#### 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.

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