Multicontinuum Homogenization for Two-Phase Model with Linear Transport

In this work, we present a multicontinuum homogenization approach for a two-phase model with linear transport, governed by coupled flow and transport equations with high-contrast coefficients. The method introduces multiple macroscopic variables to represent distinct physical characteristics of the solution, such as local averages over subregions. To capture fine-scale heterogeneities, multiscale basis functions are constructed by solving local constrained energy minimization problems. The resulting reduced-order model is defined on a coarse scale and involves the macroscopic variables and homogenized coefficients. It retains the essential features of the original fine-scale system while reducing computational costs. Numerical examples are provided to validate the proposed model. The results demonstrate that the solutions obtained from the proposed model accurately approximate those from the original model.