Geodesic
The shock waves structure in the gas-particles mixture with chaotic pressure
Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 3-20.

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The propagation of shock waves in a mixture of gas and fine solid particles is considered in the frame of the mathematical model Anderson taking into account the differences between phases velocities and pressures. An approximate mathematical model of the flow is offered, which ignores the dependence of the first phase pressure on the particles volume concentration, but takes into account the terms, representing the particle volume concentration multiplied on a gas phase pressure gradient. The mathematical model has a hyperbolic type in this case. Classification of the shock waves types is done that are realized in the mixture for these heterogeneous media mechanics equations. The propositions about shock waves types are illustrated by numerical calculations in the stationary and non-stationary statements. For this purpose the original numerical TVD-type method is developed.
Keywords: mixture of gas and solid particles, particle phase pressure, shock wave structure, frozen and dispersion shock waves, numerical methods. 
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A. V. Fedorov; I. A. Bedarev. The shock waves structure in the gas-particles mixture with chaotic pressure. Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2017_29_6_a0/

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