Geodesic
Mathematical modeling of the two-phase fluid flow in inhomogeneous fractured porous media using the double porosity model and finite element method
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 1, pp. 165-182

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Numerical simulation of the two-phase fluid flow in a fractured porous media using the double porosity model with a highly inhomogeneous permeability coefficient has been studied. A system of equations has been presented for the case of two-phase filtration without capillary and gravitational effects, which is a connected system of equations for pressure and saturation in a porous medium that contains a system of cracks. Different variants of specifying the flow functions between the porous medium and cracks have been considered. The numerical implementation for velocity and pressure approximation is based on the finite element method. To discretize the saturation equation, the classical Galerkin method with counter-flow approximation has been used. The results of numerical calculations for the model problem using various interflow functions have been presented.
Keywords: two-phase filtration, inhomogeneous media, fractured-porous media, double porosity model, interflow functions, finite element method, numerical stabilization. 
@article{UZKU_2018_160_1_a16,
     author = {V. I. Vasilyev and M. V. Vasilyeva and A. V. Grigorev and G. A. Prokopiev},
     title = {Mathematical modeling of the two-phase fluid flow in inhomogeneous fractured porous media using the double porosity model and finite element method},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {165--182},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_1_a16/}
}
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V. I. Vasilyev; M. V. Vasilyeva; A. V. Grigorev; G. A. Prokopiev. Mathematical modeling of the two-phase fluid flow in inhomogeneous fractured porous media using the double porosity model and finite element method. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 1, pp. 165-182. http://geodesic.mathdoc.fr/item/UZKU_2018_160_1_a16/