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Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects pp 150–158Cite as

Classes of Exact Solutions for the Discrete Boltzmann Models

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Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 43))

Summary

For the discrete Boltzmann models [1] (DBM) the velocities take only a finite number of discrete values v i For their exact solutions the building blocks were the classes of self-similar solutions which, for binary collisions, are in general like the Broadwell shock wave, solutions of scalar Riccati equations. All (1 + 1)—dimensional, (2 + 1), 2D, 3D solutions which, up to now, have been constructed are linear combinations of these self-similar solutions and we report the new results found since a previous review paper [2]. However very recent results [3] show that, for DBM, another class of self-similar solutions corresponding to coupled Riccati equations exists also. For the multiple collisions other new classes of self-similar solutions have been found when quaternary and fifth-order collisions are present [3].

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Authors and Affiliations

  1. Service de Physique Théorique, CE Saclay, 91191, Gif-sur-Yvette, France

    Henri Cornille

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  1. Henri Cornille
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Andrea Donato Francesco Oliveri

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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Cornille, H. (1993). Classes of Exact Solutions for the Discrete Boltzmann Models. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_18

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  • DOI: https://doi.org/10.1007/978-3-322-87871-7_18

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07643-6

  • Online ISBN: 978-3-322-87871-7

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