Modeling Non-Equilibrium Gas Flows - Manuel Torrilhon

Abstract

Rarefied gas flows, or equally gas micro-flows, require modeling based on the statistical description of kinetic gas theory. Such flows exhibit strong non-equilibrium behavior due to insufficient particle interactions, that is, the Knudsen number - the ratio between the mean free path and a macroscopic length - becomes significant. The traditional equations of gas dynamics with the constitutive laws of Navier-Stokes and Fourier for stress tensor and heat flux are known to loose their validity in these situations.
However, the statistical approaches based on a particle velocity probability density following Boltzmann's equation is computationally expensive and also can not provide much fluid-dynamic intuition for the non-equilibrium phenomena.

The regularized 13-moment-equations (R13) extend the classical fluid dynamic equations for processes with moderate Knudsen numbers. The system is based on Grad's 13-moment equations known from kinetic gas theory and extended thermodynamics. We will discuss the derivation of the equations within the framework of moment approximations in kinetic theory while discussing various other similar approaches. The regularized 13-moment-equations offer a compromise between stability and robustness, simplicity and physical accuracy. It is also possible to formulate boundary conditions obtained from kinetic gas theory for the R13 system and we present results for standard flow stuations but in rarefied regimes, which show interesting non-intuitive features.

Extensions of the moment approach in kinetic theory and more numerical simulation result will also be presented in the talks of James McDonald and Armin Westerkamp.