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Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

 and    | Mar 22, 2017

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1. T. K. Bose, High Temperature Gas Dynamics. Springer, 2003.10.1007/978-3-662-07762-7Search in Google Scholar

2. E. Nagnibeda and E. Kustova, Non-Equilibrium Reacting Gas Flows. Springer, 2009.10.1007/978-3-642-01390-4Search in Google Scholar

3. I. Müller and T. Ruggeri, Rational Extended Thermodynamics. Springer, 1998.10.1007/978-1-4612-2210-1Search in Google Scholar

4. V. Giovangigli, Multicomponent Flow Modeling. Birk¨auser, 1999.10.1007/978-1-4612-1580-6Search in Google Scholar

5. N. Xystris and J. Dahler, Kinetic theory of simple reacting spheres, The Journal of Chemical Physics, vol. 68, pp. 387-401, 1978.10.1063/1.435772Search in Google Scholar

6. A. Rossani and G. Spiga, A note on the kinetic theory of chemically reacting gases, Physica A, vol. 272, pp. 563-573, 1999.10.1016/S0378-4371(99)00336-2Search in Google Scholar

7. R. Monaco, M. Pandolfi Bianchi, and A. J. Soares, BGK-type models in strong reaction and kinetic chemical equilibrium regimes, Journal of Physics A, vol. 38, pp. 10413-10431, 2005.Search in Google Scholar

8. J. F. Bourgat, L. Desvillettes, P. Le Tallec, and B. Perthame, Microreversible collisions for polyatomic gases and Boltzmann’s theorem, European Journal of Mechanics - B/Fluids, vol. 13, pp. 237-254, 1994.Search in Google Scholar

9. W. Marques, Light scattering from extended kinetic models: polyatomic ideal gases, Physica A, vol. 264, pp. 40-51, 1999.10.1016/S0378-4371(98)00427-0Search in Google Scholar

10. A. Chikhaoui, J. P. Dudon, S. Genieys, E. V. Kustova, and E. A. Nagnibeda, Multitemperature kinetic model for heat transfer in reacting gas mixture flows, Physics of Fluids, vol. 12, pp. 220-232, 2000.10.1063/1.870302Search in Google Scholar

11. T. Ruggeri and M. Sugiyama, Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, 2015.10.1007/978-3-319-13341-6Search in Google Scholar

12. 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, European Journal of Mechanics - B/Fluids, vol. 24, pp. 219-236, 2005.10.1016/j.euromechflu.2004.07.004Search in Google Scholar

13. M. Groppi and G. Spiga, Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas, Journal of Mathematical Chemistry, vol. 26, pp. 197-219, 1999.10.1023/A:1019194113816Search in Google Scholar

14. S. Chapman and T. G. Cowling, The Mathematical Theory of Non- Uniform Gases. Cambridge University Press, 1970.Search in Google Scholar

15. P. Bhatnagar, E. Gross, and K. Krook, A model for collision processes in gases, Physical Review, vol. 94, pp. 511-525, 1954.10.1103/PhysRev.94.511Search in Google Scholar

16. P.Welander, On the temperature jump in a rarefied gas, Arkyv f¨or Fysik, vol. 7, pp. 507-553, 1954.Search in Google Scholar

17. A. Bellouquid, J. Calvo, J. Nieto, and J. Soler, On the relativistic BGK- Boltzmann model: asymptotics and hydrodynamics, Journal of Statistical Physics, vol. 149, pp. 284-316, 2012.10.1007/s10955-012-0600-0Search in Google Scholar

18. F. J. McCormack, Construction of linearized kinetic models for gaseous mixtures and molecular gases, Physics of Fluids, vol. 16, pp. 2095-2105, 1973.Search in Google Scholar

19. P. Andries, K. Aoki, and B. Perthame, A consistent BGK type model for gas mixtures, Journal of Statistical Physics, vol. 106, pp. 993-1018, 2002.10.1023/A:1014033703134Search in Google Scholar

20. V. Garz´o and A. Santos, Kinetic Theory of Gases in Shear Flows. Nonlinear Transport. Springer, 2003.10.1007/978-94-017-0291-1Search in Google Scholar

21. S. Brull and J. Schneider, On the ellipsoidal statistical model for polyatomic gases, Continuum Mechanics and Thermodynamics, vol. 20, pp. 489-508, 2009.10.1007/s00161-009-0095-3Search in Google Scholar

22. B. Rahimi and H. Struchtrup, Macroscopic and kinetic modelling of rarefied polyatomic gases, Journal of Fluid Mechanics, vol. 806, pp. 437-505, 2016.10.1017/jfm.2016.604Search in Google Scholar

23. M. Groppi, G. Russo, and G. Stracquadanio, Boundary conditions for semi-Lagrangian methods for the BGK model, Communications in Applied and Industrial Mathematics, vol. 7, pp. 135-161, 2016.10.1515/caim-2016-0025Search in Google Scholar

24. M. Bisi, M. Groppi, and G. Spiga, Kinetic Bhatnagar-Gross-Krook model for fast reactive mixtures and its hydrodynamic limit, Physical Review E, vol. 81, 036327, 2010.Search in Google Scholar

25. M. Bisi and M. J. C´aceres, A BGK relaxation model for polyatomic gas mixtures, Communications in Mathematical Sciences, vol. 14, pp. 297-325, 2016.10.4310/CMS.2016.v14.n2.a1Search in Google Scholar

26. M. Groppi and G. Spiga, A Bhatnagar-Gross-Krook-type approach for chemically reacting gas mixtures, Physics of Fluids, vol. 16, pp. 4273-4284, 2004.Search in Google Scholar

27. M. Bisi and G. Spiga, On kinetic models for polyatomic gases and their hydrodynamic limits, Ricerche di Matematica, doi:10.1007/s11587-016-0289-5, in press.Search in Google Scholar

28. J. R. Mika and J. Banasiak, Singularly Perturbed Evolution Equations with Applications to Kinetic Theory. World Scientific, 1995.Search in Google Scholar

29. T. Arima, T. Ruggeri, M. Sugiyama and S. Taniguchi, Nonlinear extended thermodynamics of real gases with 6 fields, International Journal of Non-Linear Mechanics, vol. 72, pp. 6-15, 2015.10.1016/j.ijnonlinmec.2015.02.005Search in Google Scholar

30. T. Arima, S. Taniguchi, T. Ruggeri, andM. Sugiyama, Extended thermodynamics of real gases with dynamic pressure: An extension of Meixner’s theory, Physics Letters A, vol. 376, pp. 2799-2803, 2012.Search in Google Scholar

31. G. M. Kremer, M. Pandolfi Bianchi, and A. J. Soares, A relaxation kinetic model for transport phenomena in a reactive flow, Physics of Fluids, vol. 16, 037104, 2006.Search in Google Scholar

32. M. Groppi, S. Rjasanow, and G. Spiga, A kinetic relaxation approach to shock structure in fast reactive mixtures, Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, P10010, 2009.Search in Google Scholar

33. S. R. De Groot and P. Mazur, Nonequilibrium Thermodynamics. North- Holland, 1962. Search in Google Scholar

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Mathematics, Numerical and Computational Mathematics, Applied Mathematics