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Shock structure in extended thermodynamics with second-order maximum entropy principle closure

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Abstract

An investigation on the features of the shock structure solution of the 13-moment system of extended thermodynamics with a second-order closure based on the maximum entropy principle is presented. The results are compared to those obtained by means of the traditional first-order closure and to those obtained in the framework of kinetic theory by solving the Boltzmann equation with a BGK model for the collision term. It is seen that when adopting a second-order closure, the strength of the subshock that appears in the shock structure profile for large enough Mach numbers is remarkably reduced with respect to what is found with the first-order closure, and the overall profile of the shock structure solution is in better agreement with the results obtained with the kinetic theory approach. The analysis is extended to the case of the 14-moment system of a polyatomic gas, and some preliminary results are presented also for this case.

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Notes

  1. For \(\hbox {N}_2\) gas, the relaxation time \(\tau _{\varPi }\) is several orders of magnitude larger than \(\tau _{\sigma }\) and \(\tau _{q}\).

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Acknowledgements

This work was partially supported by GNFM/INdAM; one of the authors (A.M.) was also partially supported by the Italian MIUR PRIN2017 project “Multiscale phenomena in Continuum Mechanics: singular limits, off-equilibrium and transitions”(project number: 2017YBKNCE).

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Correspondence to Andrea Mentrelli.

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Communicated by Andreas Öchsner.

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Mentrelli, A., Ruggeri, T. Shock structure in extended thermodynamics with second-order maximum entropy principle closure. Continuum Mech. Thermodyn. 33, 125–150 (2021). https://doi.org/10.1007/s00161-020-00892-2

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