Maximilian Hörl, SFB 1313 doctoral researcher at the Institute of Applied Analysis and Numerical Simulation (IANS), was honored with the Bürkert University Prize for Final Theses during the annual celebration (Jahresfeier) of the University of Stuttgart. The award recognizes the exceptional quality and innovation demonstrated in his master’s thesis, titled "Flow in Porous Media with Fractures of Varying Aperture," which was supervised by SFB 1313 project leader Christian Rohde.
Abstract of the master's thesis
We study the flow of a single-phase fluid in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. First, for Darcy flow with possibly discontinuous permeability, wellposedness is shown and a regularity result is derived by establishing equivalence between different weak formulations. Then, for an isolated fracture, we follow a domain decomposition approach into bulk and fracture subdomains and show the equivalence of the domain-decomposed flow problem to the corresponding single-domain problem on the overall domain. Proceeding from the domain-decomposed flow problem, we derive a new mixed-dimensional interface model, where fractures are represented by (n-1)-dimensional interfaces between n-dimensional subdomains for n ≥ 2. In particular, we suggest a generalization of a previous model (Martin, Jaffré & Roberts 2005) by accounting for asymmetric fractures with spatially varying aperture. Besides, a weak version of the Leibniz rule for the differentiation of parameter integrals, which is central for the derivation of the model, is formulated and proven. In addition, a proof of the wellposedness of the new interface model under appropriate conditions is given. We expect that the new model is particularly convenient for the description of curvilinear or winding fractures, for fractures with aperture fluctuations, or for modeling surface roughness. Further, we introduce three simplified variants of the new interface model which incorporate less information about the varying fracture aperture. Then, interior penalty discontinuous Galerkin discretizations are formulated for the different variants of the reduced model and for a full-dimensional reference model. Moreover, we perform two- and three-dimensional numerical experiments in order to validate the new model and explore its capabilities. In simulations with sinusoidal fractures, we examine the model error as a function of the mean aperture for the new reduced model and its variants. Besides, we investigate the effect of surface roughness in simulations featuring random fractures with Gaussian aperture.