N.P. Petrov1, S.N. Petrova2, N. V. Korzhavina3, E. V. Lisovsky4

1 Ural State University of Economics (Ekaterinburg, Russia)
2 Technical University of the Ural Mining and Metallurgical Company
(Verkhnyaya Pyshma, Russia), 
2 Ural State Low University (Ekaterinburg, Russia)
3  Technical University of the Ural Mining and Metallurgical Company (Verkhnyaya Pyshma, Russia)
4 Kaluga branch of the Bauman Moscow State Technical University (Kaluga, Russia)
 

Analysis and synthesis of mathematical models of liquid filtration is one of the most relevant areas of mathematical modeling. Generalizations and modifications of the model of different-colored liquids are aimed at improving approaches to solving important filtration problems in in challenging hydrogeological environment. The purpose of the article is to improve models of fluid motion and search for exact solutions to various boundary value problems. The possibilities of constructing and researching models of the same type of problems in isotropic and anisotropic layers are considered. The problems of finding exact solutions for a number of boundary value problems are studied. In particular, the problems of advancing the interface of various liquids in the filtration flow created by the vortex are considered. The possibilities of developing algorithmic and software for solving problems of modeling filtration flows are discussed. The results can be used in the tasks of mathematical modeling of liquid media, in the tasks of ensuring environmental safety in the development of oil and gas and construction technologies in in challenging hydrogeological environment.

Petrov N.P., Petrova S.N., Korzhavina N.V., Lisovsky E.V. Pressure filtration of multicolored liquid in challenging hydrogeological environment. Science Intensive Technologies. 2022. V. 23. № 8. P. 15−24. DOI: https://doi.org/10.18127/j19998465-202208-02 (in Russian)

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