Thinking of flows crossing through regular porous media, we numerically explore the behavior of weak solutions to a two-scale elliptic-parabolic system that is strongly coupled by means of a suitable nonlinear dispersion term. The two-scale system of interest originates from the fast-drift periodic homogenization of a nonlinear convective-diffusion-reaction problem, where the structure of the non-linearity in the drift fits to the hydrodynamic limit of a totally asymmetric simple exclusion process for a population of particles. In this article, we focus exclusively on numerical simulations that employ two decoupled approximation schemes, viz. 'scheme 1' - a Picard-type iteration - and 'scheme 2' - a time discretization decoupling. Additionally, we describe a computational strategy which helps to drastically improve computation times. Finally, we provide several numerical experiments to illustrate what dispersion effects are introduced by a specific choice of microstructure and model ingredients.

翻译：针对流体流经规则多孔介质的情形，本文通过数值方法探究由适当非线性色散项强耦合的两尺度椭圆-抛物系统弱解的行为。此两尺度系统源于非线性对流-扩散-反应问题的快漂移周期均匀化过程，其中漂移项的非线性结构适配于粒子群体全非对称简单排斥过程的水动力学极限。本文仅聚焦于两种解耦逼近方案的数值模拟：方案一为Picard型迭代，方案二为时间离散解耦。此外，我们提出一种可显著缩短计算时间的计算策略。最后通过若干数值实验，阐明特定微结构及模型参数选择所引入的色散效应。