Multicontinuum Homogenization for Coupled Flow and Transport Equations

TL;DR

This paper develops a multicontinuum homogenization approach for coupled flow and transport equations, deriving a multiscale model with effective properties and validating it through numerical experiments.

Contribution

The paper introduces a novel multicontinuum homogenization method with coupled constraint cell problems for multiscale flow and transport modeling.

Findings

Effective multicontinuum system derived with homogenized properties

Numerical validation shows accuracy across various conditions

Method captures multiscale effects without boundary artifacts

Abstract

In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and formulate novel coupled constraint cell problems to capture the multiscale property, where oversampled regions are utilized to avoid boundary effects. Assuming the smoothness of macroscopic variables, we obtain a multicontinuum system composed of macroscopic elliptic equations and convection-diffusion-reaction equations with homogenized effective properties. Finally, we present numerical results for various coefficient fields and boundary conditions to validate our proposed algorithm.