Title: Unsaturated poromechanics: Modeling, analysis, and numerical solution
Abstract:Flow in deformable porous media is highly relevant in many applications, ranging from subsurface to biomedical applications. In a broader sense, mathematically such processes are commonly described by coupling equations for linear elasticity and flow in porous media. In this talk, we discuss the particular case of unsaturated flow in deformable media. The resulting poromechanics model is nonlinear and strongly coupled. In comparison to many other previously studied poromechanics models, the off-diagonal coupling terms are non-linear and in a certain sense not compatible, resulting in challenges when it comes to the analysis. We discuss both the existence of weak solutions as well as its numerical approximation, and efficient and robust solution using iterative coupling schemes.