Algebraic flux correction finite element method with semi-implicit time stepping for solute transport in fractured porous media

Abstract

This work is concerned with the numerical modeling of the Darcy flow and solute transport in fractured porous media for which the fractures are modeled as interfaces of codimension one. The hybrid-dimensional flow and transport problems are discretizaed by a lumped piece-wise linear finite element method, combined with the algebraic correction of the convective fluxes. The resulting transport discretization can be interpreted as a conservative finite volume scheme that satisfies the discrete maximum principle, while introducing a very limited amount of numerical diffusion. In the context of fractured porous media flow the CFL number may vary by several order of magnitude, which makes explicit time stepping unfeasible. To cope with this difficulty we propose an adaptive semi-implicit time stepping strategy that reduces to the low order linear implicit discretization in the high CFL regions that include, but may not be limited to the fracture network. The performance of the fully explicit and semi-implicit variants of the method are investigated through the numerical experiment.