Spline-Based Methods for Fluid-Structure Interaction

Computer-aided design uses Non-Uniform Rational B-Splines (NURBS) to represent and communicate geometry. Therefore, a NURBS description of a given design can generally be considered the exact description. The development of isogeometric methods has made this splinebased geometry description available for numerical analysis methods. As a result of the possible combination with plate and shell theory, isogeometric analysis (IGA) is already versatile in structural analysis. In fluid dynamics three-dimensional analysis is usually indispensable. Admittedly, the application of IGA is fundamentally independent of the spatial dimensions. However, it is still very difficult to create volume splines at the moment. Alternatively, classical finite element methods can be extended to take account of the given geometry at least at the limits. An example of these methods is the NURBS-enhanced finite element method (NEFEM).

The thesis presents the solution of fluid-structure interactions using the same spline description at the interface. On the structural side, the spline is used in an isogeometric formulation. On the liquid side, the same spline is used in NEFEM. The dissertation introduces the entire solution methodology of the surface-coupled problem, based on an implicit staggered approach. The use of the identical spline representation on both sides enables a consistent and conservative spatial coupling, whereby an individual discretization on both sides is possible. Existing acceleration techniques for partitioned approaches are discussed in the context of the spline-based method and combined to a modified variant.

The numerical advantages of the presented combination of IGA and NEFEM are verified by simple stationary and transient test cases. A test case with a closed domain with deformable boundaries proves that the proposed combination is able to exceed the accuracy of the coupling of Lagrangian finite elements and IGA. By applying the methodology in a fluid-structure interaction with contact, it is shown that known advantages of IGA on the structural side can be transferred to fluid-structure interaction. The spline-based description not only offers advantages in linking the individual fields. The spline-based boundary description is also advantageous for problems of fluid-structure interaction and free surfaces. Corresponding extensions of the boundary conditions are discussed. The methodology is demonstrated on a three-dimensional test case.