Generalized Multiscale Finite Element Method for Multicontinuum Coupled Flow and Transport Model

In this paper, we consider a coupled flow and transport process described by partial differential equations for pressure and concentration. We derive the multicontinuum coupled flow and transport model using the multicontinuum homogenization method. We formulate cell problems with constraints that take into account various homogenized effects. For the resulting multicontinuum model, we develop a multiscale solver based on the Generalized Multiscale Finite Element Method. The combined approach of multicontinuum and multiscale modeling makes it possible to consider complex heterogeneous media with high contrast. We present numerical results for a model problem with two continua and heterogeneous coefficients separable into microscopic and macroscopic parts. The results show the high efficiency of the proposed multiscale approach.