A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity

A 3D incompressible thermal lattice Boltzmann model is proposed in this paper to solve 3D incompressible thermal flow problems. Two different particle velocity models of D3Q15 and D3Q19 are incorporated in our thermal model. It is indicated that the present thermal model is simple and easy for implementation. It is validated by its application to simulate the 3D natural convection of air in a cubical enclosure, which is heated differentially at two vertical side walls. Good agreement was obtained between the present results and those from a Navier–Stokes solver.