Geodesic
The structure of a shock wave's front in a heterogeneous mixture of two isothermal viscous gases
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 4, pp. 461-475

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The problem of a shock wave frontline structure is studied for a heterogeneous mixture of two viscous gases with pair interaction forces. In the pending physical model we assume that the both components of the mixture have isothermal equations of the state and the pair interaction is carried out through the momentum exchange between the components. The pair interaction force is assumed to be linear with respect to the difference of the components velocities. In the work we justify the method of construction of discontinuous solutions for ideal gases by the analysis of the limiting transition from viscous mixture to ideal one in the framework of the theory of fast-slow dynamical systems. It is noted that in the limit case only four shock wave types with different structures of the frontline are possible. For all four types we provide results of numerical calculations of the shock wave frontline structure.
Keywords: shock wave, structure of front, heterogeneous mixture, pair interaction, isothermal gas. 
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     author = {S. M. Voronin and V. A. Adarchenko and A. V. Panov},
     title = {The structure of a shock wave's front in a heterogeneous mixture of two isothermal viscous gases},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {461--475},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a6/}
}
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S. M. Voronin; V. A. Adarchenko; A. V. Panov. The structure of a shock wave's front in a heterogeneous mixture of two isothermal viscous gases. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 4, pp. 461-475. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a6/