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The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali and I. V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional thermal model on the standard square lattice with nine velocities is developed and validated in the thermal Couette and Rayleigh-Bénard natural convection problems.
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Prasianakis et al. (2007) studied this question.
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