Gradient discretization of hybrid dimensional Darcy flows in fractured porous media
The authors consider the anisotropic Darcy flow described by equations div~\(\mathbf q =h\) and \(\mathbf q=-\Lambda \nabla u\), where \(\Lambda\) is the permeability tensor. Equations in the weak formulation are stated. The conditions on the fractures \(\Gamma\) have the form div\(_{\tau} \mathbf q - [\mathbf q \cdot \mathbf n] =h_f\) and \(\mathbf q=-\Lambda_f \nabla_{\tau} \gamma u\), where div\(_{\tau}\) and \(\nabla_{\tau}\) denote the tangential operators on the surfaces \(\Gamma\). Here, \(\gamma\) is the trace operator, \(\mathbf n\) the unit normal vector to \(\Gamma\). Hence, the flow is considered in two manifolds with different dimensions. The gradient numerical scheme is applied to the hybrid dimensional flow model.
scientific article; zbMATH DE number 6666243
scientific article