Flow morphology and patterns in porous media convection: A persistent homology analysis

TL;DR

This paper applies persistent homology, a topological data analysis technique, to quantify and analyze complex flow patterns in porous media convection, providing new insights into flow structures and heat transport behavior.

Contribution

It introduces the use of persistent homology to objectively quantify flow patterns in porous media convection, linking topological measures with macroscopic heat transport properties.

Findings

Persistent homology measures correlate with Nusselt number.

Flow patterns evolve systematically with Rayleigh-Darcy number.

Public datasets of simulations are provided for further research.

Abstract

Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to contaminant transport in groundwater. Key processes are affected by convective heat transport or diffusion of chemical species in porous formations. Intense convection flow and mixing create complex, dynamic patterns that are difficult to predict and measure. The present work focuses on the use of topological data analysis, in particular, the measures emerging from the growing field of persistent homology (PH), to quantify these patterns. These measures are objective and quantify structures across all temperature or concentration values simultaneously. These techniques, when applied to classical porous media setups, such as one-sided and Rayleigh-B\'enard flow configurations, provide new insights into the system's structure, flow patterns, and macroscopic mixing properties. Using large datasets we make publicly available, comprising original simulations as well as those presented in previous works, we correlate the behaviour of the heat transport rate (quantified by the Nusselt number) with the evolution of the flow structures (quantified by the PH measures). Finally, we provide a detailed analysis of the flow evolution over a wide range of governing parameters, namely the Rayleigh-Darcy number and the domain size.