532.51 Modeling non-Newtonian liquid permeability in three-dimensional composite structures on the base of asymptotic homogenization method

Dimitrienko Y. I. (Bauman Moscow State Technical University), Li S. -. (Bauman Moscow State Technical University)

ASYMPTOTIC HOMOGENIZATION METHOD, NON-NEWTONIAN LIQUID, PERIODIC POROUS MEDIA, FILTRATION LAW, RHEOLOGICAL PROPERTIES


doi: 10.18698/2309-3684-2019-3-1938


The paper describes investigating a mathematical model of the process of a non-Newtonian liquid multiscale filtration in three-dimensional periodic porous media by asymptotic homogenization. The so-called local problem of filtration in a single pore is formulated as well as the local non-Newtonian-viscous defining relationship. An iterative finite element method is developed for solving a local problem in 1/8 periodicity cell, based on the physical symmetry of the structure. The distribution of the components of the filtration rate, pressure micro-fields and non-Newtonian viscosity in a single pore is calculated. On the basis of Darcy's law the nonlinear filtration law is analyzed, the effect of liquid rheological properties on permeability is shown.


Bardzokas D.I., Zobnin A.I. Matematicheskoe modelirovanie fizicheskikh protsessov v kompozitsionnykh materialakh periodicheskoy struktury [Mathematical modeling of physical processes in composite materials of periodic structure]. Moscow, Editorial URSS Publ., 2003, 376 p.
Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov [Averaging processes in periodic media. Mathematical problems of the composite material mechanics]. Moscow, Nauka Publ., 1984, 352 p.
Dimitrienko Yu.I. Thermomechanics of composites under high temperatures. Springer, 2015, 434 p.
Idris Z, Orgéas L, Geindreau C, Bloch, J.F., Auriault, J.L Modelling and Simulation in Materials Science and Engineering, 2004, vol.12, pp.995–1015.
Dimitrienko Yu.I., Zakharova Yu.V., Bogdanov I.O. Humanities and Science University Journal, 2016, no.19, pp.33–43.
Dimitrienko Yu.I., Shpakova Yu.V., Bogdanov I.O., Sborshchikov S.V. Inzhenernyy zhurnal: Nauka i innovatsii — Engineering Journal: Science and Innovation, 2015, no.12, pp.14–54.
Dimitrienko Yu.I., Bogdanov I.O. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2017, no.2, pp.3–27.
Dimitrienko Yu.I., Ivanov M.Yu. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2008, no.1, pp.39–56.
,, Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2008, no.3, pp.90–104.
Dimitrienko Yu.I., Bogdanov I.O. Inzhenernyy zhurnal: Nauka i innovatsii – Engineering Journal: Science and Innovation, 2018, no.3, pp.17–38.
Dimitrienko Yu.I. Transport in porous media, 1999, vol.35, pp.299–326.
Dimitrienko Yu.I., Dimitrienko I.D. European Journal of Mechanics/B-Fluids, 2013, no.1, pp.174–179.
Wang J.G., Leung C.F., Chow Y.K. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, vol.27, no.7, pp.565–583.
Koponen A., Kandhai D., Hellen E., Alava M., Hoekstra A., Kataja M., Niskanen N., Sloot P., Timonen J., Physical Review Letters, 1998, vol.80, no.4, pp.716–719.
Auriault J.L, Royer P., Geindreau C. International Journal of Engineering Science, 2002, vol.40, pp.1151–1163.
Orgéas L., Idrisl Z., Geindreau C., Bloch, J.F., Auriault, J.L. Chemical Engineering Science, 2006, vol.61, pp.4490–4502.
Orgéas L., Geindreau C., Auriault J.L., Bloch, J.F., Auriault, J.L. Journal of Non-Newtonian Fluid Mechanics, 2007, vol.145, pp.15–29.
Dimitrienko Yu.I., Sokolov A.P. Matematicheskoe modelirovanie — Mathematical Models and Computer Simulations, 2012, vol.24, no.5, pp.3–20.
Dimitrienko Yu.I., Kashkarov A.I., Makashov A.A. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2007, no.1, pp.26–46.
Dimitrienko Yu.I., Gubareva E.A., Sborshchikov S.V. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2016, no.2, pp.3–23.
Dimitrienko, Yu.I. Li S. Matematicheskoe modelirovanie i chislennye menody — Mathematical Modeling and Computational Methods, 2018. № 2.pp.70–95.
Dimitrienko Yu.I. Nelineinaya mekhanika sploshnoi sredy [Nonlinear Continuum Mechanics]. Moscow, Fizmatlit Publ., 2009, 624 p.
Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnoy sredy [Continuum Mechanics. Vol.2. Universal laws of continuous media mechanics and electrodynamics]. Moscow, BMSTU Publ., 2011, 560 p.
Dimitrienko Yu.I. Tensor analysis and nonlinear tensor functions. Springer, 2002, 662 p.
Bird R.B, Armstrong R.C., Hassager O. Dynamics of polymeric liquids. Vol.1: Fluid mechanics. John Wiley & Sons Publ., 1987, 649 p.
Zienkiewicz O.C., Taylor R.L., Zhu J.Z., The Finite Element Method: Its Basis and Fundamentals. Elsevier Publ., 2005, 733 p.


Димитриенко Ю.И., Шугуан Ли. Моделирование проницаемости неньютоновских жидкостей в трехмерных композитных структурах на основе метода асимптотической гомогенизации. Математическое моделирование и численные методы. 2019. № 3.c.19–38.



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