Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition

A thermal lattice BGK model with doubled populations, together with a new boundary condition for temperature and heat flux, is proposed to simulate the two-dimensional natural convection flow in a cavity. Numerical results for the problem of insulated horizontal walls and vertical walls at different temperatures are presented; they are found to be in good agreement with those of previous works. In addition, the problem of insulated horizontal walls and vertical walls heated and cooled by means of an imposed heat flux is discussed. Numerical results are presented as compared with theoretical values and they are found to be in satisfactory agreement. Therefore, the method can capture fundamental behaviors in thermal flows of engineering interest. © 2004 Elsevier SAS. All rights reserved.