A two-scale domain decomposition method for computing the flow through a porous layer limited by a perforated plate

A two-scale domain decomposition method is developed in order to study situations where the macroscopic description of a given transport process in porous media does not represent a sufficiently good approximation near singularities (holes, wells, etc.). The method is based on a decomposition domain technique with overlapping. The governing equations at the scale of the microstructure are solved in the vicinity of the singularities whereas the volume averaged transport equations are solved at some distance of the singularities. The transfer of information from one domain to the other is performed using results of the method of volume averaging. The method is illustrated through the computation of the overall permeability of a porous layer limited by a perforated plate. As shown in the example treated, the method allows one to estimate the useful size of the microscopic region near the singularities. As illustrated in the paper, the method can lead to a considerable gain in memory requirement compared to a full direct simulation.