Hybrid Lattice Boltzmann and Finite Volume Method for Natural Convection

A hybrid lattice Boltzmann and finite volume method is proposed for fluid flow and heat transfer simulation. The lattice Boltzmann method was applied to obtain the velocity field, whereas the finite volume method was used to obtain the temperature field. The two-dimensional nine discrete velocities (D2Q9) model and nonequilibrium extrapolation scheme boundary condition were used in the lattice Boltzmann method, and the SIMPLE algorithm with the QUICK scheme was employed in the finite volume method. Natural convection with different Rayleigh numbers was solved by the hybrid method, and the results agreed very well with those obtained from a pure finite volume method and pure thermal lattice Boltzmann method. This is the first time that the hybrid lattice Boltzmann with the finite volume method has been applied to solve natural convection problem.