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Lattice Boltzmann Methods for Reactive and Other Flows

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Turbulent Combustion Modeling

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 95))

Abstract

The lattice Boltzmann method (LBM) is receiving increasing attention in recent years as an alternative approach for computational fluid dynamics. Through its kinetic theory origin, the method inherits the physically appealing particle picture that can be adapted to simulate multiscale and multiphysics systems with sizes ranging from the microscale (where the continuum hypothesis may break down) to macroscale applications. The method is characterized by its straightforward implementation in complex geometries and the fact that it involves only nearest neighbor interactions without global operations, making LBM algorithms ideally suited for parallelization. However, the method in general employs a larger number of degrees of freedom per grid point than classical CFD approaches, and parallel implementation may be essential in order to meet the higher memory requirements. In this chapter, an overview of the method and its applications is presented focusing on recent model developments for the description of the averaged macroscopic behavior of isothermal and non-isothermal, single- and multi-component and reactive flows.

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References

  1. Abe, T.: Derivation of the Lattice Boltzmann Method by Means of the Discrete Ordinate Method for the Boltzmann Equation. J. Comp. Phys. 131, 241–246 (1997)

    Article  MATH  Google Scholar 

  2. Alder, B.J., Wainright, T.E.: Studies in molecular dynamics: I. General methods. J. Chem. Phys. 32, 459–466 (1959)

    Article  Google Scholar 

  3. Ansumali, S., Karlin, I.V.: Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 66, 026311 (2002)

    Article  MathSciNet  Google Scholar 

  4. Ansumali, S.: Minimal kinetic modeling of hydrodynamics. PhD thesis, ETH Dissertation No 15534, Swiss Federal Institute of Technology, Zurich, Switzerland (2004)

    Google Scholar 

  5. Ansumali, S., Karlin, I.V., Öttinger, H.C.: Minimal entropic kinetic models for simulating hydrodynamics. Europhys. Lett. 63, 798–804 (2003)

    Article  Google Scholar 

  6. Ansumali, S., Karlin, I.V., Succi, S.: Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model. Physica A 338, 379–394 (2004)

    Article  MathSciNet  Google Scholar 

  7. Ansumali, S., Karlin, I.V., Frouzakis, C.E., Boulouchos, K.: Entropic lattice Boltzmann method for microflows. Physica A 359, 289–305 (2005)

    Article  Google Scholar 

  8. Ansumali, S., Karlin, I.V., Arcidiacono, S., Abbas, A., Prasianakis, N.: Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy. Phys. Rev. Lett. 98, 124502 (2007)

    Article  Google Scholar 

  9. Ansumali, S., Arcidiacono, S., Chikatamarla, S.S., Prasianakis, N.I., Gorban, A.N., Karlin, I.V.: Quasi-equilibrium lattice Boltzmann method. Eur. Phys. J. 56, 135–139 (2007)

    Google Scholar 

  10. Ansumali, S., Karlin, I.V.: Consistent Lattice Boltzmann Method. Phys. Rev. Lett. 95, 260605 (2005)

    Article  Google Scholar 

  11. Arcidiacono, S., Mantzaras, J., Ansumali, S., Karlin, I.V., Frouzakis, C.E., Boulouchos, K.: Simulation of binary mixtures with the lattice Boltzman method. Phys. Rev. E 74, 056707 (2007)

    Article  MathSciNet  Google Scholar 

  12. Arcidiacono, S., Karlin, I.V., Mantzaras, J., Frouzakis, C.E.: Lattice Boltzmann model for the simulation of multicomponent mixtures. Phys. Rev. E 76, 046703 (2007)

    Article  Google Scholar 

  13. Arcidiacono, S., Mantzaras, J., Karlin, I.V.: Lattice Boltzmann simulation of catalytic reactions. Phys. Rev. E 78, 046711 (2008)

    Article  Google Scholar 

  14. Asinari, P.: Viscous coupling based lattice Boltzmann model for binary mixtures. Phys Fluids 17, 067102 (2005)

    Article  MathSciNet  Google Scholar 

  15. Asinari, P., Luo, L.-S.: A consistent lattice Boltzmann equation with baroclinic coupling for mixtures. J. Comp. Phys. 227, 3878–3895 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Bardow, A., Karlin, I.V., Gusev, A.A.: General characteristic-based algorithm for off-lattice Boltzmann simulations. Europhys. Lett. 75, 434–440 (2006)

    Article  Google Scholar 

  17. Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Universiy Press (1994)

    Google Scholar 

  18. Boghosian, B.M., Yepez, J., Coveney, P.V., Wagner, A.: Entropic Lattice Boltzmann Methods. Proc. Roy. Soc. Lon. A 457, 717–766 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Cercignani, C.: The Boltzmann equation and its applications. In Applied Mathematical Sciences, Vol. 61, Springer-Verlag, New York (1988)

