Simulation of natural convection flow by the thermal lattice boltzmann method

In this paper, the thermal lattice Boltzmann scheme has been improved, which was proposed by J. G. M. Eggels and J. A. Somers, and a new equilibrium solution for temperature distribution function has been presented on the incompressible flow assumption. This new equilibrium solution can correct the compressibility effect on macroscopic temperature, and modify the statistical definition of macroscopic temperature. The halfway bounce-back boundary condition was used in the method proposed by J. G. M. Eggels and J. A. Somers for velocity and temperature. However, the boundary condition was not accurate for the temperature in the physical view. Therefore, a non-equilibrium extrapolation scheme, which is a simple algorithm and very easy to implement, has been adopted for velocity and temperature in the boundaries. Subsequently, the improved TLBM has been used to simulate the natural convection in the cavity at Ra = 10⁶ and Pr = 0.71 for air. The flow parameters obtained in the simulation agreed very well with those of other numerical methods, to indicate that the improved TLBM can be used to simulate the non-isothermal flows efficiently and accurately.