Recent progress in multi‐scale modeling and simulation of flow and solute transport in porous media

Abstract The heterogeneity and multi‐scale characteristics of porous media (such as soil aquifers) bring a series of uncertainties in studying flow and solute transport. In particular, the mathematical representation of these physical processes at different temporal and spatial scales, that is, the constitutive equations and parameters, is largely varied, which creates grand challenges in multi‐scale modeling and numerical simulation of flow and solute transport in porous media. In recent years, we acknowledge that at‐scale models and simulations have been greatly progressed, which means that at each individual scale, the transport phenomena, numerical methods, and solvers have been developed and utilized at different levels. However, the long‐standing problem, scale coupling between the pore‐ and Darcy‐scale in porous media, has not been well resolved. In this review, we present an overview and classification of the current multi‐scale models, aiming to understand small‐scale flow and solute transport processes when/where needed in a larger system. This review begins with a brief introduction of the pore‐ and Darcy‐scale theories. Two groups of multi‐scale models that are state‐of‐the‐art, based on the Darcy–Brinkman–Stokes equation and the domain decomposition method, respectively, are explained in the context of research progress in model theory, numerical algorithms, and applications. Future research perspectives and challenges are also discussed from both modeling and application points of view. This review is expected to provide a fundamental understanding of flow and solute transport in porous media and concept of developing multi‐scale models to bridge the gaps between processes in adjacent scales. This article is categorized under: Science of Water > Water Quality Science of Water > Methods Science of Water > Hydrological Processes