Two component lattice Boltzmann model with flux limiters

• Authors: Artur Cristea , Victor Sofonea
• Languages of publication: EN

Abstracts

EN

A two-dimensional finite difference lattice Boltzmann model for two-component fluid systems is introduced. Phase separaton is achieved using an appropriate expression of the bulk free energy. Flux limiter techniques are used to improve the numberical accuracy of this model.

Keywords

EN

lattice Boltzmann; hase separation; flux limiters; 47.11.+j 47.55.Kf

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2004
• Volume: 2
• Issue: 2
• Pages: 382-396

Dates

published

1 - 6 - 2004

online

1 - 6 - 2004

Contributors

author

Artur Cristea

• Laboratory for Numerical Simulation and Paralel Computing in Fluid Mechanics Center for Fundamental and Advanced Technical Research, Romanian Academy, Bd. Mihai Viteazul 24, R-300223, Timi§oara, Romania

author

Victor Sofonea

• Laboratory for Numerical Simulation and Paralel Computing in Fluid Mechanics Center for Fundamental and Advanced Technical Research, Romanian Academy, Bd. Mihai Viteazul 24, R-300223, Timi§oara, Romania

References

• [1] K Huang: Statistical Mechanics, John Willey and Sons Inc., New York, 1963.
• [2] P.L. Bhatnagar, E.P. Gross and M. Krook: “A model for collision processes in gases I: small amplitude processes in charged and neutral one-component system”, Physical Review Vol. 94, (1954), pp. 511–525. http://dx.doi.org/10.1103/PhysRev.94.511[Crossref]
• [3] X. He, X. Shan and G. Doolen: “Discrete Boltzmann equation model for nonideal gases”, Physical Review E, Vol. 57, (1998), pp. R13-R16. http://dx.doi.org/10.1103/PhysRevE.57.R13[Crossref]
• [4] N.S. Martys, X. Shan and H. Chen: “Evaluation of the external force term in the discrete Boltzmann equation”, Physical REview E, Vol. 58, (1998), pp. 6855–6857. http://dx.doi.org/10.1103/PhysRevE.58.6855[Crossref]
• [5] D.H. Rothman and S. Zaleski: Lattice-Gas Cellular Automata, Simple Models of Complex Hydrodynamics, Cambridge University Press, Cambridge, 1997.
• [6] B. Chopard and M. Dorz: Cellular Automata Modeling of Physical Systems, Cambridge University Press, Cambridge, 1998.
• [7] S. Chen and G.D. Doolen: “Lattice Boltzmann method for fluid flows”, Annual Review of Fluid Mechanics, Vol. 30, (1998), pp. 329–364. http://dx.doi.org/10.1146/annurev.fluid.30.1.329[Crossref][WoS]
• [8] D.A. Wolf-Gladrow: Lattice Gas Cellular Automata and Lattice Boltzmann Models, Springer Verlag, Berlin, 2000.
• [9] S. Succi: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, Oxford, 2001.
• [10] X. He and L.S. Luo: “A priori derivation of the lattice Boltzmann equation”, Physical Review E, Vol. 55, (1997), pp. R6333-R6336. http://dx.doi.org/10.1103/PhysRevE.55.R6333[Crossref]
• [11] X. He and L.S. Luo: “Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation”, Physical Review E, Vol. 56, (1997), pp. 6811–6817. http://dx.doi.org/10.1103/PhysRevE.56.6811[Crossref]
• [12] V. Sofonea and R.F. Sekerka: “BGK models for diffusion in isothermal binary fluid systems”, Physica A, Vol. 299, (2001), pp. 494–520. http://dx.doi.org/10.1016/S0378-4371(01)00246-1[Crossref]
• [13] L.S. Luo: “Unified Theory of Lattice Boltzmann Models for Nonideal Gases”, Phhsical Review Letters, Vol. 81, (1998), pp. 1618–1621. http://dx.doi.org/10.1103/PhysRevLett.81.1618[Crossref]
• [14] L.S. Luo: “Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases”, Physical Review E, Vol. 62, (2000), pp. 4982–4996. http://dx.doi.org/10.1103/PhysRevE.62.4982[Crossref]
• [15] N. Cao, S. Chen, S. Jin and D. Martinez: “Physical symmetry and lattice symmetry in the lattice Boltzmann method”, Physical Review E, Vol. 55, (1997), pp. R21-R24. http://dx.doi.org/10.1103/PhysRevE.55.R21[Crossref]
