Nesting Theory of Many Moments and Maximum Entropy Principle

Tommaso Ruggeri and Masaru Sugiyama
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Tommaso Ruggeri: University of Bologna, Department of Mathematics and Research Center on Applied Mathematics
Masaru Sugiyama: Nagoya Institute of Technology

Chapter Chapter 9 in Classical and Relativistic Rational Extended Thermodynamics of Gases, 2021, pp 243-271 from Springer

Abstract: Abstract We consider molecular extended thermodynamics (molecular ET) of rarefied polyatomic gases with the system composed of two hierarchies of balance equations for the moments of a distribution function. The internal degrees of freedom of a molecule are properly taken into account in the distribution function. By the reasoning of physical relevance, the truncation orders of the two hierarchies are shown to be dependent on each other. And the two closure procedures based on the maximum entropy principle and on the entropy principle are also proved to be equivalent to each other. Characteristic velocities of a hyperbolic system of balance equations for a polyatomic gas are compared to those obtained for a monatomic gas. The lower bound estimate for the maximum equilibrium characteristic velocity established for a monatomic gas is proved to be valid also for a rarefied polyatomic gas, that is, the estimate is independent of the degrees of freedom of a molecule. As a consequence, also for polyatomic gases, when the number of moments increases the maximum characteristic velocity becomes unbounded.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-59144-1_9

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DOI: 10.1007/978-3-030-59144-1_9

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