1. OPUS
2. Universität Stuttgart
3. 08 Fakultät Mathematik und Physik

Autor(en):	Burbulla, Samuel
Titel:	Mixed-dimensional modeling of flow in porous media
Erscheinungsdatum:	2023
Dokumentart:	Dissertation
Seiten:	iv, 160
URI:	http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-127310 http://elib.uni-stuttgart.de/handle/11682/12731 http://dx.doi.org/10.18419/opus-12712
Zusammenfassung:	Modeling flow in dynamically fracturing porous media is of high interest for a wide range of natural and technical applications, for instance, geothermal energy production or carbon capture and storage. In this work, we present new mixed-dimensional models for flow in porous media including fractures with time- and space-dependent geometries. The models are implemented using our new grid implementation Dune-MMesh which is tailored for the discretization of mixed-dimensional partial differential equations with fully conforming interface of codimension one. First, we propose a mixed-dimensional model for capillarity-free two-phase flow in dynamically fracturing porous media. The model is discretized by a fully conforming finite-volume moving-mesh algorithm that explicitly tracks the fracture geometry. Further, generalizing an earlier model for single-phase flow in fractured porous media, we derive a dimensionally reduced model including spatially varying apertures. In several numerical examples, using a mixed-dimensional discontinuous Galerkin discretization, the model demonstrates significant improvements for curvilinear fracture geometries. Finally, we propose a mixed-dimensional phase-field model for fracture propagation in poro-elastic media combining discrete fracture and phase-field modeling approaches. The corresponding discontinuous Galerkin discretization tracks the fracture geometry by adding facets to the fracture triangulation according to the phase-field indicator and is validated with results known from literature.
Enthalten in den Sammlungen:	08 Fakultät Mathematik und Physik

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