Three-dimensional mixed finite element-finite volume approach for the solution of density-dependent flow in porous media

The density-dependent flow and transport problem in groundwater on three-dimensional triangulations is solved numerically by means of a mixed hybrid finite element scheme for the flow equation combined with a mixed hybrid finite element-finite volume (MHFE-FV) time-splitting-based technique for the transport equation. This procedure is analyzed and shown to be an effective tool in particular when the process is advection dominated or when density variations induce the formation of instabilities in the flow field. From a computational point of view, the most effective strategy turns out to be a combination of the MHFE and a spatially variable time-splitting technique in which the FV scheme is given by a second-order linear reconstruction based on the least-squares minimization and the Barth-Jespersen limiter. The recent saltpool problem introduced as a benchmark test for density-dependent solvers is used to verify the accuracy and reliability of this approach.