Fluid-dynamic limit of the Enskog equation with the guaranteed H-theorem

TL;DR

This paper demonstrates that a modified Enskog equation, which guarantees the H-theorem, accurately recovers the fluid-dynamic behavior of dense gases, aligning with the original equation's transport properties.

Contribution

It shows that the modified Enskog equation maintains the same fluid-dynamic description as the original, ensuring thermodynamic consistency while guaranteeing the H-theorem.

Findings

Modified Enskog equation recovers Navier-Stokes-Fourier equations

Ensures thermodynamic consistency via H-theorem

Maintains accurate fluid-dynamic transport properties

Abstract

The fluid-dynamic limit of the Enskog equation with a slight modification is discussed on the basis of the Chapman-Enskog method. This modified version of the Enskog equation has been shown recently by the present authors to ensure the H-theorem. In the present paper, it is shown that the modified version recovers the same fluid-dynamic description of the dense gas as the original Enskog equation, at least up to the level of the Navier-Stokes-Fourier set of equations inclusive. Since the original Enskog equation is known to recover the fluid-dynamical transport properties well, this result implies that the modified version of the Enskog equation provides consistent descriptions both thermodynamically and fluid-dynamically.