A study of fluid-structure interaction on overlapping grids with a focus on flexible beams
Fluid-structure interaction problems appear in many areas of science and engineering. Adequately understanding these problems is crucial to the study of such disciplines as aeroelastic flutter, wind turbine performance, implosions and explosions, and hemodynamics, to name a few. One technique to explore these problems is the use of numerical simulations. Although methods for the accurate and efficient numerical simulation of many problems involving only flexible structures or those involving only fluids have existed for a long time, the simulation of coupled problems, in which a flexible structure (or structures) interact with fluids remains challenging. The source of the difficulty with these problems is the construction of schemes for the coupling between the fluid and the solid that are both accurate and stable. There are two general approaches to designing a coupling procedure. In the first, the so-called monolithic approach, a single solver is implemented that handles both the fluid equations and the solid equations in a single framework. In this scheme, the solver handles the fluid and solid equations simultaneously, resulting in a strong coupling between the two. The second approach, named the partitioned approach, handles the fluid and structure domains separately. Whereas in the monolithic scheme there is a single solver for both the fluid and the structure, in the partitioned scheme there are separate solvers for the fluid and the structure. This separation heavily restricts the communication and coordination that can occur between the two solvers. Typically the only communication done in these schemes is through the application of boundary conditions (where the fluid applies a boundary condition on the fluid, and the solid one (or more) on the fluid). This makes the implementation of partitioned schemes easy, especially because they can take advantage of existing algorithms and software developed for the simulation of fluid flow or computational mechanics. However, they have a weakness – accuracy and stability are much harder to achieve. Stability is a particular problem for these schemes, as they are prone to the so-called added-mass effect.