A Finite Volume Method on NURBS Geometries and its Application in Fluid Flow and Isogeometric Fluid-Structure Interaction

Computer-aided design and numerical analysis have to go hand in hand in the modern development of industrial components. Unfortunately, both mathematical disciplines use different representations of geometry, which requires an expensive and error-prone conversion step. This thesis aims at removing this bottleneck in the framework of the finite volume method by adopting the geometry description of computer-aided design in the form of non-uniform rational B-splines. Based on the incompressible Navier-Stokes equations, the main steps of the discretization are presented. Since the computational grid is inherently defined by the spline parameterization, a mesh generation step can be omitted. Furthermore, curved boundaries can be resolved exactly at the coarsest level of discretization. As real-life applications mostly require geometries involving several spline patches, we extend our approach to this case by means of domain decomposition techniques. Moreover, the resulting fluid solver is combined with a structural solver based on isogeometric finite elements in a partitioned coupling algorithm for fluid-structure interaction. It can be shown that a gap-free and non-overlapping interface can be guaranteed even in the case of non-matching grids. Numerical examples underline the benefits of the presented approach.