Mathematical modeling of rarefied gas mixtures in non-equilibrium

Abstract

The gaseous mixtures are encountered more often than a single gas in practice. The modeling of gas flows—especially, in the so-called transition regime—is a challenging problem. In this regime, the traditional fluid dynamical models, e.g., Navier-Stokes-Fourier equations, fail to fully describe the flow whereas the direct solutions, e.g. by direct simulation Monte Carlo (DSMC) or by discrete velocity method are computationally very expensive. In this talk, the extended Grad’s moment equations and associated boundary conditions, which have been derived through Maxwell accommodation model, will be presented for modeling gas-mixture flows. In addition to this, some interesting results on few benchmark problems of binary gas mixtures in fluid mechanics, that have been studied through the derived moment equations and boundary conditions, will also be presented. Finally, a new set of equations, termed as the regularized 17-moment (R17) equations for binary gas mixtures will be presented. The R17 equations are third order accurate in the Knudsen number and are equivalent to super-Burnett equations for binary gas mixtures.