Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics

Abstract We show that, in the theory of extended thermodynamics, rarefied monatomic gases can be identified as a singular limit of rarefied polyatomic gases. Under naturally conditioned initial data we prove that the system of 14 field equations for polyatomic gases in the limit has the same solutions as those of the system of 13 field equations for monatomic gases where there exists no dynamic pressure. We study two illustrative examples in the process of the limit, that is, the linear waves and the shock waves in order to grasp the asymptotic behavior of the physical quantities, in particular, of the dynamic pressure.

[1]  Takashi Arima,et al.  Extended thermodynamics of real gases with dynamic pressure: An extension of Meixnerʼs theory , 2012 .

[2]  T. Ruggeri,et al.  Extended thermodynamics of dense gases , 2012 .

[3]  T. Ruggeri,et al.  Shock structures and sub shocks in rarefied polyatomic gases based on extended thermodynamics , 2013 .

[4]  Tommaso Ruggeri,et al.  Dispersion relation in the high frequency limit and non linear wave stability for hyperbolic dissipative systems , 1992 .

[5]  Tommaso Ruggeri,et al.  On the shock structure problem for hyperbolic system of balance laws and convex entropy , 1998 .

[6]  Maximum entropy principle for rarefied polyatomic gases , 2013 .

[7]  G. M. Kremer.  Extended thermodynamics of non-ideal gases , 1987 .

[8]  Takashi Arima,et al.  Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics , 2013 .

[9]  M. C. Carrisi,et al.  On some remarkable properties of an extended thermodynamic model for dense gases and macromolecular fluids , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  I. Liu,et al.  Hyperbolic system for viscous fluids and simulation of shock tube flows , 1990 .

[11]  I. Müller,et al.  Rational Extended Thermodynamics , 1993 .

[12]  Liu I-Shih.  Extended thermodynamics of fluids and virial equations of state , 1985 .

[13]  H. Grad.  On the kinetic theory of rarefied gases , 1949 .

[14]  W. Dreyer,et al.  Maximisation of the entropy in non-equilibrium , 1987 .

[15]  Tommaso Ruggeri,et al.  Moment equations in the kinetic theory of gases and wave velocities , 1997 .

[16]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .