2025/12/26 by Marco De Paoli, De Paoli, Marco, Sergio Pirozzoli +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph) #Slime Mold and Myxomycetes Research #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2512.21958
openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to geothermal energy extraction. 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-Bénard 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.