[1]
|
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, 55, U.S. Government Printing Office, Washington, D.C., 1964.
|
[2]
|
T. Arima, A. Mentrelli and T. Ruggeri, Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments, Ann. Physics, 345 (2014), 111-140.
doi: 10.1016/j.aop.2014.03.011.
|
[3]
|
T. Arima, T. Ruggeri, M. Sugiyama and S. Taniguchi, Non-linear extended thermodynamics of real gases with 6 fields, Int. J. Non-Lin. Mech., 72 (2015), 6-15.
doi: 10.1016/j.ijnonlinmec.2015.02.005.
|
[4]
|
T. Arima, T. Ruggeri, M. Sugiyama and S. Taniguchi, Recent results on nonlinear extended thermodynamics of real gases with six fields Part I: General theory, Ric. Mat., 65 (2016), 263-277.
doi: 10.1007/s11587-016-0283-y.
|
[5]
|
C. Baranger, M. Bisi, S. Brull and L. Desvillettes, On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases, Kinet. Relat. Models, 11 (2018), 821-858.
doi: 10.3934/krm.2018033.
|
[6]
|
M. Bisi, T. Ruggeri and G. Spiga, Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics, Kinet. Relat. Models, 11 (2018), 71-95.
doi: 10.3934/krm.2018004.
|
[7]
|
C. Borgnakke and P. S. Larsen, Statistical collision model for Monte Carlo simulation of polyatomic gas mixture, J. Comput. Phys., 18 (1975), 405-420.
doi: 10.1016/0021-9991(75)90094-7.
|
[8]
|
L. Boudin, B. Grec, M. Pavić-Čolić and F. Salvarani, A kinetic model for polytropic gases with internal energy, PAMM Proc. Appl. Math. Mech., 13 (2013), 353-354.
doi: 10.1002/pamm.201310172.
|
[9]
|
J.-F. Bourgat, L. Desvillettes, P. Le Tallec and B. Perthame, Microreversible collisions for polyatomic gases and Boltzmann's theorem, European J. Mech. B Fluids, 13 (1994), 237-254.
|
[10]
|
C. Cercignani, The Boltzmann Equation and Its Applications, Applied Mathematical Sciences, 67, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1039-9.
|
[11]
|
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, London, 1970.
|
[12]
|
L. Desvillettes, Sur un modèle de type Borgnakke-Larsen conduisant à des lois d'energie non-linéaires en température pour les gaz parfaits polyatomiques, Ann. Fac. Sci. Toulouse Math. (6), 6 (1997), 257-262.
doi: 10.5802/afst.864.
|
[13]
|
L. Desvillettes, R. Monaco and F. Salvarani, A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions, Eur. J. Mech. B Fluids, 24 (2005), 219-236.
doi: 10.1016/j.euromechflu.2004.07.004.
|
[14]
|
W. Dreyer, Maximisation of the entropy in non-equilibrium, J. Phys. A, 20 (1987), 6505-6517.
doi: 10.1088/0305-4470/20/18/047.
|
[15]
|
I. M. Gamba and M. Pavić-Čolić, On the Cauchy problem for Boltzmann equation modelling a polyatomic gas, preprint, arXiv: 2005.01017.
|
[16]
|
V. Giovangigli, Multicomponent Flow Modeling, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 1999.
doi: 10.1007/978-1-4612-1580-6.
|
[17]
|
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331-407.
doi: 10.1002/cpa.3160020403.
|
[18]
|
M. Groppi and G. Spiga, Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas, J. Math. Chem., 26 (1999), 197-219.
doi: 10.1023/A:1019194113816.
|
[19]
|
M. N. Kogan, Rarefied Gas Dynamics, Springer, Boston, MA, 1969.
doi: 10.1007/978-1-4899-6381-9.
|
[20]
|
S. Kosuge and K. Aoki, Shock-wave structure for a polyatomic gas with large bulk viscosity, Phys. Rev. Fluids, 3 (2018).
doi: 10.1103/PhysRevFluids.3.023401.
|
[21]
|
S. Kosuge, H.-W. Kuo and K. Aoki, A kinetic model for a polyatomic gas with temperature-dependent specific heats and its application to shock-wave structure, J. Stat. Phys., 177 (2019), 209-251.
doi: 10.1007/s10955-019-02366-5.
|
[22]
|
E. W. Lemmon and R. T. Jacobsen, Viscosity and thermal conductivity equations for nitrogen, oxygen, argon and air, Int. J. Thermophys., 25 (2004), 21-69.
doi: 10.1023/B:IJOT.0000022327.04529.f3.
|
[23]
|
C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065.
doi: 10.1007/BF02179552.
