Geodesic
Two-dimensional effects on the interaction of a shock wave with a cloud of particles
Numerical methods and programming, Tome 21 (2020) no. 3, pp. 207-224.

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A statistical approach based on the kinetic equation for the probability density function of the distribution of particle velocity and temperature is used to develop a continuum model describing pseudoturbulent flows of the dispersed phase. The introduction of the probability density function allows one to obtain a statistical description of an ensemble of particles instead of a dynamic description of individual particles based on Langevin equations of motion and heat transfer. The equations for the first and second moments of the dispersed phase are derived and the numerical simulation of the unsteady gas–particle flow arising due to the interaction of a shock wave with a cloud of particles is performed. The governing equations are of the hyperbolic type and are written in a conservative form. They are solved by a Godunov numerical method of high order of accuracy. Two-dimensional effects on the formation of the shock-wave structure of the gasparticle flow and distributions of particle concentration and other flow quantities in time and space are discussed.
Keywords: two-phase flow; numerical simulation; shock wave; particle; concentration; cloud of particles. 
@article{VMP_2020_21_3_a1,
     author = {K. N. Volkov and V. N. Emelyanov and A. G. Karpenko and I. V. Teterina},
     title = {Two-dimensional effects on the interaction of a shock wave with a cloud of particles},
     journal = {Numerical methods and programming},
     pages = {207--224},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a1/}
}
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K. N. Volkov; V. N. Emelyanov; A. G. Karpenko; I. V. Teterina. Two-dimensional effects on the interaction of a shock wave with a cloud of particles. Numerical methods and programming, Tome 21 (2020) no. 3, pp. 207-224. http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a1/