    MATH  Google Scholar 

  20. Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases, 3rd edition, Cambridge University Press, London (1970)

    Google Scholar 

  21. Chen, S., Wang, Z., Shan, X., Doolen, G.D.: Lattice Boltzmann computational fluid dynamics in three dimensions. J. Stat. Phys. 68, 379–400 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  22. Chen, S., Doolen, G.D.: Lattice Boltzmann methods for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)

    Article  MathSciNet  Google Scholar 

  23. Chen, S., Kandasamy, S., Orszag, S., Shock, R., Succi, S., Yakhot, V.: Extended Boltzmann Kinetic Equation for Turbulent Flows. Science 301, 633–646 (2003)

    Article  Google Scholar 

  24. Chen, S., Liu, Z., Zhang, C., He, Z., Tian, Z., Shi, B., Zheng, C.: A novel coupled lattice Boltzmann model for low Mach number combustion simulation. Appl. Math. Comp. 193, 266–284 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  25. Chiavazzo, E.: Invariant manifolds and lattice Boltzmann method for combustion, PhD Thesis, ETH Dissertation No. 18233, Swiss Federal Institute of Technology, Zurich, Switzerland (2009)

    Google Scholar 

  26. Chiavazzo, E., Karlin, I.V., Frouzakis, C.E., Boulouchos, K.: Method of invariant grid for model reduction of hydrogen combustion. Proc. Combust. Inst. 32, 519–526 (2009)

    Article  Google Scholar 

  27. Chiavazzo, E, Karlin, I.V., Gorban, A.N., Boulouchos, K.: Combustion simulation via lattice Boltzmann and reduced chemical kinetics. J. Stat. Mech. P06013 (2009)

    Google Scholar 

  28. Chikatamrla, S.S., Ansumali, S., Karlin, I.V.: Entropic lattice Boltzmann models for hydrodynamics in three dimensions. Phys. Rev. Lett. 97, 010201 (2006)

    Article  MathSciNet  Google Scholar 

  29. Chikatamrla, S.S., Ansumali, S., Karlin, I.V.: Grad’s approximation for missing data in lattice Boltzmann simulations. Europhys. Lett. 74, 215–221 (2006)

    Article  MathSciNet  Google Scholar 

  30. Chikatamarla, S.S.: Hierarchy of Lattice Boltzmann Models for Fluid Mechanics, PhD Thesis, ETH Dissertation No. 17893, Swiss Federal Institute of Technology, Zurich, Switzerland

    Google Scholar 

  31. Chikatamarla, S.S., Karlin, I.V.: Lattices for the lattice Boltzmann method. Phys. Rev. E 79, 046701 (2009)

    Article  MathSciNet  Google Scholar 

  32. Chikatamarla, S.S., Frouzakis, C.E., Karlin, I.V., Tomboulides, AG, Boulouchos, K., Lattice Boltzmann method for direct numerical simulation of turbulent flows. J. Fluid Mech. (submitted)

    Google Scholar 

  33. Coltrin, M.E., Kee, R.J., Rupley, F.M.: Sandia National Laboratories, Report No. SAND90-8003C (1996)

    Google Scholar 

  34. Cottet, G.-H., Koumoutsakos, P.: Vortex Methods, Theory and Practice, Cambridge University Press (2000)

    Book  Google Scholar 

  35. Djenidi, L.: Lattice-Boltzmann simulation of grid-generated turbulence. J. Fluid Mech. 552, 13–55 (2006)

    Article  MATH  Google Scholar 

  36. Español, P., Warren, P.B.: Statistical-mechanics of dissipative particle dynamics. Europhysics Lett. 30, 191–196 (1995)

    Article  Google Scholar 

  37. Español, P.: Fluid particle model. Phys. Rev. E 57, 2930–2948 (1998)

    Article  Google Scholar 

  38. Filippova, O., Hänel, D.: Grid refinement for lattice-BGK models. J. Comput. Phys. 147, 219–228 (1998)

    Article  MATH  Google Scholar 

  39. Filippova, O., Hänel, D.: Lattice-BGK model for low Mach number combustion. Int. J. Mod. Phys. C 9, 1439–1445 (1998)

    Article  Google Scholar 

  40. Filippova, O., Hänel, D.: A novel Lattice BGK approach for low Mach number combustion. J. Comp. Phys. 158, 139–160 (2000)

    Article  MATH  Google Scholar 

  41. Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett. 56, 1505–1508 (1986)

    Article  Google Scholar 

  42. Gorban, A.N., Karlin, I.V.: Invariant Manifolds for Physical and Chemical Kinetics. Lect. Notes Phys. 660, Springer, Berlin, Heidelberg

