Lattice Boltzmann simulations of thermal convective flows in two dimensions

• Published in: Computers & mathematics with applications (1987) Vol. 65; no. 2; pp. 262 - 286
• Main Authors: Wang, Jia, Wang, Donghai, Lallemand, Pierre, Luo, Li-Shi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2013
• Subjects: Boundary conditions for thermal flows; Computer simulation; MRT lattice Boltzmann model for thermo-hydrodynamics in 2D; Rayleigh–Bénard convection; Square cavity with differentially heated vertical walls; MRT lattice Boltzmann model for thermo-hydrodynamics in 2D; Boundary conditions for thermal flows; Square cavity with differentially heated vertical walls; Rayleigh–Bénard convection
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2012.07.001

In this paper we study the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model for incompressible thermo-hydrodynamics with the Boussinesq approximation. We use the MRT thermal LBE (TLBE) to simulate the following two flows in two dimensions: the square cavity with differentially heated vertical walls and the Rayleigh–Bénard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra=103–106, and the Prandtl number Pr=0.71; and for the Rayleigh–Bénard convection in a rectangle, Ra=2⋅103, 104 and 5⋅104, and Pr=0.71 and 7.0.