  A novel lattice Boltzmann (LB) model with self-tuning equation of state (EOS)
is developed in this work for simulating coupled thermo-hydrodynamic flows. The
velocity field is solved by the recently developed multiple-relaxation-time
(MRT) LB equation for density distribution function (DF), by which a
self-tuning EOS can be recovered. As to the temperature field, a novel MRT LB
equation for total energy DF is directly developed at the discrete level. By
introducing a density-DF-related term into this LB equation and devising the
equilibrium moment function for total energy DF, the viscous dissipation and
compression work are consistently considered, and by modifying the collision
matrix, the targeted energy conservation equation is recovered without
deviation term. The full coupling of thermo-hydrodynamic effects is achieved
via the self-tuning EOS and the viscous dissipation and compression work. The
present LB model is developed on the basis of the standard lattice, and various
EOSs can be adopted in real applications. Moreover, both the Prandtl number and
specific heat ratio can be arbitrarily adjusted. Furthermore, boundary
condition treatment is also proposed on the basis of the judicious
decomposition of DF into its equilibrium, force (source), and nonequilibrium
parts. The local conservation of mass, momentum, and energy can be strictly
satisfied at the boundary node. Numerical simulations of thermal Poiseuille and
Couette flows are carried out with three different EOSs, and the numerical
results are in good agreement with the analytical solutions. Then, natural
convection in a square cavity with a large temperature difference is simulated
for the Rayleigh number from $10^3$ up to $10^8$. Good agreement between the
present and previous numerical results is observed, which further validates the
present LB model for coupled thermo-hydrodynamic flows.
