Geodesic
A computational model of fluid filtration in fractured porous media
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 2, pp. 145-166.

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The paper discusses a computational 3D double porosity model of a two-phase incompressible fluid filtration in a fractured-porous medium. Conservation laws are formulated in the integral form, and for their spatial approximation, a combination of the mixed finite element method to determine the total flow and pressure velocities is used and the finite volume method to determine the saturations in porous blocks and in fractures. The approximation of equations for saturations according to an explicit scheme with upwinding to eliminate unphysical oscillations is carried out. The model under consideration includes the injection and production wells with total flow rates. For the total velocities and pressures, the Neumann problem is formulated, for which the condition of unique solvability is indicated and a method for solving it without additional conditions is proposed. For an explicit upwind scheme for solving equations for saturations, a weak maximum principle is established, illustrated by computational experiments. 
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M. I. Ivanov; I. A. Kremer; Yu. M. Laevsky. A computational model of fluid filtration in fractured porous media. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 2, pp. 145-166. http://geodesic.mathdoc.fr/item/SJVM_2021_24_2_a2/

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