Variational multiscale method in large eddy simulations of turbulent flows for fluid-structure interaction

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The inclusion of turbulence effects is absolutely mandatory for many fluid-structure-interaction problems of engineering interest. Nowadays Large Eddy Simulation seems to be the only reasonable approach for treating these turbulence effects for a wide class of problems and in a computationally acceptable way. A newly developed three-level finite element method will be employed and upgraded to serve as basement for the Variational Multiscale Method/Large Eddy Simulation approach that will be developed and studied within this project. The three levels stand for the resolved coarse scales, the resolved small scales and the unresolved small scales, respectively, where the first level is approximated in a standard FE sense, the second level is resolved in a residual free bubble manner and the third level is used for the determination of a subgrid viscosity. After intensive studies of this basic approach the main focus of the project will be on global-local strategies for the small scale equations, the analysis and adaption of scale spaces and subgrid-models and on the embedding of this multiscale strategy in overall solution approaches. The second project period will concentrate on the extension to time-dependent domains and on the incorporation into our three-field fluid structure interaction solver. This will be a major step in the treatment of problem classes of utmost engineering interest, like aerodynamical problems of wind-excited thin-walled structures, vortex shedding of flexible bodies and some biomechanical problems.