Numerical fluid-structure coupling schemes for high-frequency surface motion

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The central objective of this project is the numerical simulation of effects on the macroscale that are caused by surface structures (riblets) and/or surface actuation by transversal waves in the spanwise direction on a compressible turbulent flow to predict the local skin friction distribution. Since for the flow regime of interest neither the surface structures nor the actuation frequency can be resolved directly by a discretization of the total computational domain we wish to develop upscaling methods based on homogenization or multiscale modelling. These methods are to be used to transfer those riblet structures and actuation parameters that indeed reduce friction drag into boundary formulations that make macroscopic analyses possible. A central contribution during the first funding period was the development of an appropriate framework for a perturbation analysis that, in contrast to the known methods applies to the relevant geometric and turbulent length scales. A pivotal role is played by the identification of suitable cell problems on the microscale whose solution is used to formulate new effective boundary conditions on the macroscale. While these concepts are formulated in the most transparent way for laminar flows they carry over to turbulent regimes when using appropriate turbulence models which can always be interpreted as regularized Navier Stokes equations. In view of the envisaged relevant geometric and turbulent length scales we believe that, beyond low parameter turbulence models, projection models such as the Variational Multiscale Method are ultimately best suited to correctly capture the interaction of flow and geometric structure/actuation. In the first funding period, the focus was on the development of an upscaling strategy for steady state problems. In addition to the further development of the concepts for turbulent regimes their extension to unsteady problems is the central goal in the second funding period.