Lattice Boltzmann simulations of thermal convective flows in two dimensions

Yu, 2003, Viscous flow computations with the method of lattice Boltzmann equation, Prog. Aerospace Sci., 39, 329, 10.1016/S0376-0421(03)00003-4 Luo, 2010, Lattice Boltzmann method for computational fluid dynamics, 651 Alexander, 1993, Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, 47, R2249, 10.1103/PhysRevE.47.R2249 McNamara, 1993, Analysis of the lattice Boltzmann treatment of hydrodynamics, Physica A, 194, 218, 10.1016/0378-4371(93)90356-9 Chen, 1995, Heat-transfer in lattice BGK modeled fluid, J. Stat. Phys., 81, 71, 10.1007/BF02179969 McNamara, 1995, Stabilization of thermal lattice Boltzmann models, J. Stat. Phys., 81, 395, 10.1007/BF02179986 McNamara, 1997, A hydrodynamically correct thermal lattice Boltzmann model, J. Stat. Phys., 87, 1111, 10.1007/BF02181274 Lallemand, 2003, Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions, Phys. Rev. E, 68, 036706, 10.1103/PhysRevE.68.036706 Eggels, 1995, Numerical-simulation of free convective flow using the lattice-Boltzmann scheme, Int. J. Heat Fluid Flow, 16, 357, 10.1016/0142-727X(95)00052-R He, 1997, A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55, R6333, 10.1103/PhysRevE.55.R6333 He, 1997, Theory of lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56, 6811, 10.1103/PhysRevE.56.6811 He, 1998, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146, 282, 10.1006/jcph.1998.6057 Guo, 2002, A coupled lattice BGK model for the Boussinesq equations, Int. J. Numer. Meth. Fluids, 39, 325, 10.1002/fld.337 Guo, 2007, Thermal lattice Boltzmann equation for low Mach number flows: decoupling model, Phys. Rev. E, 75, 036704, 10.1103/PhysRevE.75.036704 Lallemand, 2003, Hybrid finite-difference thermal lattice Boltzmann equation, Int. J. Mod. Phys. B, 17, 41, 10.1142/S0217979203017060 Lallemand, 2000, Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, 61, 6546, 10.1103/PhysRevE.61.6546 d’Humières, 2002, Multiple-relaxation-time lattice Boltzmann models in three-dimensions, Philos. Trans. R. Soc. Lond. A, 360, 437, 10.1098/rsta.2001.0955 Luo, 2011, Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations, Phys. Rev. E, 83, 056710, 10.1103/PhysRevE.83.056710 d’Humières, 1992, Generalized lattice-Boltzmann equations, Vol. 159, 450 Ginzburg, 2005, Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Adv. Water Res., 28, 1171, 10.1016/j.advwatres.2005.03.004 Ginzburg, 2005, Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations, Adv. Water Res., 28, 1196, 10.1016/j.advwatres.2005.03.009 Ginzburg, 2006, Variably saturated flow described with the anisotropic lattice Boltzmann methods, Comput. Fluids, 35, 831, 10.1016/j.compfluid.2005.11.001 Ginzburg, 2007, Lattice Boltzmann modeling with discontinuous collision components: hydrodynamic and advection–diffusion equations, J. Stat. Phys., 126, 157, 10.1007/s10955-006-9234-4 Ginzburg, 2007, Lattice Boltzmann and analytical modeling of flow processes in anisotropic and heterogeneous stratified aquifers, Adv. Water Res., 30, 2202, 10.1016/j.advwatres.2007.05.001 Ginzbourg, 1996, Local second-order boundary methods for lattice Boltzmann models, J. Stat. Phys., 84, 927, 10.1007/BF02174124 Ginzburg, 2003, Multireflection boundary conditions for lattice Boltzmann models, Phys. Rev. E, 68, 066614, 10.1103/PhysRevE.68.066614 Lockard, 2002, Evaluation of PowerFLOW for aerodynamic applications, J. Stat. Phys., 107, 423, 10.1023/A:1014539411062 Pan, 2006, An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids, 35, 898, 10.1016/j.compfluid.2005.03.008 P. Dellar, An interpretation and derivation of the lattice Boltzmann method using Strang