Energy Conserving Discrete Boltzmann Equation for Nonideal Systems.
Energy Conserving Discrete Boltzmann Equation for
Martys, N. S.
International Journal of Modern Physics C, Vol. 10, No.
7, 1367-1382, 1999.
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 flows, a previous proposed
notideal gss 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 wss 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.