Energy conserving discrete Boltzmann equation for nonideal systems
The BBGKY formalism is utilized to obtain a set of moment equations to be satisfied by the collision operator in an energy conserving discrete Boltzmann equation for the case of a nonlocal interaction potential. A modified BGK form of the collision operator consistent with these moment equations is described. In the regime of isothermal hows, a previous proposed nonideal gas model is recovered. Other approaches to constructing the collision operator 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 model and found, at early times, to be strongly affected by the constraint of total energy conservation. The long time behavior of the density autocorrelation function was consistent with the theory of hydrodynamic fluctuations.
nonideal systems bbgky bgk thermal lattice boltzmann hydrodynamic fluctuations discrete boltzmann methods lennard-jones fluid