiatti, G., Chibbaro, S., Sbragaglia, M. and Succi, S., Lattice Bolzmann models with mid-range interactions, Commun. Comput. Phys., 2(6) (2007), 1071–1084.Google Scholar
[16]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. and Toschi, F., Generalized lattice Boltzmann method with multirange pseudopotential, Phys. Rev. E., 75 (2007), 026702.Google Scholar
[17]Falcucci, G., Chiatti, G., Succi, S., Kuzmin, A. and Mohamad, A. M., Rupture of a ferrofluid droplet in external magnetic fields using a single-component lattice Boltzmann model for nonideal fluids, Phys. Rev. E., 79 (2009), 056706.Google Scholar
[18]Falcucci, G., Succi, S. and Ubertini, S., Lattice Boltzmann simulations of phase-separating flows at large density ratioes: the case of doubly-attractive pseudo-potentials, submitted.Google Scholar
[19]Clanet, C., Bguin, C., Richard, D. and Qur, D., Maximal deformation of an impacting drop, J. Fluid. Mech., 517 (2004), 199–208.CrossRefGoogle Scholar
[20]Chibbaro, S., Falcucci, G., Chiatti, G., Chen, H., Shan, X. and Succi, S., Lattice Boltzmann models for non-ideal fluids with arrested phase-separation, Phys. Rev. E., 77 (2008), 036705.CrossRefGoogle Scholar
[21]Falcucci, G., Chibbaro, S., Succi, S., Shan, X. and Chen, H., Lattice Boltzmann spray-like fluids, EPL., 82 (2008), 24005.Google Scholar
[22]Luo, L. S. and Girimaji, S. S., Theory of the lattice Boltzmann method: two-fluid model for binary mixtures, Phys. Rev. E., 67 (2003), 036302.CrossRefGoogle ScholarPubMed
[23]Swift, M. R., Orlandini, E., Osborn, W. R. and Yeomans, J. M., Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev. E., 54 (1996), 5041–5052.CrossRefGoogle ScholarPubMed
[24]Jacqmin, D., Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comput. Phys., 155 (1999), 96–127.CrossRefGoogle Scholar
[25]Sbragaglia, M., Chen, H.. Shan, X. and Succi, S., Continuum free-energy formulation for a class of lattice Boltzmann multiphase models, EPL., 86(2) (2009), 24005.Google Scholar
[26]Orlandini, E., Swift, M. R. and Yeomans, J. M., A lattice Boltzmann model of binary-fluid mixtures, EPL., 32 (1995), 463.CrossRefGoogle Scholar
[27]Swift, M. R., Osborn, W. R. and Yeomans, J. M., Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75 (1995), 830–833.CrossRefGoogle ScholarPubMed
[28]Gonnella, G., Orlandini, E. and Yeomans, J. M., Lattice Boltzmann simulations of lamellar and droplet phases, Phys. Rev. E., 58 (1998), 480–485.Google Scholar
[29]Lamura, A., Gonnella, G. and Yeomans, J. M., A lattice Boltzmann model of ternary fluid mixtures, EPL., 45 (1999), 314.Google Scholar
[30]Xu, A., Gonnella, G. and Lamura, A., Phase separation of incompressible binary fluids with lattice Boltzmann methods, Phys. A. Stat. Mech. App., 331(1-2) (2004), 10–22.Google Scholar
[31]Sofonea, V., Lamura, A., Gonnella, G. and Cristea, A., Finite-difference lattice Boltzmann models with flux limiters for liquid-vapor systems, Phys. Rev. E., 70 (2004), 046702.CrossRefGoogle ScholarPubMed
[32]Wagner, A. J. and Pooley, C. M., Interface width and bulk stability: requirements for the simulation of deeply quenched liquid-gas systems, Phys. Rev. E., 76 (2007), 045702(R).Google Scholar
[33]Guo, Z., Zheng, C. and Shi, B., Discrete lattice effects of the forcing term in the lattice Boltz-mann method, Phys. Rev. E., 65 (2004), 046308.Google Scholar
[34]Becker, J., Junk, M., Kehrwald, D., Thömmes, G. and Yang, Z., A combined lattice BGK/level set method for immiscible two-phase flows, Comput. Math. Appl., 58 (2009), 950–964.Google Scholar
[35]Kupershtokh, A. L., Medvedev, D. A. and Karpov, D. I., On equations of state in a lattice Boltzmann method, Comput. Math. Appl., 58 (2009), 965–974.Google Scholar
[36]Lee, T. and Lin, C.-L., A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 206 (2005), 16–47.CrossRefGoogle Scholar
[37]Lee, T. and Fischer, P. F., Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gasses, Phys. Rev. E., 74 (2006), 046709.CrossRefGoogle Scholar
[38]Lee, T., Effects of incompressibility on the elimination of parasitic currents in the lattice Boltz-mann equation method for binary fluids, Comput. Math. Appl., 58(5) (2009), 987–994.CrossRefGoogle Scholar
