Efficient numerical methods for non-equilibrium models for flow and reactive transport in complex media

Flows and reactive transport in porous media are encountered in many societally relevant applications, such as oil recovery, CO2 sequestration, geothermal energy, building materials, or biosystems. Typically, such processes occur at different scales, involving complex media with hierarchically-organized structures. This project is devoted to the derivation of reliable mathematical models, and the development of accurate discretization methods, providing mass conservative results, and having guaranteed convergence rates. The work will addressed explicitly non-equilibrium effects like dynamic capillarity and hysteresis, as encountered in one- and two-phase porous media flows, and the impact of chemical processes on the medium properties.