Renewable energies and Data Science: Solvers for hybrid modelling in porous media – design, implementation, analysis

We investigate solver aspects for PDE and data-based numerical schemes that provide discretizations for coupled multiphase 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 to develop a new class of solvers that combine physics- and data-based preconditioning techniques and their parallel implementation. We are pursuing both solver concepts based on the monolithic and partitioned paradigms. Preconditioners are tailored to the differential operators in the underlying equations in a block-like fashion, or are induced by Schwarz-type domain decomposition methods. Machine learning and other data-driven techniques could be used to act as surrogate models or to determine numerical parameters that optimize the performance of the discretization and solvers on the fly.

The project has been initiated to strengthen the collaboration between SimTech and the Porous Media Group at the University of Bergen and to gain expertise from the application problems pursued there. This is part of a larger alliance between the Universities of Stuttgart and Bergen.