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Numerical Modeling of Gas Flows in the Transition between Rarefied and Continuum Regimes

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Book cover Numerical Flow Simulation I

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 66))

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Summary

In the present paper we derive fluid dynamic equations by performing asymptotic analysis for the generalized Boltzmann equation for polyatomic gases. In particular, we consider the steady state, one-dimensional Boltzmann equation with one additional internal energy and different relaxation times. Moreover, we present a new approach to define coupling procedures for the Boltzmann equation and Navier-Stokes equations based on the 14-moments expansion of Levermore. These coupled models are validated by numerical simulations.

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References

  1. Bourgat, J. F., Desvillettes, L., Le Tallec, P. and Perthame, B.: Microreversible collisions for polyatomic gases and Boltzmann’s theorem, European Journal of Mechanics, B/Fluids, 13,no 2, 237–254 (1994).

    MathSciNet  MATH  Google Scholar 

  2. Charrier, P., Dubroca, B. and Feugeas, J.L.: Etude numérique de modèles aux moments de Levermore en 2 dimensions, personal communication, 1996.

    Google Scholar 

  3. Chapman, S. and Cowling, T.G.: The Mathematical Theory of Nonuniform Gases, Cambridge University Press (3th edition, 1970 ).

    Google Scholar 

  4. Ferziger, J.H. and Kaper, H.G.: Mathematical theory of transport processes in gases, North-Holland (1972).

    Google Scholar 

  5. Grad, H.: On the Kinetic Theory of Rarefied Gazes, Comm. Pure Appl. Math 2, pp 331–407, 1949.

    MathSciNet  MATH  Google Scholar 

  6. Hash, D. and Hassan, A.: A Hybrid DSMC/Navier-Stokes Solver, AIAA 95–0410.

    Google Scholar 

  7. Junck, M.: About the domain of definition of Levermore’s five moment system, personal communication, June 1997.

    Google Scholar 

  8. Kuéer, I.: Dissociation and Recombination in an Inhomogeneous Gas, Physica A, 176, 542–556 (1991).

    Article  MathSciNet  Google Scholar 

  9. Le Tallec, P. and Mallinger, F.: Coupling Boltzmann and Navier-Stokes equations by half fluxes, Journal of Computational Physics, 136, 51–67, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  10. Le Tallec,P. and Perlat, J.-P.: Coupling Kinetic Models with NavierStokes equations, to appear in CFD Review, 1998.

    Google Scholar 

  11. Le Tallec, P. and Perlat, J.-P., “ Asymptotic Kinetic Models for Transitional Flows ”, Proceedings of the “ International Conference on Numerical Modelling in Continuum Mechanics ”, M. Feistauer ed., Prague 1997.

    Google Scholar 

  12. Le Tallec, P. and Perlat, J.-P.: Numerical Analysis of Levermore’s Moment System, Rapport de recherche INRIA 3124, Mars 1997.

    Google Scholar 

  13. Levermore, D.: Moment Closure Hierarchies for Kinetic Theories, Department of Mathematics, University of Arizona,submitted to the journal of statistical physics, May 1995.

    Google Scholar 

  14. Levermore, D. and Morokoff, W.J.: The Gaussian Moment Closure for Gas Dynamics, SIAM J. on Applied Mathematics, submitted February 1996.

    Google Scholar 

  15. Levermore, D.: Entropy Based Moment Closures for Kinetic Equations. Transport Theory and Statistical Physics, April 1996.

    Google Scholar 

  16. Neunzert, H. and Struckmeier, J.: Particle Methods for the Boltzmann Equation, ACTA NUMERICA 1995, Cambridge (1995).

    Google Scholar 

  17. Perlat, J.P.: Modélisation et Calcul parallèle d’une couche limite cinétique, Universit Pierre et Marie Curie, Paris VI, Janvier 1998.

    Google Scholar 

  18. Sack, W: Modellierung und Numerik für reaktive Strömungen in verdünnten Gasen, PhD thesis, University of Kaiserslautern, October 1995.

    Google Scholar 

  19. Tiwari, S. and Klar, A.: An Adaptive Domain Decomposition Procedure for Boltzmann and Euler Equations, to appear in Journal of Comp. & Appl. Math.

    Google Scholar 

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© 1998 Springer Fachmedien Wiesbaden

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Günther, M., Le Tallec, P., Perlat, J.P., Struckmeier, J. (1998). Numerical Modeling of Gas Flows in the Transition between Rarefied and Continuum Regimes. In: Hirschel, E.H. (eds) Numerical Flow Simulation I. Notes on Numerical Fluid Mechanics (NNFM), vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44437-4_11

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  • DOI: https://doi.org/10.1007/978-3-540-44437-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53590-1

  • Online ISBN: 978-3-540-44437-4

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