Lattice Boltzmann simulations of thermal convective flows in two dimensions

Authors:
Jia Wang;Donghai Wang;Pierre Lallemand;Li-Shi Luo
Affiliations:
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China;State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China;Beijing Computational Science Research Center, Beijing, 100084, China;Department of Mathematics & Statistics and Center for Computational Sciences, Old Dominion University, Norfolk, VA 23529, USA and Beijing Computational Science Research Center, Beijing, 100084, Ch ...
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

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-Benard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra=10^3-10^6, and the Prandtl number Pr=0.71; and for the Rayleigh-Benard convection in a rectangle, Ra=2@?10^3, 10^4 and 5@?10^4, and Pr=0.71 and 7.0.