Modeling of Darcy’s Flow in Generally Anisotropic Porous Media Containing Discontinuity Surface by SGBEM-FEM Coupling

In this paper we present a computational procedure for modeling steady-state, Darcy’s flow in a generally anisotropic porous medium containing the discontinuity surface. This computational technique provides a useful means to gain an insight into certain real problems, e.g. flow in a porous reservoir containing seals and/or fractures. The technique employs a weakly singular, symmetric Galerkin boundary element method (SGBEM) to model fluid flow within a (local and homogeneous) region containing the discontinuity surface while employs a standard Galerkin finite element method (FEM) to treat fluid flow in the remaining (possibly very complex and nonhomogeneous) region. The SGBEM is based on a pair of weakly singular, weak-form fluid pressure and fluid flux integral equations which contains only weakly singular kernels of O(1/r) and is applicable to both isotropic and generally anisotropic permeability [

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,

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]. The formulations of the two methods are properly combined to obtain a final formulation which is in a symmetric form.

In the numerical implementation, the region modeled by the SGBEM and that by the FEM are discretized such that meshes on the interface of the two regions are conforming. The important features of the current technique include those: 1) standard

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elements can be employed everywhere in the discretization of the region modeled by the SGBEM since the integral formulation in only weakly singular; 2) special tip elements are utilized along the boundary of the discontinuity surface to accurately capture asymptotic behavior of the jump of the fluid pressure; 3) an efficient interpolation strategy is adopted to evaluate the kernels for generally anisotropic permeability; and 4) the coupling formulation gives rise to a symmetric system of algebraic equations. To demonstrate the accuracy and capability of the coupling technique, two example problems are presented.