Timo Koch, former post-doctoral researcher at the Institute for Modelling Hydraulic and Environmental Systems (IWS) and member of SFB 1313 (Task Force "Software and Data"), received a prize (endowed with 500 euros) from the SimTech Industrial Consortium e.V. (IC SimTech e.V.) for his excellent doctoral thesis. He defended his dissertation "Mixed-dimension embedded models for flow and transport processes in porous media with embedded tubular network systems" in February 2020. The prize will be awarded on 17.02. during the online general meeting of IC SimTech.
Timo Koch accomplished his PhD in the framework of the Graduate School of SimTech, funded by the German Research Fondation (DFG).
Dissertation Abstract
Flow in vascularized biological tissue, root water uptake, or flow around injection or extraction wells can be modeled by coupled mixed-dimensional PDE systems. Conceptually, such systems can be described as porous media with embedded tubular transport networks. We describe numerical methods for the simulation of such systems. The compartments are spatially discretized by non-matching computational grids: a three-dimensional mesh for the porous medium domain, and a geometrically embedded mesh of connected line segments for the network domain. A generalized abstract form of mixed-dimension embedded models is presented which summarizes several existing methods. A particularity of solutions to mixed-dimensional PDEs with dimensional gap two (0D-2D or 1D-3D) is the occurrence of singularities where the network center-lines intersect the porous domain. We introduce a new numerical scheme which removes these singularities by smoothing kernels, and exhibits improved convergence behavior and accuracy for coarse grid resolutions. The method is developed for isotropic, as well as anisotropic porous media. Furthermore, a new mixed-dimension embedded model for tissue perfusion and NMR signal generation is presented. Detailed perfusion simulations on the capillary scale are shown to reproduce image contrast of clinical (organ-scale) MRI data from multiple sclerosis patients. Similar modeling techniques and methods are then used to simulate root water uptake. For the implementation of such applications, a common software framework is developed by use of the open-source simulator \DuMuX The framework allows the implementation of coupled mixed- and equidimensional models in a unified way, using software abstractions. Possible framework applications go beyond the methods presented in this work.