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

Convective mixing is essential in geophysical and industrial fields, ranging from carbon dioxide sequestration to contaminant transport in groundwater. Key processes are affected by convective heat or chemical species diffusion in porous formations. Intense convection flow and mixing create complex, dynamic patterns that are difficult to predict and measure. Early efforts use Fourier-based analysis and cell sizes to describe these emerging patterns. Topological measures offer efficient and detailed analysis of structures in a scalar field, such as temperature or solute concentration. These methods, grounded in computational topology, have been applied to various systems including materials science, granular matter, Rayleigh-Bénard convection, and systems with different chemical compositions. Persistent-homology-based measures are objective and quantify structures across all temperature or concentration values simultaneously. We utilize these techniques on classical porous media setups, such as Rayleigh-Bénard and one-sided flow configurations. They provide new insights into system structures and link macroscopic mixing properties with flow patterns.