Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.     

Sediment transport patterns at Trafalgar offshore windfarm

A simple analytical model of wave propagation has been developed in order to study the potential sediment transport patterns due to the action of currents and waves in the neighborhood of cylindrical structures as well inside a group of these structures. The attention is focused on the study of Trafalgar offshore windfarm, a case in which it has been necessary to analyze the flow trough porous structures in order to model fish growing-cages planned to be installed at each aerogenerator structure. The results are obtained by averaging over one period of wave in order to evaluate the net potential sediment transport. The analysis of the results reveals how the processes of wave diffraction and reflection give rise to periodic patterns of sediment transport around and between the structures.