# Numerical fluid-structure-coupling schemes for high-frequent surface waves

### Contents of this document:

### Team

Project Managers: | |

Prof. Dr. Wolfgang Dahmen | dahmen@igpm.rwth-aachen.de |

Prof. Dr. Siegfried Müller | mueller@igpm.rwth-aachen.de |

Scientific Staff : | |

Dr. Giulia Deolmi | deolmi@igpm.rwth-aachen.de |

### Description of the Project

The primary objective of the project is the development of numerical coupling tools that allow for the simulation of the interaction between the fluid and the surface of an airplane wing, where the turbulent boundary layer is influenced in order to reduce drag. Such micro-scale mechanisms are to be realized by high-frequent transversal surface waves or riblet surface structures.The scientific focus of the project is thus the formulation of coupling conditions between the turbulent flow field and the high-frequently actuated surface or micro-scale structures, where the non-stationary geometry can no longer directly be resolved by a discretization. Therefore homogenization techniques or multiscale modeling techniques have to be developed that model the influence of the micro-scale surface structure/actuation of a turbulent flow field by effective boundary conditions applied to a virtually smooth wall. On the other hand, the turbulent scales can also not be directly resolved. For this purpose, the turbulent flow field is to be modeled by the Variational Multiscale Method. Thus two upscaling approaches have to be coupled, to account for the the tremendous range of physically relevant scales.

By means of such effective boundary conditions the flow field and the structure are to be coupled. In order to avoid the development of a monolithic solver for the coupled problem, available efficient solvers for the flow and the structure, respectively, are to be applied in an alternating way that allow for (i) a correct synchronization of the flow solver and the structural solver, (ii) the fulfillment of consistency properties such as the geometric conservation law and (iii) the correct balance of the energy at the material interface. This is essential to guarantee high accuracy at long integration times.

### Working Plan

The primary tasks of the project are:

**Effective boundary conditions:**

For a flat plate a multiscale modeling approach is to be developed for a virtually smooth wall that provides effective boundary conditions and thus modeling the influence of micro-structures or micro-waves at the surface on a turbulent flow field. For the relevant range of Reynolds numbers this has not yet been investigated.-
**Time and space adaptive discretizations:**

For the discretization of the homogenized surface a variational multiscale method has to be combined with duality concepts that allow for a goal-oriented computation of flow functionals, e.g. drag, that maintains the relevant physical parameters. **Validation:**

The homogenization concepts and discretization concepts are to be validated by means of an oscillating or a structured flat plate with and without pressure gradient.**Coupling strategies:**

On the basis of the effective boundary conditions, coupling strategies for the fluid-structure interaction problem are to be developed that, in particular, allow for a correct energy balance at the material interface.

### Publications

Frank Bramkamp, Philipp Lamby, Siegfried Müller, An adaptive multiscale finite volume solver for unsteady and steady flow computations, J. Comp. Phys, 197, No.2, 460-490 (2004). preprint: Report No. 235, 2003, IGPM, RWTH Aachen.W. Dahmen, Th. Gotzen, Siegfried Müller, R. Schäfer, Adaptive multiresolution finite volume discretization of the Variational Multiscale Method. General Framework, Report No. 332, 2011, IGPM, RWTH Aachen.