Speaker
Description
In this presentation, we address the application of variational methods to partial differential equation (PDE) systems, particularly within the context of geological phenomena. Our work leverages the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework and its variants, such as damped Hamiltonian or extended gradient systems, to describe porosity waves processes. The description of porosity waves is characterized by fluid-filled pressure waves that propagate through porous media due to localized variations in porosity and permeability. The presentation also outlines the mathematical analysis that supports these models. The focus is on ensuring well-posedness and structure-preservation. By integrating the principles of GENERIC, we ensure that the models respect key physical constraints, such as energy conservation and entropy production, while remaining adaptable to diverse geological scenarios. This is a joint work with Dirk Peschka (WIAS Berlin) and Marita Thomas (WIAS and FU Berlin) within the project C09 "Dynamics of rock dehydration on multiple scales" of the CRC 1114 "Scaling Cascades in Complex Systems".
