Shock structure and multiple sub-shocks in Grad 10-moment binary mixtures of monoatomic gases
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The problem of sub-shock occurrence within a shock structure solution is investigated for an inert binary mixture of monoatomic gases, modelled by a Grad 10-moment approximation of the Boltzmann equations. The main purpose of this paper is to show by numerical simulations the existence of discontinuous shock structure solutions for values of the shock speed below the maximum unperturbed characteristic velocity. Moreover, for suitable concentrations of the two species, and for shock velocities beyond the maximum unperturbed characteristic velocity, each constituent of the mixture generates a jump discontinuity, and the shock structure solution exhibits two sub-shocks.
KeywordsGrad 10 moment approximation Mixtures of gases Sub-shock formation Rankine–Hugoniot conditions Riemann problem
Mathematics Subject Classification35Q20 58J45 35L67
This work is performed in the frame of activities sponsored by INdAM–GNFM, by Universities of Messina, and of Enna Kore. G. Martalò is a post-doc fellow supported by the National Institute of Advanced Mathematics (INdAM). This work is dedicated to Professor Tommaso Ruggeri on the occasion of his 70th birthday. The authors would like to express their deep and sincere gratitude to Professor Ruggeri for all the extremely useful discussions, the deep analysis and the constructive criticisms, which turned out to be crucial for the development of their research.
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