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Sub-shock Formation in Reacting Gas Mixtures

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From Particle Systems to Partial Differential Equations III

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 162))

Abstract

The shock-wave structure problem is investigated for a gas mixture of four species, undergoing a reversible bimolecular reaction, modelled by a 10 moment Grad closure of reactive Boltzmann equations. The presence of jump discontinuities within the shock structure solution is discussed, the supersonic regime is characterized, and the critical values of Mach number allowing the formation of sub-shocks in the field variables of one or more components of the mixture are pointed out.

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Acknowledgments

This work is performed in the frame of activities sponsored by INdAM–MIUR and by the Universities of Messina and Parma. The work of G. Martalò has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the “Investments for the future” Programme IdEx Bordeaux—CPU (ANR-10-IDEX-03-02). F. Conforto and G. Martalò are grateful to GNFM for the financial support of the research project “Sub-shock formation in gas mixtures”. M. Bisi and G. Martalò have been supported also by the French-Italian program Galileo, project G14-34, “Kinetic modelling and numerical simulations of reactive gaseous mixtures and plasmas for nuclear fusion”. Fruitful discussions with A. Mentrelli and T. Ruggeri on the subject of the present work are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Parma, Parco Area delle Scienze, 53/A, Parma, Italy

    Marzia Bisi

  2. Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, University of Messina, v.le F. Stagno d’Alcontres 31, Messina, Italy

    Fiammetta Conforto

  3. Institut de Mathématiques de Bordeaux, CNRS and Université de Bordeaux, 351, cours de la Libération, 33405, Talence, France

    Giorgio Martalò

  4. INRIA Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, 33405, Talence, France

    Giorgio Martalò

Authors
  1. Marzia Bisi
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  2. Fiammetta Conforto
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  3. Giorgio Martalò
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Correspondence to Fiammetta Conforto .

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Editors and Affiliations

  1. University of Minho Department of Mathematics, Braga, Portugal

    Patrícia Gonçalves

  2. University of Minho Department of Mathematics, Braga, Portugal

    Ana Jacinta Soares

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Bisi, M., Conforto, F., Martalò, G. (2016). Sub-shock Formation in Reacting Gas Mixtures. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-319-32144-8_3

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