Generalized multiscale enriched Galerkin method for flow in heterogeneous porous media

This paper is concerned with a mass-conservative multiscale finite element framework for single-phase flow in highly heterogeneous porous media. The method combines the local mass conservation and low computational cost of the Enriched Galerkin method within the Generalized Multiscale Finite Element Method (GMsFEM) framework, resulting in the Generalized Multiscale Enriched Galerkin (GMsEG) method. The GMsEG method embeds the fine-scale heterogeneity into the continuous multiscale basis functions by solving local eigen-problems, and the continuous multiscale finite element space is enriched by the piecewise constant space on the coarse grid. The resulting method preserves the mass conservation property and can resolve fine-grid heterogeneity while remaining computationally efficient. Well-posedness and convergence estimates of the method are established, and numerical experiments in various heterogeneous porous media demonstrate the efficiency and accuracy of the method, as well as highlight the significance of employing a mass conservative method when flow and transport problems are coupled together. © 2026 World Scientific Publishing Company.