Thermal lattice Boltzmann equation for low Mach number flows: Decoupling model

A lattice Boltzmann model is proposed for solving low Mach number thermal flows with viscous dissipation and compression work in the double-distribution-function framework. A distribution function representing the total energy is defined based on a single velocity distribution function, and its evolution equation is derived from the continuous Boltzmann equation. A lattice Boltzmann equation model with clear physics and a simple structure is then obtained from a kinetic model for the decoupled hydrodynamic and energy equations. The model is tested by simulating a thermal Poiseuille flow and natural convection in a square cavity, and it is found that the numerical results agree well with the analytical solutions and/or the data reported in previous studies.