Abstract
We discuss the structure of the shock wave solution for a system of Navier–Stokes equations, obtained as hydrodynamic limit of a BGK description of the dynamics of monoatomic gases at kinetic level. We investigate first the thickness of the transition region of the shock profile for a monoatomic gas, for varying Mach number and different physical options for the viscosity coefficient. The analysis is then extended to a binary gas mixture. Some numerical results for noble gases are presented and discussed.
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Acknowledgements
This contribution is dedicated to Professor Giuseppe Toscani on the occasion of his 70th birthday. This work was performed in the frame of activities sponsored by the Italian National Group of Mathematical Physics (GNFM-INdAM) and by the University of Parma (Italy), and supported by the Italian National Research Project Multiscale phenomena in Continuum Mechanics: singular limits, off-equilibrium and transitions (Prin 2017YBKNCE) and by the French-Italian program Galileo, G18-296 Modelli cinetici classici e quantistici e loro limiti idrodinamici: aspetti teorici e applicativi. Fruitful discussions with Professor Tommaso Ruggeri on the subject of the paper are gratefully acknowledged.
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Bisi, M., Groppi, M. & Martalò, G. On the shock thickness for a binary gas mixture. Ricerche mat 70, 251–266 (2021). https://doi.org/10.1007/s11587-020-00503-x
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DOI: https://doi.org/10.1007/s11587-020-00503-x