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Cell-centered finite-volume method for heterogeneous anisotropic poromechanics problem. (English) Zbl 1423.76308
Summary: The article introduces a finite-volume method for the poromechanics problem for heterogeneous anisotropic media. The media are characterized by the full tensors of elasticity, permeability and Biot coefficient. The pressure and displacement unknowns are collocated at centers of cells. Poromechanics represents a multi-physics problem of Darcy flow and linear elasticity coupled via Biot terms. Based on the flux and the displacement and pressure continuity conditions we derive the coupled block expression for the flux. The flux expression is split into a block-harmonic part, a transversal part and an additional contribution due to gravity. The block-harmonic part is equivalent to the two-point flux approximation method for the Darcy problem. For the approximation of the transversal part, we derive an interpolation method for the coupled pressure and displacement fields, valid over discontinuities of the tensors. Finally, we derive the flux expression for generalized boundary conditions. The flux expression does not require introduction of auxiliary unknowns at the boundary. We evaluate the performance of the proposed method on a number of numerical tests and apply the method to a problem on a grid corresponding to a real oil field.

76M12 Finite volume methods applied to problems in fluid mechanics
74S10 Finite volume methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
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