  Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within
Computer-Aided Design (CAD) tools to represent geometric objects. When using
isogeometric analysis (IGA), it is possible to use such NURBS geometries for
numerical analysis directly. Analyzing fluid flows, however, requires complex
three-dimensional geometries to represent flow domains. Defining a
parametrization of such volumetric domains using NURBS can be challenging and
is still an ongoing topic in the IGA community. With the recently developed
NURBS-enhanced finite element method (NEFEM), the favorable geometric
characteristics of NURBS are used within a standard finite element method. This
is achieved by enhancing the elements touching the boundary by using the NURBS
geometry itself. In the current work, a new variation of NEFEM is introduced,
which is suitable for three-dimensional space-time finite element formulations.
The proposed method makes use of a new mapping which results in a non-Cartesian
formulation suitable for fluid-structure interaction (FSI). This is
demonstrated by combining the method with an IGA formulation in a
strongly-coupled partitioned framework for solving FSI problems. The framework
yields a fully spline-based representation of the fluid-structure interface
through a single NURBS. The coupling conditions at the fluid-structure
interface are enforced through a Robin-Neumann type coupling scheme. This
scheme is particularly useful when considering incompressible fluids in fully
Dirichlet-bounded and curved problems, as it satisfies the incompressibility
constraint on the fluid for each step within the coupling procedure. The
accuracy and performance of the introduced spline-based space-time finite
element approach and its use within the proposed coupled FSI framework are
demonstrated using a series of two- and three-dimensional benchmark problems.
