Renewable Energies and Data Science: Solvers for Hybrid Modelling in Porous Media – Design, Implementation, Analysis

We explore solver aspects for PDE- and data-based numerical schemes that provide discretisations for coupled multi-phase flow problems. This includes free-flow/porous-media-flow coupling and coupled porous media domains with two-phase flow hierarchies. The mathematical models are fundamental for large-scale simulations in the context of geothermal energy storage and production as well as other green-energy settings. We aim at the development of a new class of solvers that combine physics- and data-based preconditioning techniques and pursue both concepts based on the monolithic and the partitioned/splitting paradigms. Preconditioners will be tailored to the differential operators in the underlying equations in a block-like fashion or are induced by Schwarz-type domain decomposition methods. We strive for data-driven techniques to act as surrogate models or determine numerical parameters optimizing the performance of the discretisation on the fly. Finally, we aim to underpin our research by rigorous analysis that is challenged by the combination of PDE- and data-based modeling. This project is a joint effort together with Florin Radu from the University of Bergen.