|
[24]
|
T. Magin, B. Graille and M. Massot, Kinetic theory derivation of transport equations for gases with internal energy, 42nd AIAA Thermophysics Conference, Honolulu, Hawaii, USA, 2011.
doi: 10.2514/6.2011-4034.
|
[25]
|
G. C. Maitland and E. B. Smith, Critical reassessment of viscosities of 11 common gases, J. Chem. Eng. Data, 17 (1972), 150-156.
doi: 10.1021/je60053a015.
|
[26]
|
I. Müller, T. Ruggeri, Extended Thermodynamics, Springer Tracts in Natural Philosophy, 37, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4684-0447-0.
|
[27]
|
E. Nagnibeda and E. Kustova, Non-Equilibrium Reacting Gas Flows. Kinetic Theory of Transport and Relaxation Processes, Heat and Mass Transfer, Springer-Verlag, Berlin, 2009.
doi: 10.1007/978-3-642-01390-4.
|
[28]
|
M. Pavić, T. Ruggeri and S. Simić, Maximum entropy principle for rarefied polyatomic gases, Phys. A, 392 (2013), 1302-1317.
doi: 10.1016/j.physa.2012.12.006.
|
[29]
|
M. Pavić-Čolić, D. Madjarević and S. Simić, Polyatomic gases with dynamic pressure: Kinetic non-linear closure and the shock structure, Int. J. Non-Lin. Mech., 92 (2017), 160-175.
doi: 10.1016/j.ijnonlinmec.2017.04.008.
|
[30]
|
M. Pavić-Čolić and S. Simić, Moment equations for polyatomic gases, Acta Appl. Math., 132 (2014), 469-482.
doi: 10.1007/s10440-014-9928-6.
|
[31]
|
B. Rahimi and H. Struchtrup, Macroscopic and kinetic modelling of rarefied polyatomic gases, J. Fluid Mech., 806 (2016), 437-505.
doi: 10.1017/jfm.2016.604.
|
[32]
|
T. Ruggeri, Maximum entropy principle closure for 14-moment system for a non-polytropic gas, Ric. Mat., (2020).
doi: 10.1007/s11587-020-00510-y.
|
[33]
|
T. Ruggeri, Non-linear maximum entropy principle for a polyatomic gas subject to the dynamic pressure, Bull. Inst. Math. Acad. Sin. (N.S.), 11 (2016), 1-22.
|
[34]
|
T. Ruggeri and M. Sugiyama, Rational Extended Thermodynamics Beyond the Monatomic Gas, Springer, Cham, 2015.
doi: 10.1007/978-3-319-13341-6.
|
[35]
|
S. Simić, M. Pavić-Čolić and D. Madjarević, Non-equilibrium mixtures of gases: Modelling and computation, Riv. Math Univ. Parma (N.S.), 6 (2015), 135-214.
|
[36]
|
Y. Sone, Kinetic Theory and Fluid Dynamics, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002.
doi: 10.1007/978-1-4612-0061-1.
|
[37]
|
Y. Sone, Molecular Gas Dynamics. Theory, Techniques, and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2007.
doi: 10.1007/978-0-8176-4573-1.
|
[38]
|
D. Stéphane, On the Wang Chang-Uhlenbeck equations, Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), 229-253.
doi: 10.3934/dcdsb.2003.3.229.
|
[39]
|
H. Struchtrup, The Boltzmann equation and its properties, in Macroscopic Transport Equations for Rarefied Gas Flows, Springer, Berlin, Heidelberg, 2005, 27–51.
doi: 10.1007/3-540-32386-4_3.
|
[40]
|
S. Taniguchi, T. Arima, T. Ruggeri and M. Sugiyama, Overshoot of the non-equilibrium temperature in the shock wave structure of a rarefied polyatomic gas subject to the dynamic pressure, Int. J. Non-Lin. Mech., 79 (2016), 66-75.
doi: 10.1016/j.ijnonlinmec.2015.11.003.
|
[41]
|
S. Taniguchi, T. Arima, T. Ruggeri and M. Sugiyama, Shock wave structure in a rarefied polyatomic gas based on extended thermodynamics, Acta Appl. Math., 132 (2014), 583-593.
doi: 10.1007/s10440-014-9931-y.
|
[42]
|
S. Taniguchi, T. Arima, T. Ruggeri and M. Sugiyama, Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: Beyond the Bethe-Teller theory, Phys. Rev. E, 89 (2014).
doi: 10.1103/PhysRevE.89.013025.
|
[43]
|
C. S. Wang Chang, G. E. Uhlenbeck and J. de Boer, The heat conductivity and viscosity of polyatomic gases, in Studies in Statistical Mechanics, Vol. II, North-Holland, Amsterdam; Interscience, New York, 1964,241–268.
|