The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options, be dealt with using an interface-tracking approach with the DeformingSpatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A difficult issue that is connected with this type of approach is the determination of a suitable coupling mechanism between the fluid velocity at the boundary and the displacement of the boundary mesh nodes. In order to avoid large mesh distortions, one goal is to keep the nodal movements as small as possible; but of course still compliant with the nopenetration boundary condition. Standard displacement techniques are full velocity, velocity in a specific coordinate direction, and velocity in normal direction. In this work, we investigate how the interfacetracking approach can be combined with isogeometric analysis for the spatial discretization. If NURBS basis functions of sufficient order are used for both the geometry and the solution, both a continuous normal vector as well as the velocity are available on the entire boundary. This circumstance allows the weak imposition of the no-penetration boundary condition. We compare this option with an alternative that relies on strong imposition at discrete points. Furthermore, we examine several coupling methods between the fluid equations, boundary conditions, and equations for the adjustment of interior control point positions.

In this work, we study the application of Model Order Reduction (MOR) to the flow of plastics melt in an extrusion die. The process is described with a non-linear model consisting of the Stokes equations in combination with a shear-thinning material model. The reduction is performed through a Proper Orthogonal Decomposition (POD) approach with subsequent projection. We perform an a-posteriori error analysis for a quantity of interest, based on the full-and reduced-order solutions. Finally, we explore the computational speedup to prove the aptitude of the reduced model in the context of many-query scenarios.

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