The Enskog theory for the self-diffusion coefficient for fluids with continuous potentials, such as the Lennard-Jones, is developed. Starting from the Green–Kubo formula ~rather than the conventional kinetic equation! and introducing the similar assumptions upon which the Boltzmann equation is based, we derived a general expression for the memory kernel and the self-diffusion coefficient. The n...

This work investigates the breakdown of the continuum relations for diffusion velocity in inert binary gas mixtures. Values of the relative diffusion velocities for components of a gas mixture may be calculated using of Chapman-Enskog theory and occur not only due to concentration gradients, but also pressure and temperature gradients in the flow as described by Hirschfelder. Because Chapman-En...

We evaluate the linear term in the density expansion of the dynamic structure factor for a classical gas using a generalized Enskog theory developed by one of the authors, which enables us to describe the dynamics at small time and length scales where the use of the Boltzmann equation is severely limited. Agreement of the theory with experiment and simulation is very good. We find that the line...

The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique. The existence of a probability density for the time-marginals of the velocity is verified in the case where th...

A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating dense fluid flows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to...

Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Ch...

We analyze the linear causality and stability of third-order fluid dynamics considering perturbations around a global equilibrium state. investigate formulation derived from kinetic theory, using Chapman-Enskog expansion, in PRC 88, 021903, which was shown to be excellent agreement with solutions microscopic theory. From this analysis, we demonstrate that theory is linearly acausal unstable suc...

The shock wave structure in a moderately dense gas is studied by numerically solving the one-dimensional Enskog kinetic equation. The numerical method is based on a combination of a nite difference scheme for the streaming term and a Monte Carlo quadrature technique to evaluate the collision integral. The obtained shock prooles are compared to the results of Navier-Stokes theory and to molecula...

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the ...