DG-GMsFEM for Dual Continuum Transport Problem in Perforated Domains

In this paper, we develop a Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsFEM) for solving dual continuum transport problems in perforated domains. The mathematical model includes the convection-diffusion equations for concentrations, with flow described by the Stokes equations. The model equations are derived by homogenizing small perforations using multicontinuum homogenization techniques. After performing this homogenization, we obtain appropriate parameters for the dual continuum transport model. The resulting system includes larger perforations, which are resolved via multiscale basis functions. For the coarse grid approximation, we introduce a multiscale model reduction technique that constructs local multiscale basis functions to generate a lower-dimensional model. The proposed reduction technique is based on DG-GMsFEM and involves two steps: (1) constructing a snapshot space and (2) solving local spectral problems for dimension reduction in this space. We present numerical results for a two-dimensional problem to demonstrate the method’s performance. Our numerical results show that the proposed method provides good results with a significant reduction of the system size.