| Issue |
E3S Web of Conf.
Volume 402, 2023
International Scientific Siberian Transport Forum - TransSiberia 2023
|
|
|---|---|---|
| Article Number | 14040 | |
| Number of page(s) | 13 | |
| Section | Materials Chemistry and Physics | |
| DOI | https://doi.org/10.1051/e3sconf/202340214040 | |
| Published online | 19 July 2023 | |
Construction of a numerical model and algorithm for solving two-dimensional problems of filtration of multicomponent liquids, taking into account the moving “oil-water” interface
Tashkent University of Information Technologies, TUIT/Multimedia Technologies, Tashkent, Uzbeksitan
* Corresponding author: elmira_nazirova@mail.ru
The paper considers a two-dimensional mathematical model of the filtration of a viscous, incompressible fluid in a deformable porous medium. The article describes a mathematical model of the problem at the “oil-water” interface with a system of parabolic differential equations. The problem posed is solved numerically using the differential-difference method based on the longitudinal-transverse scheme and the differential sweep method to determine the unknown boundary. To obtain a differential-difference problem, an algorithmic representation of a hidden scheme of alternating directions (longitudinal-transverse scheme) is used. The resulting system of differential-difference equations with initial conditions is known for each time layer along straight lines along the x axis, and then along each y axis it is solved by a differential sweep along a straight line, where the values just found correspond to time, i.e., the layer is taken as initial conditions. By approximating the differential equations in time, the position of the interface is determined for each time layer.
© The Authors, published by EDP Sciences, 2023
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