Formulation of moment equations for rarefied gases within two frameworks of non-equilibrium thermodynamics: RET and GENERIC
Date
2020
Authors
Ottinger, Hans Christian
Struchtrup, Henning
Torrilhon, Manuel
Journal Title
Journal ISSN
Volume Title
Publisher
Royal Society Publishing
Abstract
In this work, we make a further step in bringing together different approaches to non-equilibrium thermodynamics. The structure of the moment hierarchy derived from the Boltzmann equation is at the heart of rational extended thermodynamics (RET, developed by Ingo Müller and Tommaso Ruggeri). Whereas the full moment hierarchy has the structure expressed in the general equation for the nonequilibrium reversible–irreversible coup- ling (GENERIC), the Poisson bracket structure of reversible dynamics postulated in that approach is a major obstacle for truncating moment hierarchies, which seems to work only in exceptional cases (most importantly, for the five moments associated with conservation laws). The practical importance of truncated moment hierarchies in rarefied gas dynamics and microfluidics motivates us to develop a new strategy for establishing the full GENERIC structure of truncated moment equations, based on non-entropy-producing irreversible processes associated with Casimir symmetry. Detailed results are given for the special case of 10 moments.
Description
Keywords
rational extended thermodynamics, GENERIC, Boltzmann equation, moment equations, closure, Onsager–Casimir symmetry
Citation
Öttinger HC, Struchtrup H, Torrilhon M. 2020 Formulation of moment equations for rarefied gases within two frameworks of non-equilibrium thermodynamics: RET and GENERIC. Phil. Trans. R. Soc. A 378: 20190174. http://dx.doi.org/10.1098/rsta.2019.0174