Aumtumn School of the Felix-Klein-Akademie 2023

Group on the Topic »Simulation of Fluid Flows in Porous Media«

Supervisor: Dominik Becker, Department »Flow and Material Simulation«

The simulation of fluid flows in porous media is important in many applications. A prominent example is that of groundwater flow in geology, where it is used to predict water behavior in complex subsurface formations. Simulations are similarly used to better understand and, where necessary, improve the production of batteries and some composite materials. The physical basis of fluid flow is partial differential equations. Many simulation methods discretize the simulation domain. In porous media, this discretization must be fine enough so that all interstitial spaces of interest can be resolved. Now, if a large domain is to be simulated, this leads to long run times and high memory requirements, or the simulation is not possible at all. In this workshop, the team is looking at the Stokes equation. This will be used to simulate fluid flow in a »small« two-dimensional porous medium. We will then look for ways to use the simulation results of the Stokes equation on a small portion of a porous medium to approximate the flow in the entire medium.

Group on »Design and Benchmark of a Hybrid Quantum Algorithm on the Example of Routing Problems«.

Supervisor: Dominik Leib, Department »Optimization«, Fraunhofer ITWM

Anyone who studies computers, computer science and computability these days will inevitably have come across one term several times: the quantum computer. These (at least theoretically) extremely powerful machines use quantum physical effects to perform calculations. The hope is that (one day) this will give them an advantage over conventional computers. Such a quantum machine is the quantum annealer. It is a special quantum computer for solving combinatorial optimization problems and one of the first to be commercialized. It was built by the company D-Wave. We would like to control this computer and apply it to a certain class of problems.

Group on »Finding Cracks in Concrete: How Good Do the Images Have to Be?«

Supervisors: Christian Jung and Tin Barisin, AG Statistik, Department »Mathematics«, RPTU Kaiserslautern-Landau and Anna Nowacka, Department »Image Processing«, Fraunhofer ITWM.

Concrete is a brittle material, cracks are normal and occur in large quantities. The formation and propagation of crack structures in concrete specimens provides information about the material properties of the concrete mix under investigation and is tested in standardized tests. The complex crack structures can be imaged with the aid of computed tomography (CT). A prerequisite for the analysis of the cracks using the reconstructed CT images is the segmentation of the cracks in the gray scale image. In this project, we investigate different methods for segmenting cracks in 2D image data – one from machine learning and one from classical image processing. In each case, the basis is images of concrete with (synthetic) cracks and their ground truths. The goal of the project is to investigate the robustness and goodness of the methods with respect to varying degrees of noise and the selection of training data.

At the end of the project, answers to the following questions in particular should be found:

• How does the performance of the methods change with different degrees of noise in the images?
• Can the performance be influenced by the type of training data?
• Can the methods also be applied without problems to image data containing other types of concrete and cracks?