[39]Lee, T. and Liu, L., Wall boundary condition in the lattice Boltzmann equation method for nonideal gasses, Phys. Rev. E., 78 (2008), 017702.Google Scholar
[40]Chiappini, D., Bella, G., Succi, S., Toschi, F. and Ubertini, S., Improved lattice Boltzmann without parasitic currents for Rayleigh-Taylor instability, Commun. Comput. Phys., 7 (2010), 423–444.Google Scholar
[41]Chiappini, D., Bella, G., Succi, S., Toschi, F. and Ubertini, S., Application of finite difference lattice Boltzmann method to break-up and coalescence in multiphase flows, Int. J. Mod. Phys. C., 20–11 (2009), 1803.Google Scholar
[42]He, X., Chen, S. and Zhang, R., A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys., 152 (1999), 642–663.Google Scholar
[43]Nourgaliev, R. R., Dinh, T. N. and Theofanous, T. G., A pseudocompressibility method for the numerical simulation of incompressible multifluid flows, Int. J. Multiphase. Flows., 30 (2004), 901–937.Google Scholar
[44]Cabot, W. H. and Cook, A. W., Reynolds number effects on Rayleigh-Taylor instability with possible implications for type-Ia supernovae, Nat. Phys., 2 (2006), 562–568.CrossRefGoogle Scholar
[45]Karlin, I. V., Ferrante, A. and Ottinger, H. C., Perfect entropy functions of the lattice Boltzmann method, EPL., 47 (1999), 182–188.Google Scholar
[46]Boghosian, B. M., Love, P. J., Coveney, P. V. et al., Galilean-invariant lattice-Boltzmann models with H theorem, Phys. Rev. E., 68 (2003), 025103R.Google Scholar
[47]Huang, Z., De Luca, A., Atherton, T. J., Bird, M. and Rosenblatt, C., Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape, Phys. Rev. Lett., 99 (2007), 204502.Google Scholar
[48]Amati, G., Succi, S. and Piva, R., Massively parallel lattice-Boltzmann simulation of turbulent channel flow, Int. J. Mod. Phys. C., 8 (1997), 869–877.CrossRefGoogle Scholar
[49]Kandhai, D., Koponen, A., Hoekstra, A. G.et al., Lattice-Boltzmann hydrodynamics on parallel systems, Comput. Phys. Commun., 111 (1998), 14–26.Google Scholar
[50]Desplat, J. C., Pagonabarraga, I. and Bladon, P., LUDWIG: A parallel Lattice-Boltzmann code for complex fluids, Comput. Phys. Commun., 134 (2001), 273–290.Google Scholar
[51]Mazzeo, M. D. and Coveney, P. V., HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries, Comput. Phys. Commun., 178 (2008), 894–914.CrossRefGoogle Scholar
[52]Bernaschi, M., Melchionna, S., Succi, S.et al., MUPHY: A parallel multi physics/scale code for high performance bio-fluidic simulations, Comput. Phys. Commun., 180 (2009), 1495–1502.Google Scholar
[53]Dupuis, A. and Chopard, B., Theory and applications of an alternative lattice Boltzmann grid refinement algorithm, Phys. Rev. E., 67 (2003), 066707.Google Scholar
[54]Crouse, B., Rank, E., Krafczyk, M.et al., A LB-based approach for adaptive flow simulations, Int. J. Mod. Phys. B., 17(1-2) (2003), 109–112.Google Scholar
[55]Hirt, C. W. and Nichols, B. D., Volume of fluid method for dynamics of free boundaries, J. Comput. Phys., 30 (1981), 201–221.CrossRefGoogle Scholar
[56]Scardovelli, R. and Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid. Mech., 31 (1999), 567–603.Google Scholar
[57]Körner, C., Thies, M., Hofmann, T., Thürey, N. and Rüde, U., Lattice Boltzmann model for free surface flow for modeling foaming, J. Stat. Phys., 121(1/2) (2005), 179–196.Google Scholar
[58]Thürey, N., Rüde, U. and Körner, C., Interactive free surface fluids with the lattice Botlzmann method, Technical Report 05-4, Lehrstuhl fur Informatik 10 (Systemsimulation), University of Erlangen-Nueremberg.Google Scholar
[59]Thürey, N. and Rüde, U., Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids, Comput. Vis. Sci., 12 (2009), 247–263.Google Scholar
[60]Frazao, Soarez, Dam-Break Induced Flows in Complex Topographies, Theoretical, Numerical and Experimental Approaches, PhD Thesis, Louvain-la-Neuve: Université Catholique de Louvain, Civil Engineering Department, Hydraulics Division, 2002.Google Scholar
[61]Buick, J. M. and Greated, C. A., Gravity in a lattice Boltzmann model, Phys. Rev. E., 61 (2000), 5307.CrossRefGoogle Scholar
[62]Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S. and Yakhot, V., Extended Boltzmann kinetic equation for turbulent flows, Science., 301 (2003), 633–636.Google Scholar