Thermodynamically Admissible 13 Moment Equations from the Boltzmann Equation

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.

Figure 1

Skewness contribution $\overline{S}(\phi )$ to the entropy (continuous line) and linear approximation to it (dashed line).