# Simulation of filtration problems in fractured porous media with mixed finite element method (Embedded Fracture Model)

• Spiridonov Denis A., d.stalnov@mail.ru M. K. Ammosov North-Eastern Federal University Institute of mathematics and Informatics 42 Kulakovsky Street, Yakutsk 677891, Russia
• Vasilyeva Maria V., vasilyevadotmdotv@gmail.com M. K. Ammosov North-Eastern Federal University Institute of mathematics and Informatics 42 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: ﬁnite element method, built-in model of cracks, fractured medium, single-phase liquid, liquid ﬂow, law of conservation of mass, Darcy law

### Abstract

We present a mathematical model of mixed dimension for modeling ﬁltration problems in fractured porous media (built-in model of cracks). The mathematical model is described by a system of parabolic equations: d-dimensional for a porous medium and (d − 1)-dimensional for a system of cracks. The system of equations is connected by specifying a special ﬂow function. This model allows the use of grids for a matrix of a porous medium not dependent on the grid for cracks. For the numerical solution, an approximation using the mixed ﬁnite element method is constructed. The results of the numerical solution of the model problem that show the operability of the proposed method for modeling the ﬂow in fractured porous media are presented.

### References

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How to Cite
Spiridonov, D. and Vasilyeva, M. (&nbsp;) “Simulation of filtration problems in fractured porous media with mixed finite element method (Embedded Fracture Model)”, Mathematical notes of NEFU, 24(3), pp. 100-110. doi: https://doi.org/10.25587/SVFU.2018.3.10893.
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Mathematical Modeling