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Extended BGK Boltzmann for Dense Gases

Published online by Cambridge University Press:  03 June 2015

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Abstract

An alternate BGK type formulation of the Enskog equation has been recently proposed. It was shown that the new model has a valid H-theorem and correct thermal conductivity. We propose Lattice Boltzmann (LB) formulation of this new Enskog-BGK model. The molecular nature of the model is verified in case of shear flow by comparing the predicted normal stress behavior by the current model with the prediction of molecular dynamics simulations. We extend the model for multiphase flow by incorporating attractive part as Vlasov type force. To validate multiphase formulation, the results of 3D simulations of a condensing bubble in a periodic box are presented.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Ansumali, S.Mean-field Model beyond Boltzmann-Enskog Picture for Dense gases. Communications in Computational Physics, 9(5): 11171127, 2011.Google Scholar
[2]Ansumali, S., Karlin, I.V., Arcidiacono, S., Abbas, A., and Prasianakis, N.I.Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy. Physical Review Letters, 98(12): 124502, 2007.Google Scholar
[3]Kim, S.H., Pitsch, H., and Boyd, I.D.Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows. Physical Review E, 77(2): 026704, 2008.Google Scholar
[4]Kim, S.H. and Pitsch, H.Analytic solution for a higher-order lattice Boltzmann method: Slip velocity and Knudsen layer. Physical Review E, 78(1): 016702, 2008.Google Scholar
[5]Yudistiawan, W.P., Ansumali, S., and Karlin, I.V.Hydrodynamics beyond Navier-Stokes: The slip flow model. Physical Review E, 78(1): 016705, 2008.Google Scholar
[6]Toschi, F. and Succi, S.Lattice Boltzmann method at finite Knudsen numbers. EPL (Europhysics Letters), 69: 549, 2005.Google Scholar
[7]Sofonea, V. and Sekerka, R.F.Boundary conditions for the upwind finite difference lattice Boltzmann model: Evidence of slip velocity in micro-channel flow. Journal of Computational Physics, 207(2): 639659, 2005.Google Scholar
[8]Zhang, Y.H., Gu, X.J., Barber, R.W., and Emerson, D.R.Capturing Knudsen layer phenomena using a lattice Boltzmann model. Physical Review E, 74(4): 046704, 2006.Google Scholar
[9]Bhatnagar, P.L., Gross, E.P., and Krook, M.A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical Review, 94(3): 511, 1954.Google Scholar
[10]Higuera, F.J., Succi, S., and Benzi, R.Lattice gas dynamics with enhanced collisions. EPL (Europhysics Letters), 9: 345, 1989.Google Scholar
[11]Chen, H., Chen, S., and Matthaeus, W.H.Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Physical Review A, 45(8): 53395342, 1992.Google Scholar
[12]Qian, Y.H., d’Humieres, D., and Lallemand, P.Lattice BGK models for navier-stokes equation. EPL (Europhysics Letters), 17: 479, 1992.Google Scholar
[13]Shan, X. and Chen, H.Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47(3): 1815, 1993.Google Scholar
[14]Swift, M.R., Orlandini, E., Osborn, W.R., and Yeomans, J.M.Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Physical Review E, 54(5): 5041, 1996.Google Scholar
[15]He, X. and Doolen, G.D.Thermodynamic foundations of kinetic theory and lattice Boltz-mann models for multiphase flows. Journal of Statistical Physics, 107(1): 309328, 2002.Google Scholar
[16]Luo, L.-S.Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases. Phys. Rev. E, 62: 49824996, 2000.Google Scholar
[17]Ihle, T. and Kroll, D.M.Thermal lattice-Boltzmann method for non-ideal gases with potential energy. Computer Physics Communications, 129(1): 112, 2000.Google Scholar
[18]Chapman, S. and Cowling, T.G.The Mathematical theory of non-uniform gases. The Mathe-matical Theory of Non-uniform Gases, by Chapman, Sydney and Cowling, TG and Foreword by Cercignani, C., pp. 447. ISBN 052140844X. Cambridge, UK: Cambridge University Press, January 1991,1, 1991.Google Scholar
[19]Dufty, J.W., Santos, A., and Brey, J.J.Practical Kinetic Model for Hard Sphere Dynamics. Phys. Rev. Lett., 77: 12701273, 1996.Google Scholar
[20]Lutsko, J.F.Approximate Solution of the Enskog Equation far from Equilibrium. Phys. Rev. Lett., 78: 243246, 1997.Google Scholar
[21]Luo, L.-S.Unified Theory of lattice Boltzmann Models for Nonideal Gases. Phys. Rev. Lett., 81: 16181621, 1998.CrossRefGoogle Scholar
[22]Shan, X. and Chen, H.Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Physical Review E, 49(4): 2941, 1994.CrossRefGoogle ScholarPubMed
[23]Dufty, J.W., Santos, A., Brey, J.J., and Rodriguez, R.F.Model for nonequilibrium computer simulation methods. Phys. Rev. A, 33: 459466, 1986.Google Scholar
[24]Lees, A.W. and Edwards, S.F.The computer study of transport processes under extreme conditions. Journal of Physics C: Solid State Physics, 5: 1921, 1972.Google Scholar
[25]Carnahan, N.F. and Starling, K.E.Equation of state for nonattracting rigid spheres. The Journal of Chemical Physics, 51: 635, 1969.Google Scholar
[26]Lutsko, J.F.Viscoelastic effects from the Enskog equation for uniform shear flow. Phys. Rev. E, 58: 434446, 1998.Google Scholar
[27]He, X., Shan, X., and Doolen, G.D.Discrete Boltzmann equation model for nonideal gases. Physical Review E, 57(1): 1316, 1998.Google Scholar
[28]Bastea, S. and Lebowitz, J.L.Spinodal decomposition in binary gases. Physical Review Letters, 78(18): 34993502, 1997.Google Scholar
[29]Kikkinides, E.S., Kainourgiakis, M.E., Yiotis, A.G., and Stubos, A.K.Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces. Phys. Rev. E, 82: 056705, 2010.Google Scholar
[30]Rowlinson, J.S. and Widom, B.Molecular Theory of Capillarity. Dover Pubns, 2002.Google Scholar
[31]Moroni, D., Rotenberg, B., Hansen, J.P., Succi, S., and Melchionna, S.Solving the Fokker-Planck kinetic equation on a lattice. Physical Review E, 73(6): 066707, 2006.Google Scholar
[32]Lee, T. and Fischer, P.F.Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. Phys. Rev. E, 74: 046709, 2006.Google Scholar
[33]Wagner, A.J.The origin of spurious velocities in lattice Boltzmann. International Journal of Modern Physics B, 17: 193196, 2003.Google Scholar
[34]Chikatamarla, S.S. and Karlin, I.V.Entropy and galilean invariance of lattice Boltzmann theories. Phys. Rev. Lett., 97: 190601, 2006.Google Scholar
[35]Ansumali, S., Karlin, I.V., and Öttinger, H.C.Minimal entropic kinetic models for hydrody-namics. EPL (Europhysics Letters), 63:798, 2003.Google Scholar
[36]Marconi, U.M.B. and Melchionna, S.Kinetic theory of correlated fluids: From dynamic density functional to lattice Boltzmann methods. The Journal of Chemical Physics, 131: 014105, 2009.Google Scholar