• [16] V. Sofonea: Lattice Boltzmann models for multicomponent fluids, Final Report, Contract SPC-98-4061 No. F61775-98-WE101, US Air Force European Office for Aerospace Research and Development, Institute for Complex Fluids, Polytechnical University of Timi§oara, 1999, (unpublished).
• [17] J. Tölke, M. Krafczyk, M. Schulz and E. Rank: “Implicit discretization and nonuniform mesh refinement approaches for FD discretizationos of LBGK models”, International Journal of Modern Phhsics C, Vol. 9, (1998), pp. 1143–1157. http://dx.doi.org/10.1142/S0129183198001059[Crossref]
• [18] D. Kandhai, W. Soll, S. Chen, A. Hoekstra and P. Sloot: “Finite-difference lattice-BGK methods on nested grids”, Computer Physics Communications, Vol. 129, (2000), pp. 100–109. http://dx.doi.org/10.1016/S0010-4655(00)00097-7[Crossref]
• [19] T. Seta and R. Takahashi: “Numerical stability analysis of FDLBM”, Journal of Statistical Physics, Vol. 107, (2002), pp. 557–572. http://dx.doi.org/10.1023/A:1014599729717[Crossref]
• [20] V. Sofonea and R.F. Sekerka: “Viscosity of finite diffeernce lattice Boltzmann models”, Journal of Computational Physics, Vol. 184, (2003), pp. 422–434. http://dx.doi.org/10.1016/S0021-9991(02)00026-8[Crossref]
• [21] M. Watari and M. Tsutahara: “Two-dimensional thermal model of the finitediffeernce lattice Boltzmann method with high spatial isotropy”, Physical Review E, Vol. 67, (2003), pp. 036306-1–036306-7. http://dx.doi.org/10.1103/PhysRevE.67.036306
• [22] E.F. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics, Second Edition, Springer Verlag, Berlin, 1999.
• [23] B. Gustafsson, H. O. Kreiss and J. Oliger: Time Dependent Problems and Difference Methods, John Wileyand Sons, New York, 1995.
• [24] W.H. Press, S.A. Teukoslky, W.T. Vetterling and B.P. Flannery: Numerical Recipes in Fortran: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1992.
• [25] R.J. Le Veque: Numerical Methods for Conservation Laws, Birkhäuyser Verlag, Basel, 1992.
• [26] S. Teng, Y. Chen and H. Ohashi: “Lattice Boltzmann simulation of multiphase fluid flows through the total variation diminishing with artificial compression scheme”, International Journal of Heat and Fluid Flow, Vol. 21, (2000), pp. 112–121. http://dx.doi.org/10.1016/S0142-727X(99)00068-5[Crossref]
• [27] A. Cristea and V. Sofonea: “Two component lattice Boltzmann models with fluix limiter techniques”, Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science, Vol. 4 (2003), pp. 59–64.
• [28] A. Cristea and V Sofonea: “Reduction of spurious velocity in finite difference lattice Boltzmann models for liquid-vapour systems”, International Journal of Modern Phhsics C, Vol. 14, (2003), pp. 1251–1265. http://dx.doi.org/10.1142/S0129183103005388[Crossref]
• [29] V. Sofonea and R.F. Sekerka: “Diffusivity of finite diffeernce lattice Boltzmann models”, submitted to: Physical Review E, (2004).
• [30] X. Shan and H. Chen: “Lattice Boltzmann model for simulating flows with multiple phases and compoents”, Phhsical Review E, Vol. 47, (1993), pp. 1815–1819. http://dx.doi.org/10.1103/PhysRevE.47.1815[Crossref]
• [31] M. Swift, E. Orlandini, W. R Osborn and J. Yeomans: “Lattice Boltzmann simulations of liquid-gas and binary fluid systems”, Physical Review E, Vol. 54, (19960, pp. 5041–5052. http://dx.doi.org/10.1103/PhysRevE.54.5041[Crossref]
• [32] R.R. Nourgaliev, T.N. Dinh, T.G. Theofanous and D. Joseph: “The lattice Boltzmann equation method: theoretical interpretation, numerics and implications”, International Journal of Multiphase Flow, Vol. 29, (2003), pp. 117–169. http://dx.doi.org/10.1016/S0301-9322(02)00108-8[Crossref]
• [33] D. Kondepudi and I. Prigogine: Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wileyand Sons, Chichester-New York, 1998.
• [34] S. Balay, K. Buschelman, W. Gropp,l D. Kaushik, M. Knepley, L.C. McInnes, B. Smith and H. Zhang: PETSc User’s Manual, ANL-95/11-Revision 2.1.5, Argonne National Laboratory, January 27, 2003, (http://www.msc.anl.gov/petsc).

Identifiers

DOI

10.2478/BF02475638