Modified flux-vector-based Green element method for problems in steady-state anisotropic media

In this study we present a new numerical technique for solving problems in steady-state heterogeneous anisotropic media, namely the ‘flux-vector-based’ Green element method (‘qq-based’ GEM) for anisotropic media. This method, which is appropriate for problems where the permeability has either constant or continuous components over the whole domain, is based on the boundary element method (BEM) formulation for direct, steady-state flow problems in anisotropic porous media, which is applied to finite element method (FEM) meshes. For situations involving media discontinuities, an extension of this ‘qq-based’ GEM formulation is proposed, namely the modified ‘qq-based’ GEM for anisotropic media. Numerical results are presented for various physical problems that simulate flow in an anisotropic medium with diagonal layers of different permeabilities or around faults and wells, and they show that the new method, with the extensions proposed, is very suitable for steady-state problems in such media.