Lattice Boltzmann simulation of natural convection in a square cavity

In this paper, we describe the development of a lattice Boltzmann scheme fo r incompressible thermohydrodynamics Being based on kinetic theory, the sch eme simulates macroscopic fluid flows and heat transfers with the use of di stribution functions. A systematic derivation of the lattice Boltzmann sche me from the continuous Boltzmann equation is discussed in details. We find that a 5-velocity model can be employed to simulate heat transfer in such a case where the viscous and compressive heating effects are negligible. As a benchmark, numerical simulations of natural convection in a square cavity are carried out. Through the results, the scheme is found to have a second -order convergence rate. In addition, the scheme is verified to be as accur ate as conventional methods over a wide range of Rayleigh numbers.