Efficient simulation of flows through complex geometries in the PDE framework peano

Flow through porous media is a much discussed topic in computational science and engineering with a variety of applications ranging from modelling biological tissues and fuel cells, or oil and gas exploration scenarios. In this class of problems, the geometric volume under observation is significantly larger than its underlying geometric structure. One approach to overcoming this issue is to use different models on different scales and to utilize fine-scale data to enhance the coarse-scale solution. From the computational point of view, the challenges on the micro-scale lie in the discretization of the complex geometries and efficient exploitation of today's parallel hardware, such as super-computers. Currently, the PDE framework, Peano, contains several parallelized modules. However, the Navier-Stokes-based flow component, Peano Fluid, is still sequential. In this thesis, I extend Peano Fluid---based on adaptive Cartesian grids in combination with the Peano space-filling curve and a low-order FEM discretization-to a highly parallel flow solver for complex geometries. In particular, I optimize the geometry handling for high numbers of geometric elements as they are common in porous media setups, and make the code highly portable, such that it can be executed on various state-of-the-art parallel systems. For the creation of benchmark geometries, I introduce ScenGen: a modular tool, which supports the creation of various complex porous media and molecular dynamics settings. The parallel performance of my modified flow solver is as fast as state-of-the-art solvers such as those realized in frameworks such as DUNE, Sundance or OpenFOAM. My focus lies on low memory requirements and geometry discretization as well as high parallel performance, where my solver is more efficient than other approaches. An additional innovation is that Peano Fluid also supports parallel adaptive mesh refinement. Various benchmark simulations show good scalability behavior. Using my new tools, I make the micro-scale results available as input data of macro-scale solvers by transforming the steady-state flow solutions into permeability data. Altogether, I deliver a powerful set of tools ready for simulation of flows through porous media and with broad potential for application in other fields of CFD.