During my PhD, I held a 3-month PhD fellowship in the Department of Physics at the University of Torino, where I worked with Prof. Guido Boffetta and the Complex Systems group on the numerical simulation of convective mixing in porous media, a collaboration that became the core of this paper. Visiting Torino allowed me to immerse myself in advanced computational fluid dynamics and to better understand how fundamental fluid-mechanical instabilities manifest in porous structures, a topic at the crossroads of physics, engineering, and environmental science.

The work examines a fluid-dynamic process that is simple in setup yet rich in physics: convective mixing driven by buoyancy in a porous medium with a free interface separating two miscible fluids. This configuration is a canonical model for situations in which a lighter fluid overlies a heavier one, and diffusive transport across the interface gradually alters the density field until an instability develops and vigorous mixing sets in. Such flows are fundamental to many natural and engineered systems, from groundwater contaminant transport and heat transfer in thermal insulation to geological carbon dioxide (CO₂) sequestration, where dense CO₂-rich brine can sink into deeper aquifers.

In this study, we use high-resolution direct numerical simulations of the governing Darcy-scale flow equations to capture the initiation and evolution of convection when miscible fluids interact across a free interface in a porous medium. Our simulations were performed in both two-dimensional (2D) and three-dimensional (3D) geometries to quantify how spatial dimensionality affects plume development, mixing dynamics, and dissolution fluxes.

A key finding is that, although both 2D and 3D simulations display similar qualitative convective behaviours, such as the formation of rising and sinking plumes that promote mixing, their mixing rates and structures differ. Specifically, the 2D setup tends to produce stronger convective fluxes and more rapid interface deformation compared to the 3D case, with dissolution fluxes approximately 15% higher. This highlights the need for caution when applying 2D results to real 3D systems, as dimensional effects can significantly influence outcomes. (Springer)

What made this project particularly rewarding was the opportunity to collaborate across disciplines, blending physical intuition from fluid dynamics with computational techniques and environmental motivation. The fellowship in Torino was not just a change of scenery but a chance to grow as a researcher: to ask deeper questions about why mixing occurs the way it does and how seemingly small modelling choices (such as geometry or dimensionality) can have large consequences for interpretation. The result is more than a paper; it is a window into the multiscale complexity of convective processes that shape many phenomena in science and engineering.

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