splitting, Comput. Math. Appl. (2011) published online (http://dx.doi.org/10.1016/j.camwa.2011.08.047). Ginzbourg, 1994, Boundary flow condition analysis for the three-dimensional lattice Boltzmann model, J. Phys. II, 4, 191 Ginzburg, 2008, Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions, Commun. Comput. Phys., 3, 427 Ginzburg, 2008, Study of simple hydrodynamic solutions with the two-relaxation-times lattice Boltzmann scheme, Commun. Comput. Phys., 3, 519 Ginzburg, 2010, Optimal stability of advection–diffusion lattice Boltzmann models with two relaxation times for positive/negative equilibrium, J. Stat. Phys., 139, 1090, 10.1007/s10955-010-9969-9 Kuzmin, 2011, The role of the kinetic parameter in the stability of two-relaxation-time advection–diffusion lattice Boltzmann schemes, Comput. Math. Appl., 61, 3417, 10.1016/j.camwa.2010.07.036 Ginzburg, 2012, Truncation errors, exact and heuristic stability analysis of two-relaxation-times lattice Boltzmann schemes for anisotropic advection–diffusion equation, Commun. Comput. Phys., 11, 1439, 10.4208/cicp.211210.280611a Luo, 1998, Unified theory of the lattice Boltzmann models for nonideal gases, Phys. Rev. Lett., 81, 1618, 10.1103/PhysRevLett.81.1618 Guo, 2002, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E, 65, 046308, 10.1103/PhysRevE.65.046308 de Vahl Davis, 1983, Natural-convection in a square cavity: a comparison exercise, Int. J. Numer. Meth. Fluids, 3, 227, 10.1002/fld.1650030304 de Vahl Davis, 1983, Natural-convection of air in a square cavity: a bench-mark numerical-solution, Int. J. Numer. Meth. Fluids, 3, 249, 10.1002/fld.1650030305 Yu, 2012, Compact computations based on a stream-function-velocity formulation of two-dimensional steady laminar natural convection in a square cavity, Phys. Rev. E, 85, 036703, 10.1103/PhysRevE.85.036703 Mayne, 2000, h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem, Int. J. Numer. Meth. Heat Fluid Flow, 10, 598, 10.1108/09615530010347187 Hortmann, 1990, Finite volume multigrid prediction of laminar natural-convection: bench-mark solutions, Int. J. Numer. Meth. Fluids, 11, 189, 10.1002/fld.1650110206 Croce, 2000, Incompressible flow and heat transfer computations using a continuous pressure equation and nonstaggered grids, Numer. Heat Transfer B, 38, 291, 10.1080/10407790050192780 Le Quéré, 1985, Computation of natural convection in two-dimensional cavities with Chebyshev polynomials, J. Comput. Phys., 57, 210, 10.1016/0021-9991(85)90043-9 Le Quéré, 1991, Accurate solutions to the square thermally driven cavity at high Rayleigh number, Comput. Fluids, 20, 29, 10.1016/0045-7930(91)90025-D Gelfgat, 2006, Implementation of arbitrary inner product in the global Galerkin method for incompressible Navier–Stokes equations, J. Comput. Phys., 211, 513, 10.1016/j.jcp.2005.06.002 Giesdal, 2006, Spectral element benchmark simulations of natural convection in two-dimensional cavities, Int. J. Numer. Meth. Fluids, 50, 1297, 10.1002/fld.1121 Hou, 1995, Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., 118, 329, 10.1006/jcph.1995.1103 Dellar, 2001, Bulk and shear viscosities in lattice Boltzmann equations, Phys. Rev. E, 64, 031203, 10.1103/PhysRevE.64.031203 Dellar, 2003, Incompressible limits of lattice Boltzmann equations using multiple relaxation times, J. Comput. Phys., 190, 351, 10.1016/S0021-9991(03)00279-1 Mezrhab, 2004, Hybrid lattice-Boltzmann finite-difference simulation of convective flows, Comput. Fluids, 33, 623, 10.1016/j.compfluid.2003.05.001 Reid, 1958, Some further results on the Bénard problem, Phys. Fluids, 1, 102, 10.1063/1.1705871 Clever, 1974, Transition to time-dependent convection, J. Fluid Mech., 65, 625, 10.1017/S0022112074001571