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.
Highlights
Closure is an important issue in developing simplified physical theories from more fundamental levels of description
As standard hydrodynamics can be recovered from the five moments of the single-particle velocity distribution that correspond to the mass, momentum, and energy densities, it is tempting to use larger sets of moments to construct theories of fluid dynamics going beyond standard hydrodynamics
There are further requirements from fundamental principles, such as the validity of a suitable version of the second law of thermodynamics for nonequilibrium systems. We refer to this type of criteria as thermodynamic admissibility, where we here rely on general equation for the nonequilibrium reversible–irreversible coupling (GENERIC)4–6 as a thermodynamic framework
Summary
Closure is an important issue in developing simplified physical theories from more fundamental levels of description. There are further requirements from fundamental principles, such as the validity of a suitable version of the second law of thermodynamics for nonequilibrium systems We refer to this type of criteria as thermodynamic admissibility, where we here rely on general equation for the nonequilibrium reversible–irreversible coupling (GENERIC) as a thermodynamic framework. In producing simplified theories of rarefied gas dynamics from the Boltzmann equation, it is natural to supplement the five hydrodynamic fields associated with the local conservation laws by five-second moments characterizing the momentum flux, and three third moments characterizing the energy flux. A detailed discussion of the resulting equations is offered in Sec. IV, including the entropy balance, the proper hydrodynamic limit, and second-order matching in the Knudsen scaling with Grad’s original equations, which appears to not be completely possible. Appendix B offers a brief discussion of Onsager–Casimir symmetry
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
