Extended thermodynamics. An alternative to the Navier-Stockes-Fourier theory of gases

This paper describes the results of a recent dissertation by W. Weiss [1]. The objective of this work is twofold: i) determination of the range of validity of the Navier-Stokes-Fourier theory of a monatomic gas ii) determination of the ranges of validy of the extended thermodynamic theories of 13, 14, 20, 35.. and -in general- $n$ moments. The field equations of extended thermodynamics form a system of quasilinear first order differential equations of symmetric hyperbolic character. In its simplest form it takes 13 variables into account, namely the densities of mass, momentum and energy and the stress and heat flux. In that case the results correspond to the results of Grad’s 13-moment theory in the kinetic theory of gases. Further extensions contain more moments among the variables; generically there are $n$ variabies. As measures of reliability we choose the ranges of frequency and wavelength, in which a given $n$ -type extended thermodynamics describes the dispersion of sound and the scattering of light well. It turns out that $n$ must be bigger the higher the sound frequency is and the smaller the wave length of a fluctuation is that scatters ligh. This knowledge is important for the proper selection of a theory for a given boundary and initial value problem: In the temporal and spatial Fourier spectrum of the data we must only have such frequencies and wavelengths for which sound dispersion and light scattering are well-described by the theory