KINETIC EQUATIONS WITH INTERMOLECULAR POTENTIALS: AVOIDING THE BOLTZMANN ASSUMPTION

The Boltzmann equation describes the time evolution of a dilute gas, and is the best known transport equation in kinetic theory. Its drawback is that, although it allows for a variety of long and short range intermolecular potentials, it does not predict non-ideal transport coefficients. To model gas kinetics in denser regimes, the most successful Boltzmann-like equation has been the Enskog equation, which takes into account molecular diameters. However, it does have the drawback that it does not include intermolecular potentials. We present several extentions of the Enskog theory which model intermolecular forces. The first of these includes a piecewise-constant short range potential. The second models longrange forces by coupling the Enskog equation to the electromagnetic field via a Vlasov collision term. Finally, we introduce discrete velocity models. All of these open new fields for numerical analysis.