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Coupling of Lattice Boltzmann Equation and Finite Volume Method to Simulate Heat Transfer in a Square Cavity

Ahmed Mezrhab1, Hassan Naji2

1 Corresponding author. Faculté des Sciences, Département de Physique, Laboratoire de Mécanique & Energétique, 60000 Oujda, Maroc. Tel.: +212-36 50 06 01/02; fax: +212-36 50 06 03; E-mail address:;
2 USTL/Polytech’lille/LML UMR 8107 CNRS, Département de Mécanique, F-59655 Villeneuve, d’Ascq Cedex, France.

Fluid Dynamics & Materials Processing 2009, 5(3), 283-296.


The objective of this paper is to assess the effectiveness of the coupled Lattice Boltzmann Equation (LBE) and finite volume method strategy for the simulation of the interaction between thermal radiation and laminar natural convection in a differentially heated square cavity. The vertical walls of the cavity are adiabatic, while its top and bottom walls are cold and hot, respectively. The air velocity is determined by the lattice Boltzmann equation and the energy equation is discretized by using a finite volume method. The resulting systems of discretized equations have been solved by an iterative procedure based on a preconditioned conjugate gradient method. Only the surface radiation is taken into account and the walls of the enclosure are assumed to be diffuse-grey. The achieved simulations have shown that the coupling between the lattice Boltzmann equation and the finite volume method gives excellent results. It was also observed that the surface radiation standardizes the temperature inside the cavity and causes a considerable increase of the heat transfer.


Cite This Article

Mezrhab, A., Naji, H. (2009). Coupling of Lattice Boltzmann Equation and Finite Volume Method to Simulate Heat Transfer in a Square Cavity. FDMP-Fluid Dynamics & Materials Processing, 5(3), 283–296.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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