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Shock Wave Structure of Multi-Temperature Euler Equations from Kinetic Theory for a Binary Mixture

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Abstract

A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities.

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References

  1. Bisi, M., Martalò, G., Spiga, G.: Multi-temperature hydrodynamic limit from kinetic theory in a mixture of rarefied gases. Acta Appl. Math. 122, 37–51 (2012)

    MATH  MathSciNet  Google Scholar 

  2. Bisi, M., Martalò, G., Spiga, G.: Multi-temperature fluid-dynamic model equations from kinetic theory in a reactive gas: the steady shock problem. Comput. Math. Appl. 66, 1403–1417 (2013)

    Article  MathSciNet  Google Scholar 

  3. Boillat, G., Ruggeri, T.: On the shock structure problem for hyperbolic system of balance laws and convex entropy. Contin. Mech. Thermodyn. 10, 285–292 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cercignani, C.: Rarefied Gas Dynamics. From Basic Concepts to Actual Calculations. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  5. Currò, C., Fusco, D.: Discontinuous travelling wave solutions for a class of dissipative hyperbolic models. Rend. Mat. Acc. Lincei 16, 61–71 (2005)

    MATH  Google Scholar 

  6. Groppi, M., Spiga, G., Takata, S.: The steady shock problem in reactive gas mixtures. Bull. Inst. Math. Acad. Sin. 2, 935–956 (2007)

    MATH  MathSciNet  Google Scholar 

  7. Groppi, M., Spiga, G., Zus, F.: Euler closure of the Boltzmann equations for resonant bimolecular reactions. Phys. Fluids 18, 057105 (2006)

    Article  MathSciNet  Google Scholar 

  8. Madjarevic, D., Simic, S.: Shock structure in Helium-Argon mixture—A comparison of hyperbolic multi-temperature model with experiment. Europhys. Lett. 102, 44002 (2013)

    Article  Google Scholar 

  9. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics. Springer, New York (1988)

    Google Scholar 

  10. Ruggeri, T., Simic, S.: Average temperature and Maxwellian iteration in multi-temperature mixtures of fluids. Phys. Rev. E 80, 026317 (2009)

    Article  Google Scholar 

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Acknowledgements

Fruitful discussions with F. Conforto and S. Simic on the subject of the present work are gratefully acknowledged.

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Authors and Affiliations

  1. Dip. di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy

    Marzia Bisi & Giampiero Spiga

  2. Dip. di Matematica, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy

    Giorgio Martalò

Authors
  1. Marzia Bisi
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  2. Giorgio Martalò
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  3. Giampiero Spiga
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Correspondence to Giorgio Martalò.

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Bisi, M., Martalò, G. & Spiga, G. Shock Wave Structure of Multi-Temperature Euler Equations from Kinetic Theory for a Binary Mixture. Acta Appl Math 132, 95–105 (2014). https://doi.org/10.1007/s10440-014-9939-3

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  • DOI: https://doi.org/10.1007/s10440-014-9939-3

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