ОСЕРЕДНЕНI МОДЕЛI БАГАТОФАЗНОЇ ДИФУЗIЇ В ПОРИСТИХ СЕРЕДОВИЩАХ
DOI:
https://doi.org/10.17721/2706-9699.2019.3.05Ключові слова:
багатофазна дифузiя, процеси фiльтрацiї, пористi середовища, моделювання, початково-крайовi задачi, осередненi моделiАнотація
Розглядаються нестацiонарнi процеси взаємної дифузiї багатофазних потокiв рiдин, якi не змiшуються мiж собою, в пористих середовищах з перiодичною структурою. Математичною моделлю для таких процесiв є початково-крайова задача дифузiї для середовищ, утворених великою кiлькiстю «блокiв», що мають слабку проникнiсть, i роздiлених зв’язковою системою «розломiв» з високою проникнiстю. Прийняття до уваги такої будови пористих середовищ призводить до залежностi рiвнянь цiєї задачi вiд двох малих параметрiв мiкромасштабностi пористого середовища та проникностi блокiв. Будуть отриманi усередненi початково-крайовi задачi, розв’язки яких наближають розв’язки даної початково-крайової задачi.
Посилання
Alt H. W. end Luckhaus S. Quasilinear elliptic-parabolic differential equations. Mathematische Zeitschrift. 1983. Vol. 183:3. P. 311–341.
Kroener D. end Luckhaus S. J. Flow of oil and water in a porous medium. J. Differential Equations. 1984. Vol. 55:2. P. 276–288.
Mandal A. and Bera A. Modeling of flow of oil-in-water emulsions through porous media. Petroleum Science. 2015. Vol. 12:2. P. 273–281.
Endo Kokubun M. A., Radu F. A., Keilegavlen E., Kumar K., and Spildo K. Transport of polymer particles in oil-water ow in porous media: enhancing oil recovery. Transport in Porous Media. 2019. Vol. 126. P. 501–519.
Bourgeat A., Luckhaus S., and Mikelic A. Convergence of the homogenization hrocess for a double-porosity model of immiscible two-phase flow. SIAM J. Math. Analysis. 1996. Vol. 27:6. P. 1520–1543.
Amazianea B. and Pankratov L. Homogenization of amodel for water–gas flow through double-porosity media. Math. Meth. Appl. Sci. 2016. Vol. 39. P. 425–451.
Sandrakov G. V. The homogenization of nonstationary equations with contrast coefficients. Dokl. Mathematics. 1997. Vol. 56:1. P. 586–589.
Sandrakov G. V. Homogenization of elasticity equations with contrasting coefficients. Sb: Mathematics. 1999. Vol. 190:12. P. 1749–1806.
Sandrakov G. V. Multiphase models of nonstationary diffusion in homogenization. Comput. Math. Math. Phys. 2004. Vol. 44:10. P. 1741–1756.
Sandrakov G. V. Homogenization of variational inequalities for non-linear diffusion problems in perforated domains. Izvestiya: Math. 2005. Vol. 69:5. P. 1035–1059.
Sandrakov G. V. Multiphase homogenized diffusion models for problems with several parameters. Izvestiya: Mathematics. 2007. Vol. 71:6. P. 1193–1252.
Sandrakov G. Homogenization of some hydrodynamics problems. Modern Problems of Mathematical Modeling, Computaional Methods and Information Technologies. Proceedings of the International Scientific Conf. 2–4 March 2018, Rivne. P. 156–157.
Sandrakov G. Modeling of hydrodynamics processes with phase transition. Information Technologies and Computer Modelling. Proceedings of the International Scientific Conf. 14–19 May 2018, Ivano-Frankivsk. P. 303–306.
Sandrakov G. Modeling of heterogeneous fluid dynamics with phase transition. Information Technologies in Education, Science and Technology. Proceedings of Int. Scientific-Practical Conf. 17–18 May 2018, Cherkasy. P. 142–143.
Sandrakov G. V. Methods of modeling of hydrodynamic processes with phase transitions. Slovak international scientific J. 2018. Vol. 1:23. P. 44–49. (In Russian)
Sandrakov G. V. Modeling of phase transitions graphite-diamond. East European Scientific J. 2018. Vol. 39:11. P. 37–42. (In Ukrainian)
Sandrakov G. V. Modeling and homogenization of hydrodynamics processes with the oscillating data. East European Scientific J. 2018. Vol. 40:12. P. 56–62. (In Ukrainian)
Sandrakov G. Modeling and homogenization of hydrodynamics processes with the vanishing viscosity. Int. School-Workshop on Differential Equations and Applications. 18–20 June, 2019, Vinnytsia. Book of Abstracts. p. 62–63.
Sandrakov G. V., Lyashko S. I., Bondar E. S., Lyashko N. I. Modeling and optimization of microneedle systems. J. Automation and Information Sciences. 2019. Vol. 51:6. P. 1–11.
Sandrakov G. Homogenized models with memory effects for composites. Int. School-Workshop on Differential Equations and Applications. 18-20 June, 2019, Vinnytsia. Book of Abstracts. P. 63–64.
Bensoussan A., Lions J.-L., and Papanicolau G. Asymptotic analysis for periodic structures. North-Holland, Amsterdam 1978.
Bakhvalov N. S. and Panasenko G. P. Homogenization: averaging processes in periodic media. Kluwer, Dordrecht 1989.
Duvaut G. end Lions J.-L. Les inequations en mecanique et en physique. Dunod, Paris 1972.
