Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures

We present a numerical approximation of Darcy's flow through porous medium that incorporates networks fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements edges/faces may be in arbitrary number (potentially unlimited) whose measure arbitrarily small. approach is then very well suited to tame the geometrical complexity featured by most applications computational geoscience field. From modelling point view, we adopt reduction strategy treats as manifolds codimension one employ primal version law describe both bulk fracture network. In addition, some physically consistent conditions couple two problems, allowing jump pressure at their interface, they prescribe behaviour fluid along intersections, imposing continuity flux conservation. Both discretizations are obtained employing Symmetric Interior Penalty DG method extended polytopic setting. The key instrument obtain polyDG problem network generalization concepts average intersection, so contribution from all taken into account. prove well-posedness discrete formulation perform an error analysis obtaining priori hp-error estimates. All our theoretical results validated performing preliminary tests known analytical solution.