Simplified thermal lattice Boltzmann model for incompressible thermal flows

Considering the fact that the compression work done by the pressure and the viscous heat dissipation can be neglected for the incompressible flow, and its relationship with the gradient term in the evolution equation for the temperature in the thermal energy distribution model, a simplified thermal energy distribution model is proposed. This thermal model does not have any gradient term and is much easier to be implemented. This model is validated by the numerical simulation of the natural convection in a square cavity at a wide range of Rayleigh numbers. Numerical experiments showed that the simplified thermal model can keep the same order of accuracy as the thermal energy distribution model, but it requires much less computational effort.