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**A two-scale approach for fluid flow in fractured porous media.**
*(English)*
Zbl 1194.76139

Summary: A two-scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are nonlinear due to the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

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\textit{J. Réthoré} et al., Int. J. Numer. Methods Eng. 71, No. 7, 780--800 (2007; Zbl 1194.76139)

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