Geodesic
On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 155-169

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The paper considers a model of double porosity for a fractured porous medium using a combination of classical and gradient mass transfer functions among cracks and porous blocks in the case of a flow of a weakly compressible single-phase fluid. As compared to well-known models, such a mass transfer function allows one to take into account the anisotropic properties of filtration in a more general form. The results of numerical tests for two-dimensional and three-dimensional model problems are presented. The computational algorithm is based on the use of finite element approximation with respect to space and completely implicit approximations with respect to time. 
@article{SJVM_2018_21_2_a2,
     author = {A. V. Grigorev and Yu. M. Laevsky and P. G. Yakovlev},
     title = {On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {155--169},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/}
}
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A. V. Grigorev; Yu. M. Laevsky; P. G. Yakovlev. On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 155-169. http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a2/