Study on forcing schemes in the thermal lattice Boltzmann method for simulation of natural convection flow problems

The present study addresses the effect of various schemes for applying an external force term on the accuracy and performance of the thermal lattice Boltzmann method (LBM) for simulation of free convection problems. Herein, the forcing schemes of Luo, shifted velocity method, Guo, and exact difference method are applied by considering three velocity discrete models of D2Q4, D2Q5, and D2Q9. The accuracy and performance of these schemes are evaluated with the simulation of three natural convection problems, namely, free convection in a closed cavity, in a square enclosure with a hot obstacle inside, and the Rayleigh-Benard problem. The obtained results based on the present thermal LBM with different forcing schemes and velocity discrete models are compared with the existing experimental and numerical data in the literature. This comparison study indicates that imposing all employed forcing schemes leads to similar performance for the simulation of free convection problems studied at the middle range of Rayleigh numbers. It is found that the Luo forcing scheme is simple for implementation in comparison with the other three forcing schemes and provides the results with acceptable accuracy at moderate Rayleigh numbers. At higher Rayleigh numbers, however, the Guo scheme is not only numerically stable but a more precise forcing scheme in comparison with the other three methods. It is illustrated that employing the discrete velocity model of D2Q4 has more appropriate numerical stability along with less computational cost in comparison with two other discrete velocity models for simulation of natural convection heat transfer.