Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

TL;DR

This paper reviews the derivation of fluid dynamics from kinetic theory, highlighting the non-uniqueness of the closure procedure and the impact of different moment choices on transport coefficients.

Contribution

It demonstrates that the traditional 14-moment approximation and the choice of equations of motion are not unique, affecting the resulting transport coefficients.

Findings

Multiple moment choices lead to different transport coefficients.

The 14-moment approximation is one among many possible closures.

The form of the equations remains consistent despite different moment choices.

Abstract

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.