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Modeling Non-Equilibrium Gas Flows

Prof. Dr. Manuel Torrilhon

RWTH Aachen

13.06.2012 14:00 Uhr
Seminarraum 2001, Geb. 04.16


Rarefied gas flows, or equally gas micro-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. Instead the flow needs to be modeled on the basis of kinetic gas theory and the Boltzmann equation. However, this statistical approach 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 briefly discuss the derivation of the equations and their properties like stability, asymptotic accuracy and entropy. It is also possible to formulate boundary conditions obtained from kinetic gas theory for the R13 system and we present results for standard internal and external flow problems, like channel flow and flow past a sphere, which show interesting non-intuitive features in the rarefied situation.


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