International audienc

The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.

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Fracturing and refreezing of sea ice in the Kara sea are investigated using complex network analysis. By going to the dual network, where the fractures are nodes and their intersections links, we gain access to topological features which are easy to measure and hence compare with modeled networks. Resulting network reveal statistical properties of the fracturing process. The dual networks have a broad degree distribution, with a scale-free tail, high clustering and efficiency. The degree-degree correlation profile shows disassortative behavior, indicating preferential growth. This implies that long, dominating fractures appear earlier than shorter fractures, and that the short fractures which are created later tend to connect to the long fractures. The knowledge of the fracturing process is used to construct growing fracture network (GFN) model which provides insight into the generation of fracture networks. The GFN model is primarily based on the observation that fractures in sea ice are likely to end when hitting existing fractures. Based on an investigation of which fractures survive over time, a simple model for refreezing is also added to the GFN model, and the model is analyzed and compared to the real networks.

Desert roses are gypsum crystals that consist of intersecting disks. We determine their geometrical structure using computer assisted tomography. By mapping the geometrical structure onto a graph, the topology of the desert rose is analyzed and compared to a model based on diffusion limited aggregation. By comparing the topology, we find that the model gets a number of the features of the real desert rose right, whereas others do not fit so well.

Lattice Boltzmann methods are presented at an introductory level with a focus on fairly simple simulations that can be used to test and illustrate the model’s capabilities. Two scenarios are presented. The first is a simple laminar flow in a straight channel driven by a pressure gradient (Poiseuille flow). The second is a more complex, including a wedge where Moffatt vortices may be induced if the wedge is deep enough. Simulations of the Poiseuille flow scenario accurately capture the theoretical velocity profile. The experiment shows the location of the fluid-wall boundary and the effects viscosity has on the velocity and convergence time. The numerical capabilities of the lattice Boltzmann model are tested further by simulating the more complex Moffatt vortex scenario. The method reproduces with high accuracy the theoretical predction that Moffat vortices will not form in a wedge if the vertex angle exceeds 146°. Practical issues limitations of the lattice Boltzmann method are discussed. In particular the accuracy of the bounce-back boundary condition is first order dependent on the grid resolution.

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