Surrogate-assisted Partitioned Modeling of Fractures in Glacier Ice
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Motivated by observations of lake drainage events through fractures in glacier ice \cite{humbert}, we present a surrogate-assisted, partitioned modelling framework for simulating the coupled problem of fluid flow in high-aspect ratio fractures (length >> aperture) and viscoelastic deformation of glacier ice under short-term stress variations. A deeper understanding of the complex interaction between moving glacier ice and enclosed liquid water is crucial for improving our insight into glacier dynamics and glacier hydrology. The complex behaviour of glacier ice, characterised by its viscoelastic and thus time-dependent properties, poses significant challenges to accurate modelling. Traditional numerical methods can be computationally expensive when dealing with large-scale glacier problems. Additionally, modelling high-aspect ratio fractures in it requires solving for the reaction of the fractures and its interaction with the ice matrix, which adds another layer of complexity to the simulations. The thin geometry of the high-aspect ratio fractures demands a fine mesh resolution, often making simulations computationally infeasible. To address these challenges, we employ the hybrid-dimensional approach as described in the work of \cite{schmidt}, where the fracture is treated as a 2D domain surrounded by ice modelled in 3D. We establish the partitioned simulation in which the ice and fracture models are solved separately, and we use surrogate modelling techniques to approximate ice behaviour. The ice and fracture models are constructed using the open-source Finite Element toolbox FEniCSx, and the open-source coupling library preCICE handles the coupling. The surrogate models are built based on high-fidelity simulations using the open-source Python package BayesValidRox. As the software components used are general-purpose in computational mechanics, this workflow is flexible and can easily be extended to other applications.
