Many natural and man-made structures are thin-walled - from the valves in our bodies to the wings of a bird to textile architecture. Most of these thin-walled structures are lightweight, which is advantageous in order to save resources and energy, and they are easily deformable. As with bluff bodies the structure influences the flow around it. However, thin-walled structures usually are influenced by the flow in return and often, this passive adaptation is even part of the design. Comparable to this, bluff bodies are moved or morphed to cause a change in the flow, such as the blades of a wind turbine.
Numerical simulations of the flow interaction can help to predict a structures behavior, to understand where a problem may come from, to understand what other problems might be caused by it, and finally to find the optimal structure or strategy. Where body-conforming approaches would fail or require frequent re-meshing because of large displacements of the structure or even topology changes, non-conforming fixed-mesh approaches, like the Embedded Boundary Method (EBM), can be employed.
The aim here is to further develop an EBM Finite Element formulation for robust and efficient fluid simulations and FSI studies of moving, highly flexible or morphing structures.
Using the Embedded Boundary Method (EBM), the Finite Element (FE) fluid mesh is not fitted to the structure and conforming, instead the structure gets integrated into the existing fluid mesh. Fluid elements which are intersected by the embedded structural geometry are split, the fluid volume gets integrated and boundary terms are applied. In case thin-walled structures are embedded, such as membranes, a discontinuous shape function space (see Fig. 1-2).
EBM inherently handles geometrical changes without the need for remeshing, as even ill-defined structural geometries can just be “thrown” into the fluid mesh. As a result, the method has a huge potential with regard to (topology) optimization and generative engineering. Additionally, it allows for large displacements and contact with regard to fluid-structure interaction (FSI).
Nevertheless, there are some challenges to the method. Some challenges that have been solved already, that need to be solved, or practices that could be improved, such as the precise geometrical approximation of the structure, enforcing the boundary conditions and the treatment of the interface.