THE STATE OF THE PROBLEM OF THE JOINT MOVEMENT OF FLUID IN THE PORE SPACE
Mussina A.A. Mukhambetzhanov S.T. Baiganova A.M.
24 June 2022al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2022#114Issue 243 - 52 pp.
This article discusses the problems of studying the issue of joint motion of liquids in the porous space. The article provides the construction of a mathematical model of the theory of filtration, which describes phase transitions. The main difficulty in constructing this model is associated with the fact that free interphase boundaries create regions that change over time, and it is required to find the temperature or concentration fields of substances in them. In this case, the coordinates of the considered phase boundaries are not initially specified and must be calculated already in the process of solving. For this, a derivation of the averaged equation for the problem of finding the rupture surface during the movement of two incompressible viscous liquids in the pores of the soil skeleton was proposed. The article deals with the case when the skeleton is an absolutely rigid body. The rationale was given for the choice of an averaged filtration model instead of a microscopic one. The main research methods are classical methods of mathematical physics, functional analysis and computation methods of the theory of partial differential equations, as well as difference methods. The formulation of the problem is given, and the definition of a generalized solution for solving the problem is provided. Next, an averaged model is derived and the existence of at least one generalized solution to the problem is proved.
adsorption , averaged model , difference scheme , joint motion of liquids , macroscopic model , microscopic model , numerical methods , phase boundary , relaxation time , sorption , Stefan problem , surfactant
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Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
Al Farabi Kazakh National University, Almaty, Kazakhstan
Zhubanov Aktobe Regional University
Al Farabi Kazakh National University
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