Stefanie Elgeti

Stefanie Elgeti, Henning Sauerland

Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface capturing context, the level-set method, the volume-of-fluid method, particle methods, as well as the phase-field method. The history of each method is presented in combination with the most recent developments in the field. Particularly, the topics of extended finite elements (XFEM) and NURBS-based methods, such as Isogeometric Analysis (IGA), are addressed. For illustration purposes, two applications have been chosen: two-phase flow involving drops or bubbles and sloshing tanks. The challenges of these applications, such as the geometrically correct representation of the free surface or the incorporation of surface tension forces, are discussed.

Clemens Fricke, Daniel Wolff, Marco Kemmerling et al.

Profile extrusion is a continuous production process for manufacturing plastic profiles from molten polymer. Especially interesting is the design of the die, through which the melt is pressed to attain the desired shape. However, due to an inhomogeneous velocity distribution at the die exit or residual stresses inside the extrudate, the final shape of the manufactured part often deviates from the desired one. To avoid these deviations, the shape of the die can be computationally optimized, which has already been investigated in the literature using classical optimization approaches. A new approach in the field of shape optimization is the utilization of Reinforcement Learning (RL) as a learning-based optimization algorithm. RL is based on trial-and-error interactions of an agent with an environment. For each action, the agent is rewarded and informed about the subsequent state of the environment. While not necessarily superior to classical, e.g., gradient-based or evolutionary, optimization algorithms for one single problem, RL techniques are expected to perform especially well when similar optimization tasks are repeated since the agent learns a more general strategy for generating optimal shapes instead of concentrating on just one single problem. In this work, we investigate this approach by applying it to two 2D test cases. The flow-channel geometry can be modified by the RL agent using so-called Free-Form Deformation, a method where the computational mesh is embedded into a transformation spline, which is then manipulated based on the control-point positions. In particular, we investigate the impact of utilizing different agents on the training progress and the potential of wall time saving by utilizing multiple environments during training.

Steffen Tillmann, Felipe A. González, Stefanie Elgeti

Purpose: In fused deposition modeling (FDM), the nozzle plays a critical role in enabling high printing speeds while maintaining precision. Despite its importance, most applications still rely on standard nozzle designs. This work investigates the influence of nozzle geometry on pressure loss inside the nozzle, a key factor in high-speed printing performance. Design/methodology/approach: We focus on optimizing the nozzle shape to minimize the pressure loss and establish a framework that allows both simple angle-based optimization and more advanced spline-based parametrization. To model the polymer melt flow, we use a Giesekus model to account for viscoelastic effects. Findings: For angle-based optimization, the pressure-loss objective exhibits two local minima: one associated with smooth flow and another with pronounced recirculation regions inside the nozzle. While the latter yields a lower pressure drop, such flow patterns are generally undesirable due to increased residence times and the associated risk of material degradation and nozzle clogging. The splinebased parametrization results in only marginal additional reductions in pressure loss compared to angle optimization, while decreasing the manufacturability of the nozzle considerably. Originality/value: This paper presents a comparative study of FDM nozzle shape optimization using a Giesekus model. We introduce a flexible optimization framework that accommodates both simple and advanced geometric parametrizations. The main contribution is the systematic comparison between angle- and spline-based parametrizations across materials and extrusion velocities, showing that most of the achievable pressure-loss reduction is already captured by the simpler and more manufacture-ready angle optimization.

Michel Make, Norbert Hosters, Marek Behr et al.

This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such representations are typically available from Computer-Aided-Design tools. Within the NEFEM, the NURBS boundary definition is utilized only for elements that are touching the domain boundaries. The remaining interior of the domain is discretized using standard finite elements. Contrary to isogeometric analysis, no volume splines are necessary. The key technical features of NEFEM will be discussed in detail, followed by a set of numerical examples that are used to compare NEFEM against conventional finite element methods with the focus on compressible flow.