An improved multiple-relaxation-time lattice Boltzmann model for incompressible thermal flows in two dimensions

An improved multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for simulating incompressible thermal flows in two dimensions. The improved model consists of two MRT-LB equations: the flow field is solved by an MRT-LB equation based on D2Q9 lattice, while the temperature field is solved by an improved thermal MRT-LB equation constructed on D2Q5 lattice. The convection term of the macroscopic temperature equation is recovered by adding a source term into the thermal MRT-LB equation, and consequently, the macroscopic temperature equation can be correctly recovered without suffering from the error term. Moreover, the temperature gradient in the source term is computed locally with second-order accuracy, and therefore the improved model retains the thermal LB method's inherent advantages. The accuracy of the improved model is validated by numerical simulations of thermal flow within a channel and natural convection within a square cavity. The predicted results agree well with the analytical solutions and/or benchmark data in the literature, and the second-order spatial accuracy of the improved model is confirmed. Furthermore, comparative study of the numerical consistency in the energy conservation is carried out, and the numerical results indicate that the improved model can achieve numerical consistency in the energy conservation in simulating incompressible thermal flows.