Mathematisches Kolloquium

Zusammenfassung: Mathematical modeling of non-equilibrium gases becomes necessary in the case of extreme processes like in rarefied or micro situations. The modeling framework is based on the statistical description of gases by kinetic theory. In this talk we consider the problem how to reduce this complex description to a deterministic set of partial differential equations for fluid variables. The resulting equations will be able to extend classical relations of gas dynamics, like the laws of Navier-Stokes and Fourier for stress and heat-flux. The new model is based on Boltzmann's equation and consists of moment equations with a specialized closure procedure. The procedure combines aspects from classical moment approximations with asymtotic expansions. The final system, called regularized 13-moment system (R13), comes in the form of relaxational partial differential equations of hyperbolic-parabolic type. This opens the field for interesting mathematical, numerical and physical investigations. We will discuss the derivation and properties of the new system, as well as specialized numerical methods. As application we present gas flow in micro-channels where several non-classical and non-intuitive phenomena need to be explained, like increasing mass flow for smaller channel widths (Knudsen paradox).