Project R-15608

AdaptPMod: Model adaptivity in the numerical simulation of porous media flows (Research)

Porous media flows appear in many fields of the highest societal relevance: geothermal energy, geological CO2 sequestration, groundwater and soil contamination, oil recovery, or in biological systems like flow through tissues. For such situations, experiments are very limited or even impossible. Therefore, the key tools in understanding such systems are mathematical modeling, analysis, and numerical simulations. Being inexpensive and with minimal environmental impact, they provide valuable information to support the decisions taken for example for the optimal management of geological resources. Commonly used mathematical models for porous media flows rely on so-called equilibrium assumptions, in which the constitutive relationships between different quantities of primary interest are assumed algebraic (a given function). In real-life systems, this is a severe limitation, as dynamics and hysteresis are completely disregarded. Moreover, several experimental results have invalidated such modeling approaches in certain flow regimes, and demonstrated the need to account for the dynamics in various regimes. The aim of this project is the development of efficient numerical algorithms for porous media flows, relying on rigorous mathematical and numerical analysis. The choice of the appropriate model is made automatically during simulation, at all discrete times and in all spatial sub-domains. Non-equilibrium effects will be included automatically when and where these are relevant.

01 January 2025 - 31 December 2028