Geodesic
The Mathematical Models for Description of Flow of Gas and Foreign Particles and for Non-Stationary Filtration of Liquids and Gas in Porous Medium
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 1, pp. 34-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author discusses different mathematical models of different levels used and developed for the description of the flow of gas or liquid mixtures with foreign “macroparticles” (solid or liquid) of a size of a micron or bigger and the non-stationary filtration of liquids and gas in porous medium. In approximation of interpenetrating continua (continuums) the author points out the role of “sheets” — the breaks lines with the surface density of particles along them. The continuous-discrete model is considered alongside with the approximation of interpenetrating continua for the problems of gas and particles flows. In this model the discrete set of individual macroparticles interacts with the continuous medium of gas or a liquid. In many problems the number of such particles is great enough but much less than the number of atoms interacting with them, as well as molecules of gas or a liquid, and in modern computing conditions the integration of equations describing the movement and collisions of all particles in the computational region becomes possible. It is important that in continuous-discrete model it is done not on the analogy with the kinetic theory of gases (such approaches also are known) with functions of distribution according to particle parameters (sizes, speeds, etc.) but strictly individually. With reference to a non-stationary filtration of liquids the model of instant saturation with attached and free liquids and with features of forward and back fronts of saturation of movement is considered. The opportunities of the phenomenological description of non-stationary gas flow through the surfaces of porosity break are marked.
Keywords: the integral conservation laws; “the sheets” in models of interpenetrating continua; the continuous-discrete model; the model of instant saturation; gas flows through surfaces of porosity break. 
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A. N. Kraiko. The Mathematical Models for Description of Flow of Gas and Foreign Particles and for Non-Stationary Filtration of Liquids and Gas in Porous Medium. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 1, pp. 34-48. http://geodesic.mathdoc.fr/item/VYURU_2014_7_1_a3/

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