Explicit fluxes and productions for large systems of the moment method based on extended thermodynamics

Abstract

The moment method of kinetic theory solves Boltzmann’s equation approximately via an infinite hierarchy of transfer equations for the moments of the distribution function. Extended thermodynamics furnishes the moment method with a rational constitutive theory. Since more and more moment equations are needed to describe extreme non-equilibrium processes, there is need for an algorithmical derivation of large explicit moment equations. This paper presents detailed techniques and formulas which are needed to implement a numerical equation generator. This includes tensorial conversion formulas as well as the core equations of the constitutive theory. In the last part of the paper, the special case of a one dimensional process is discussed. In such a case, only one generic polynomial evaluation needs to be implemented, whereas the coefficients may be easily calculated a priori.