Novel technique for solving advection-dominated fluid flow in anisotropic and heterogeneous porous media

August 11th, 2023

Advective-dominated diffusion problems in heterogeneous and anisotropic porous media play a critical role in geoscience. These problems inform our understanding of subsurface fluid dynamics, impacting, for instance, the spread of contaminants and the identification of mineral-rich areas. However, accurately capturing these physical behaviors is challenging for numerical methods due to the underlying complexities of the equation system, underscoring the need for more sophisticated computational techniques.

In our recent publication (https://doi.org/10.1016/j.cma.2023.116285), we introduced a novel numerical approach that constructs solutions across multiple scales, achieving both a stable solution and an on-the-fly adaptive refinement. We demonstrate the effectiveness and reliability of our method through various numerical experiments, which include high heterogeneity, pronounced anisotropic diffusion tensors, and convection-dominated diffusion.

By employing this method, we can obtain more precise numerical approximations to predict mineral flow deposition in complex permeability porous media, all while reducing the computational cost.

Representation of the multi-scale solution and the transition from error estimation to the fine scale using an inter-scale operator.

Results for a shock wave problem: Full-scale stabilised solution (left), refined mesh after several levels of adaptive refinement (middle). Fine-scale solution (right).