  The problem of energy conservation in the lattice Boltzmann method is solved.
A novel model with energy conservation is derived from Boltzmann's kinetic
theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the
Boltzmann equation is recovered in the domain where variations around the
reference temperature are small. Simulation of a Poiseuille micro-flow is
performed in a quantitative agreement with exact results for low and moderate
Knudsen numbers. The new model extends in a natural way the standard lattice
Boltzmann method to a thermodynamically consistent simulation tool for
nearly-incompressible flows.
