Date15. 9. 201
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This cumulative dissertation presents a complete model for simulating smoke usingpolygonal vortex filaments. Based on a Hamiltonian system for the dynamics ofsmooth vortex filaments, we develop an effcient and robust algorithm that allowssimulations in real time. The discrete smoke ring ow allows to use coarse polygonalvortex filaments, while preserving the qualitative behavior of the smooth system. Themethod handles rigidly moving obstacles as boundary conditions and simulates vortexshedding. Obstacles as well as shed vorticity are also represented as polygonal filaments.Variational vortex reconnection prevents the exponential increase of filamentlength over time, without significant modification of the uid velocity field. Thisallows for simulations over extended periods of time. The algorithm reproduces variousreal experiments (colliding vortex rings, wakes) that are challenging for classicalmethods.