Rational Extended Thermodynamics

1998 ◽  
Author(s):  
Ingo Müller ◽  
Tomasso Ruggeri
Keyword(s):  
Extended Thermodynamics ◽  
Rational Extended Thermodynamics

scholarly journals Acceleration Waves in Rational Extended Thermodynamics of Rarefied Monatomic Gases

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 139
Author(s):  
Francesca Brini ◽  
Leonardo Seccia
Keyword(s):  
Shock Wave ◽  
Extended Thermodynamics ◽  
Rarefied Gases ◽  
Acceleration Wave ◽  
One Dimensional ◽  
Acceleration Waves ◽  
Rational Extended Thermodynamics ◽  
Monatomic Gas ◽  
Non Equilibrium

Rational Extended Thermodynamics theories with different number of moments are usually introduced to study non-equilibrium phenomena in rarefied gases. Here, we use them to describe one-dimensional acceleration waves in a rarefied monatomic gas. In particular, we focus on the degeneracy of the acceleration wave to a shock wave, in order to test the validity of the models and the role played by an increasing number of moments. As a byproduct, some peculiarities of the characteristic velocities at equilibrium are analyzed as well.

scholarly journals Relationships between rational extended thermodynamics and extended irreversible thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190172 ◽  
Author(s):  
David Jou
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Extended Thermodynamics ◽  
Internal Variables ◽  
Second Law ◽  
Hamiltonian Approach ◽  
Theme Issue ◽  
Extended Irreversible Thermodynamics ◽  
Independent Variables ◽  
Rational Extended Thermodynamics

We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 43
Author(s):  
Takashi Arima ◽  
Maria Cristina Carrisi ◽  
Sebastiano Pennisi ◽  
Tommaso Ruggeri
Keyword(s):  
Bulk Viscosity ◽  
Maximum Entropy Principle ◽  
Entropy Density ◽  
Extended Thermodynamics ◽  
Bgk Model ◽  
Rest Energy ◽  
Polyatomic Gases ◽  
The Cauchy Problem ◽  
Entropy Principle ◽  
Rational Extended Thermodynamics

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

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