Entropic 13 Moment Equations from Boltzmann's Kinetic Equation

TL;DR

This paper derives a set of 13 moment equations for rarefied gases using thermodynamic principles, ensuring entropy consistency and linking to classical hydrodynamics.

Contribution

It introduces a thermodynamically consistent framework for 13 moment equations with explicit entropy and closure approximations, bridging kinetic theory and hydrodynamics.

Findings

Explicit entropy expression satisfying an H theorem

Hamiltonian formulation of free flight transport

Recovery of standard hydrodynamics as a limit

Abstract

We use guiding principles from nonequilibrium thermodynamics to develop an admissible set of 13 moment equations for rarefied gas flows. The main benefits of our thermodynamic approach are an explicit entropy expression fulfilling an $H$ theorem and a sound Hamiltonian formulation of the reversible free flight transport. To calculate the entropy and to find explicit closure approximations, we propose a simple set of approximate 13 parameter solutions to Boltzmann's kinetic equation. We discuss how standard hydrodynamics is recovered as a limiting case.