Thermodynamically admissible 13-moment equations

Date

2022-01

Authors

Struchtrup, Henning
Ottinger, Hans Christian

Journal Title

Journal ISSN

Volume Title

Publisher

PHysics of Fluids

Abstract

Grad's 13-moment equations describe transport in mildly rarefied gases well, but are not properly embedded into nonequilibrium thermodynamics since they are not accompanied by a formulation of the second law. In this work, the Grad-13 equations are embedded into the framework of GENERIC (general equation for the nonequilibrium reversible–irreversible coupling), which demands additional contributions in the equations to guarantee thermodynamic structure. As GENERIC building blocks, we use a Poisson matrix for the basic convection behavior and antisymmetric friction matrices to correct for additional convective transport terms. The ensuing GENERIC-13 equations completely match the Grad-13 equations up to second-order terms in the Knudsen number and fulfill all thermodynamic requirements.

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Citation

Henning, S., & Ottinger, Hans Christian. (2022). Thermodynamically admissible 13-moment equations. Physics of Fluids. 34, 017105 https://doi.org/10.1063/5.0078780