Das SimTech Industrial Consortium e.V. (IC SimTech e.V.) verleiht Timo Koch einen mit 500 EUR dotierten Preis für seine exzellente Dissertationsschrift. Timo Koch war bis August 2020 akademischer Mitarbeiter am Institut für Wasser- und Umweltsystemmodellierung und Mitglied im SFB 1313 (Task Force "Software and Data"). Im Februar 2020 verteidigte er erfolgreich seine Dissertation "Mixed-dimension embedded models for flow and transport processes in porous media with embedded tubular network systems". Der Preis wird ihm am 17. Februar 2021 im Rahmen der Mitgliederversammlung des IC SimTech überreicht.
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.
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