From January till March I traveled to Belgium to collaborate with Prof. Dr. Iuliu Sorin Pop at the Hasselt University. One of the main research interest of Sorin Pop is the upscaling in porous media, using homogenization and asymptotic expansions. We therefore planned to upscale the phase field model I developed in the scope of Project C02. This model includes two fluid phases and a solid phase. The solid phase consists of ions which can be dissolved in the fluid, and vice versa dissolved ions can precipitate to form solid mineral.
After arriving at Hasselt University I had the opportunity to give a 60 min Seminar for the Computational Mathematics Group about my research thus far. This brought everyone up to date and resulted in a nice discussion. I decided to try upscaling in the simplified geometry of a thin strip, as there had been a recent publication in Sorins group about upscaling of two-phase flow in a thin strip. We managed to adapt many previously used techniques, such that they can be applied in the context of a phase field model. The resulting analysis shows asymptotic consistency of the upscaling process and the sharp interface limit under mild geometric assumptions. Further work includes the numerical investigation of this upscaling result.
While Hasselt is rather small, it has a beautiful historic center. Besides work, I took a climbing course offered by Hasselt University. Unfortunately my stay in Hasselt, originally planned until April, had to be cut short due to the COVID-19 pandemic. Nevertheless collaboration with Sorin Pop continues. There are already plans for another stay in Hasselt and a double degree with Hasselt University.