    Google Scholar 

  43. Gorban, A.N., Karlin, I.V.: Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 58, 4751 (2003)

    Article  Google Scholar 

  44. Grad, H.: On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2, 331–407 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  45. Guo, Z., Zheng, C., Shi, B.: An extrapolation method for boundary conditions in lattice Boltzmann method. Phys. Fluids 14, 2007–2010 (2002)

    Article  Google Scholar 

  46. Hänel, D., Lantermann, U., Kaiser, R., Wlokas, I.: Generalized lattice-BGK concept for thermal and chemically reacting flows at low Mach numbers. Int. J. Num. Meth. Fluids 51, 351–369 (2006)

    Article  MATH  Google Scholar 

  47. He, X., Chen, C., Doolen, G.D.: A novel thermal model for the Lattice Boltzmann method in incompressible limit. J. Comp. Phys. 146, 282–300 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  48. He, X., Luo, L.-S.: A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55, R6333–R6336 (1997)

    Article  Google Scholar 

  49. He, X., Luo, L.-S.: Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811–6817 (1997)

    Article  Google Scholar 

  50. d’Humieres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.S.: Multiple relaxation-time lattice Boltzmann models in three-dimensions. Phil. Trans. R. Soc. 360, 437 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  51. Higuera, F.J., Succi, S., Benzi, R.: Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345 (1989)

    Article  Google Scholar 

  52. Higuera, F.J., Jimenez, J.: Boltzmann approach to lattice gas simulations. Europhys. Lett. 9, 663–668 (1989)

    Article  Google Scholar 

  53. Hoogerbrugge, P.J., Koelman, J.M.V.A.: Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Lett. 19, 155–160 (1992)

    Article  Google Scholar 

  54. Karlin, I.V., Gorban, A.N., Succi, S., Boffi, V.: Maximum entropy principle for lattice kinetic equations. Phys. Rev. Lett. 81, 6–9 (1998)

    Article  Google Scholar 

  55. Karlin, I.V., Ferrante, A, Öttinger, H.C.: Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47, 182–188 (1999)

    Article  Google Scholar 

  56. Karlin, I.V., Ansumali, S., Frouzakis, C.E., Chikatamarla, S.S.: Elements of the lattice Boltzmann method I: Linear advection equation. Comm. Comp. Phys. 1, 616–655 (2006)

    Google Scholar 

  57. Kim, S.H., Pitsch, H., Boyd, I.D.: Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers. J. Comp. Phys., 8655 (2008)

    Google Scholar 

  58. Krafczyk, M., Tölke, J., Luo, L.-S.: Large-eddy simulations with a multiple-relaxation-time LBE model. Int. J. Mod. Phys. B 17, 33–39 (2003)

    Article  Google Scholar 

  59. Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: Acoustic and thermal properties. in two and three dimensions, Phys. Rev. E 68, 036706 (2003)

    Article  MathSciNet  Google Scholar 

  60. Lammers, P., Beronov, K.N., Volkert, R., Brenner, G., Durst, F.: Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow. Comp. Fluids 35, 1137–1153 (2006)

    Article  MATH  Google Scholar 

  61. Lutz, A.E., Kee, R.J., Grcar, J.F., Rupley, F.M.: OPPDIF: A Fortran Program for Computing Opposed-Flow Diffusion Flames, Sandia National Laboratories, Sandia (1997)

    Google Scholar 

  62. Martinez, D.O., Matthaeus, W.H., Chen, S.: Comparison of spectral methods and lattice Boltzmann simulations of two-dimensional hydrodynamics. Phys. Fluids 6, 1285–1298 (1994)

    Article  MATH  Google Scholar 

  63. McNamara, GR, Zanetti, G.: Use of the Boltzmann Equation to Simulate Lattice-Gas Automata. Phys. Rev. Lett. 61, 2332–2335 (1988)

    Article  Google Scholar 

  64. Mei, R., Luo, L.-S., Lallemand, P., d’Humières, D.: Consistent initial conditions for lattice Boltzmann simulations. Comp. & Fluids 35, 855–862 (2006)

    Article  MATH  Google Scholar 

  65. Menon, S., Soo, J.-H.: Simulation of vortex dynamics in three-dimensional synthetic and free jets using the large-eddy lattice Boltzmann method. J. Turbul. 5, 2–26 (2004)

    Article  Google Scholar 

  66. McNamara, G., Alder, B.: Analysis of the lattice Boltzmann treatment of hydrodynamics. Physica A 194, 218–228 (1993)

    Article  MathSciNet  Google Scholar 

  67. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)

    Article  MathSciNet  Google Scholar 

  68. Philippi, P.C., Hegele, L.A., Dos Santos, L.O.E., Surmas, R.: From the continuous to the lattice Boltzmann Equation: The discretization problem and thermal models. Phys. Rev. E 73, 056702 (2006)

