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

Pore-scale modeling of solute transport in partially-saturated porous media

“…Below we describe two such methods; more detailed discussions can be found e.g. in Yang et al (2021b); Mehmani et al (2021).…”

“…Hybrid Multiscale Method (domain decomposition). A general technique that allows the use of different pore-scale models in regions of interest embedded in a larger domain where a continuum, Darcy-scale model is implemented (Yang et al, 2021b;Scheibe et al, 2015b). A scale coupling condition (a bilateral communication) is implemented for the interface of discretized subdomains to assure the continuity of fluxes and concentration fields over the macro-and pore-scale regions (Roubinet and Tartakovsky, 2013).…”

A comprehensive review on coupled processes and mechanisms of soil-vegetation-hydrology, and recent research advances

“…Scheibe et al (2015) developed a hybrid multiscale model that initially simulates the full domain at the continuum scale and applies a pore-scale model only to areas of high reactivity, increasing the accuracy of subsurface reactive transport simulations. Yang X F et al (2021) reviewed current multiscale models of water flow and solute transport in porous media (such as soil) and discussed future research perspectives and challenges from both modeling and application points of view.…”

Investigation of Coupled Processes in Fractures and the Bordering Matrix via a Micro‐Continuum Reactive Transport Model

“…In light of the scale differences and computational challenges of the pore‐scale approach, reactive transport modeling in fractured media can be conceptualized as a multiscale problem that couples a pore‐scale component in the fracture, and a Darcy‐scale component in the porous matrix (Molins et al., 2019), which is commonly referred to as multiscale modeling (Molins & Knabner, 2019; Yang et al., 2021). One approach of multiscale modeling involves the use of hybrid algorithms, which divide the domain into subdomains according to their respective characteristic length scales.…”