Recent Advances of Simplex Space-Time Finite Elements For Multi-Physics Problems
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In engineering, multi-physics problems play an important role. A prominent example is fluid-structure interaction (FSI), e.g., the deformation of elastic airplane wings under fluid loading has to be included in the design process in order to maximize the aerodynamic performance. Also in other engineering areas one can find further examples: the blood flow through flexible arteries or multiphase flow occuring in industrial applications such as sealing rings in internal combustion engines, electrolysis, foam casting, and many others. In the presented work, the different multi-physics problems are solved by time-continuous stabilized space-time finite element methods. Building on previous studies on time-dependent flow problems [1], the time-continuous simplex finite elements (C-SST) are applied on the fluid side, using an unstructured triangulation of the space-time domain. In the case of FSI and free-surface flows, a boundary-conforming approach is applied by deforming the C-SST mesh according to the moving interface via a pseudo-elastic approach [2]. Following a partitioned approach, the solver is combined with simplified models on the solid side, i.e., rigid-body or beam models, to obtain an FSI solver. Furthermore, multi-phase flows are investigated by combining simplex space-time finite elements with the level-set methods. The numerical approaches are presented along with numerical results to underline their potential.
