Multiscale Multicontinuum Homogenization for Coupled Flow and Transport in Heterogeneous Media

  • Leung, Wing Tat (City university of Hong Kong)

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Coupled flow and transport processes in heterogeneous media arise in a wide range of applications, including subsurface flow, porous media transport, and environmental fluid mechanics. The presence of high contrast coefficients, complex microstructures, and multiple interacting continua poses significant challenges for conventional numerical methods, often leading to prohibitive computational costs or loss of accuracy at coarse scales. In this talk, we present a multiscale multicontinuum homogenization framework for coupled flow and transport equations, designed to systematically capture fine-scale heterogeneities and nonlocal interactions while maintaining computational efficiency. The proposed approach constructs multiple interacting coarse-scale continua through local spectral problems and constrained energy minimization, yielding effective macroscopic equations that retain essential multiscale features of the underlying system. We derive the resulting coarse-scale flow and transport models, and demonstrate how the multicontinuum representation enables accurate resolution of mass exchange and transport pathways across scales. Numerical experiments for coupled flow–transport problems illustrate the effectiveness of the method in capturing multiscale dynamics by a coarse-scale model. The framework provides a flexible and mathematically grounded tool for the simulation of complex fluid and transport phenomena in heterogeneous environments.