Energy conserving discrete Boltzmann equation for nonideal systems

The BBGKY formalism is utilized to obtain a set of moment equations to be s atisfied by the collision operator in an energy conserving discrete Boltzma nn equation for the case of a nonlocal interaction potential. A modified BG K form of the collision operator consistent with these moment equations is described. In the regime of isothermal hows, a previous proposed nonideal g as model is recovered. Other approaches to constructing the collision opera tor are discussed. Numerical implementation of the modified BGK form, using a thermal lattice Boltzmann model, is illustrated as an example. The time dependence of the density autocorrelation function was studied for this mod el and found, at early times, to be strongly affected by the constraint of total energy conservation. The long time behavior of the density autocorrel ation function was consistent with the theory of hydrodynamic fluctuations.