Hierarchy of mathematical models for production processes of technical textiles

Source abstract

Abstract In this work we present a hierarchy of mathematical models for the numerical simulation of the production process of technical textiles. The models range from highly complex three‐dimensional fluid‐solid interactions to one‐dimensional fiber dynamics with stochastic aerodynamic drag and further to efficiently manageable stochastic surrogate models for fiber lay‐down. They are theoretically and numerically analyzed and coupled via asymptotic analysis, similarity estimates, and parameter identification. The model hierarchy is applicable to a wide range of industrially relevant production processes and enables the optimization, control, and design of technical textiles.