Hierarchy of mathematical models for production processes of technical textiles

The authors 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.