A Discussion on the Transmission Conditions for Saturated Fluid Flow Through Porous Media With Fractal Microstructure

TL;DR

This paper investigates the appropriate exchange conditions for saturated fluid flow in porous media with fractal microstructures, introducing models, analyzing them rigorously, and validating findings through numerical experiments and probabilistic approaches.

Contribution

It introduces and analyzes two deterministic models for fluid flow in fractal-structured porous media, providing new insights into exchange conditions and validating them with numerical experiments.

Findings

Validated theoretical models with numerical experiments

Explored probabilistic versions for deeper understanding

Identified suitable exchange conditions for fractal microstructures

Abstract

The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously analyzed. Also, numerical experiments for each of them are presented to verify the theoretically predicted behavior of the phenomenon and some probabilistic versions are explored numerically, to gain further insight on the phenomenon.