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.

翻译：本文通过应用多连续介质均质化方法，推导了耦合流动与输运方程的多连续介质模型。我们对流动与输运的解进行多连续介质展开，并构建了新型耦合约束单元问题以捕捉多尺度特性，其中采用过采样区域以规避边界效应。在假设宏观变量光滑的前提下，我们得到了一个由宏观椭圆型方程及具有均质化等效属性的对流-扩散-反应方程构成的多连续介质系统。最后，我们展示了多种系数场与边界条件下的数值结果，以验证所提出的算法。