CC BY 4.0Ettmüller, ManuelManuelEttmüller2025-02-272025-02-272025978-3-8396-2070-0https://doi.org/10.24406/publica-3870https://publica.fraunhofer.de/handle/publica/47955810.24406/publica-3870This thesis addresses the modeling and simulation of physical processes in the context of the production of technical textiles. The process of fiber melt spinning presents a significant challenge from a mathematical and modeling perspective, given its inherent complexity. The thesis focuses on semi-crystalline polymers, where the degree of crystallization is a critical factor. Considering a viscoelastic two-phase fiber model class, asymptotically justified boundary conditions are derived, preventing the occurrence of artificial boundary layers. In the context of a viscoelastic model hierarchy, several dimensionally reduced fiber models are analyzed and compared with respect to their performance and application regime, with a particular focus on a novel stress-averaged one-two-dimensional model. For the efficient numerical solution of the boundary value problems of ordinary and partial differential equations resulting from the fiber models, suitable problem-specific solution algorithms are developed. The capabilities of the model-simulation framework are demonstrated by investigating an industrial spinning scenario with hundreds of fibers, incorporating two-way coupled fiber-air interaction.enMathematical modelingBoundary value problemsPerturbed ordinary differential equationsFiber melt spinningModel Hierarchy500 Naturwissenschaften und Mathematik::510 Mathematik::519 Wahrscheinlichkeiten, angewandte Mathematikdoctoral thesis