    Article  MathSciNet  Google Scholar 

  69. Prasianakis, N.: Lattice Boltzmann method for thermal compressible flows, PhD Thesis, ETH Dissertation No. 17739, Swiss Federal Institute of Technology, Zurich, Switzerland

    Google Scholar 

  70. Prasianakis, N., Boulouchos, K.: Lattice Boltzmann method for simulation of weakly compressible flows at arbitrary Prandtl number. Int. J. Mod. Phys. C 18, 602 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  71. Prasianakis, N., Karlin, I.V.: Lattice Boltzmann method for thermal flow simulation on standard lattices. Phys. Rev. E 76, 016702 (2007)

    Article  Google Scholar 

  72. Prasianakis, N., Karlin, I.V.: Lattice Boltzmann method for simulation of compressible flows on standard lattices. Phys. Rev. E 78, 016704 (2008)

    Article  Google Scholar 

  73. Prasianakis, N., Karlin, I.V., Mantzaras, J., Boulouchos, K.: Lattice Boltzmann method with restored Galilean invariance. Phys. Rev. E 79, 066702 (2009)

    Article  Google Scholar 

  74. Premnatha, K.N., Pattison, M.J., Banerjee, S.: Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method. Physica A 388, 2640–2658 (2009)

    Article  Google Scholar 

  75. Sbragaglia, M., Succi, S.: Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions. Phys. Fluids 17, 093602 (2005)

    Article  Google Scholar 

  76. Sbragaglia, M., Succi, S.: A note on the lattice Boltzmann method beyond the Chapman-Enskog limits. Europhys. Lett. 73, 370 (2006)

    Article  MathSciNet  Google Scholar 

  77. Shan, X.: Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method. Phys. Rev. E 55, 2780–2788 (1997)

    Article  Google Scholar 

  78. Shan, X.W., He, X.Y.: Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80, 65–68 (1998)

    Article  Google Scholar 

  79. Shan, X., Yuan, X.-F., Chen, H.: Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation. J. Fluid Mech. 550, 413–441 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  80. Shan, X., Chen, H.: A General Multiple-Relaxation-Time Boltzmann Collision Model. Int. J. Mod. Phys. C 18, 635 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  81. Sofonea, V., Sekerka, R.F.: Boundary conditions for the upwind finite difference Lattice Boltzmann model: Evidence of slip velocity in micro-channel flow. J. Comp. Phys. 207, 639 (2005)

    Article  MATH  Google Scholar 

  82. Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, Oxford

    Google Scholar 

  83. Succi, S.: Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis. Phys. Rev. Lett. 89, 064502 (2002)

    Article  Google Scholar 

  84. Succi, S., Bella, G., Papetti, F.: Lattice kinetic theory for numerical combustion, J. Sci. Comp. 12, 395–408 (1997)

    Article  MATH  Google Scholar 

  85. Succi, S., Smith, G., Kaxiras, E.: Lattice Boltzmann simulation of reactive microflows over catalytic surfaces. J. Stat. Phys. 107, 343–366 (2004)

    Article  Google Scholar 

  86. Sterling, J.D., Chen, S.: Stability analysis of lattice Boltzmann methods. J. Comp. Phys. 123, 196–206 (1996)

    Article  MATH  Google Scholar 

  87. Sukop, M.C., Thorne, D.T.: Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer (2007)

    Google Scholar 

  88. Teixeira, C.M.: Incorporating turbulence models into the lattice-Boltzmann method. Int. J. Mod. Phys. C 9, 1159–1175 (1998)

    Article  Google Scholar 

  89. Tomboulides, A.G., Orszag, S.A.: A quasi-two-dimensional benchmark problem for low Mach number compressible codes. J. Comput. Phys. 146, 691–706 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  90. Wolf-Gladrow, D.A.: Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Springer (2000)

    MATH  Google Scholar 

  91. Yamamoto, K., He, X., Doolen, G.D.: Simulation of combustion field with lattice Boltzmann method. J. Stat. Phys. 107, 367–383 (2002)

    Article  MATH  Google Scholar 

  92. Yu, H., Luo, L.-S., Girimaji, S.S.: LES of turbulent square jet flow using an MRT lattice Boltzmann model. Comp. Fluids 35, 957–965 (2006)

    Article  MATH  Google Scholar 

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  1. Aerothermochemistry and Combustion Systems Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland

    Christos E. Frouzakis

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Correspondence to Christos E. Frouzakis .

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  1. Dept. Mechanical & Aerospace Engineering, North Carlolina State University, Stinson Drive 2601, Raleigh, 27695, North Carolina, USA

    Tarek Echekki

  2. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, United Kingdom

    Epaminondas Mastorakos

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Frouzakis, C.E. (2011). Lattice Boltzmann Methods for Reactive and Other Flows. In: Echekki, T., Mastorakos, E. (eds) Turbulent Combustion Modeling. Fluid Mechanics and Its Applications, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0412-1_19

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