Abstract
The thermal lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the thermal equilibrium distribution function is similar to the density equilibrium distribution function in the thermal lattice BGK model, except that the leading quantities are density and scalar, respectively. The heat viscous heating dissipation term in this model can be expressed in macroscopic form which includes the strain rate tensor. The viscous heating dissipation term in this model is convenient to implement. The proposed thermal lattice Boltzmann model is applied to two-dimensional thermal Poiseuille flow, thermal Couette flow, thermal Couette flow with wall injection, natural convection in a square cavity, and three-dimensional thermal Poiseuille flow in a square duct. Numerical simulations indicate that each formulation is second order accurate.