Moment Equations for Non-Equilibrium Gas Flows

Mathematical modeling of gases is important for describing non-equilibrium, micro-scale or rarefied processes in gases.
Due to the lack of sufficient collisions between particles, classical relations of Navier-Stokes and Fourier for stress and heat-flux have to be replaced by a more accurate model.

This talk will introduce a mathematical model based on Boltzmann's equation in kinetic gas theory and discuss its physical, mathematical and numerical properties. The new system, called regularized 13-moment system (R13), is formed by relaxational partial differential equations of hyperbolic- parabolic type. It contains first order equations for the thermodynamic flow quantities, density, velocity and temperature as well as second order equations for directional temperatures, shear stress and heat flux in the form of balance laws. In contrast to other models the new equations show high accuracy and linear stability for all frequencies. It is also possible to formulate reasonable boundary conditions.

The mathematical structure of the R13 equations leads to interesting numerical and analytical investigations. Several non-classical and non-intuitive phenomena can be analytically understood, like Knudsen boundary layers and increasing mass flow for smaller channel widths (Knudsen paradox). We will discuss several physical test problems like shock wave simulations and micro-channel flow.
----