Martin Schneider, Post-Doc at the Institute for Modelling Hydraulic and Environmental Systems (IWS) and member of SimTech and SFB 1313, received "The Best PhD Thesis 2018 Award" (endowed with 1000 euros) of the SimTech Industrial Consortium e.V. for his dissertation "Nonlinear finite volume schemes for complex flow processes and challenging grids". He officially got presented the award in the context of the general meeting of the Industrial Consortium of SimTech on December 6, 2019, where he presented his work. Martin Schneider did his PhD in the framework of the Graduate School of SimTech, funded by the German Research Fondation (DFG).
Numerical simulations play a crucial role in a wide range of geotechnical engineering applications, thus, it is of great importance that the schemes used to produce numerical results are reliable and robust. Additionally, efficient schemes are desirable due to the often very large spatial and temporal scales involved and the uncertain nature of the subsurface, which might require statistical analyses with a large number of model runs to be performed. Appropriate schemes have to be chosen application-dependent subject to the particular requirements. In this work, nonlinear finite-volume schemes are extensively examined, both theoretically and numerically, and compared to well-established linear schemes for several porous media test cases. Furthermore, an abstract discretization framework for elliptic equations, including the proof of convergence for nonlinear schemes, is presented.