Fimod: Fiber Dynamics Modeling

Project Topic

Mathematical modeling and simulation of fiber dynamics in air flows.

Project Description

Modeling and simulation of fiber dynamics in air flows is a central topic of the department "Transport Processes" at ITWM. In this field ITWM works mainly on the simulation based design and optimization of production processes for nonwovens and yarns. The necessary mathematical foundation of these activities is developed in cooperation with "Technomathematics Group, Department of Mathematics". The project FIMOD extends this cooperation with focus on the following topics:

• Modeling of fiber dynamics in turbulent flows
• Asymptotical analysis for the derivation of 1d fiber equations from 3d continuum mechanical models
• Appropriate numerics for 1d fiber equations
• Analysis of visco-elastic fiber equations
• Stochastical modeling of fiber deposition with respect to the production process of nonwovens

Project Members

Project Chair

• Dr. Raimund Wegener, Head of Sect. Transport Processes, Fraunhofer Institute for Industrial Mathematics (ITWM)

Participating Research Groups

• Sect. Transport Processes, Fraunhofer Institute for Industrial Mathematics (ITWM)
• Technomathematics Group, Department of Mathematics

Scientific Personnel

• Dr. Raimund Wegener (Fraunhofer Institute for Industrial Mathematics (ITWM))
• Dr. Dietmar Hietel (Fraunhofer Institute for Industrial Mathematics (ITWM))
• Dr. Robert Feßler (Fraunhofer Institute for Industrial Mathematics (ITWM))
• Dr. Marco Günther (Fraunhofer Institute for Industrial Mathematics (ITWM))
• Prof. Dr. Axel Klar (Technomathematics Group)
• Dr. Nicole Marheineke (Technomathematics Group)
• Dr. Thomas Götz (Technomathematics Group)
• PhD students
• Undergraduate students

External Cooperation

• Prof. Dr. Andreas Unterreiter (TU Berlin)

Project Events and Achievements

• Project start date: November 1st, 2005
• Project end date: December 31st, 2007

Project Publications

Numerical evidence for the non-existence of solutions of the equations describing rotational fiber spinning

T. Götz, Axel Klar, Andreas Unterreiter, Raimund Wegener. Technical Report, Berichte des Fraunhofer ITWM, Nr. 108, 2007

Systematic Derivation of an Asymptotic Model for the Dynamics of Curved Viscous Fibers

S. Panda, N. Marheineke, Raimund Wegener. In: Mathematical Methods in the Applied Sciences. 2007

Hydrodynamic Limit of the Fokker-Planck Equation Describing Fiber Lay-down Processes

L. L. Bonilla, T. Götz, Axel Klar, N. Marheineke, Raimund Wegener. In: SIAM Journal on Applied Mathematics. 2007

Dynamics of Curved Viscous Fibers

S. Panda, N. Marheineke, Raimund Wegener. In: Progress in Industrial Mathematics at ECMI 2006. Springer, 2007

Dynamics of Curved Viscous Fibers with Surface Tension

N. Marheineke, Raimund Wegener. Technical Report, In: Berichte des Fraunhofer ITWM. Volume 115, Fraunhofer ITWM, 2007

A Stochastic Model and Associated Fokker-Planck Equation for the Fiber Lay-down Process in Nonwoven Production Processes

T. Götz, Axel Klar, N. Marheineke, Raimund Wegener. In: SIAM Journal on Applied Mathematics. Volume 67, Number 6, P. 1707--1717, 2007

Fiber Dynamics in Turbulent Flows: Specific Taylor Drag

N. Marheineke, Raimund Wegener. In: SIAM Journal on Applied Mathematics. Volume 68, Number 1, P. 1--23, 2007

Fiber Dynamics in Turbulent Flows: General Modeling Framework

N. Marheineke, Raimund Wegener. In: SIAM Journal on Applied Mathematics. Volume 66, Number 5, P. 1703--1726, March, 2006

Mathematical Force Concept for the One-Way-Coupling of Dynamic Fibers and Turbulent Flows

N. Marheineke, Raimund Wegener. In: Proc. Appl. Math. Mech. 6. Wiley, Submitted, 2006

Slender Body Theory for the Dynamics of Curved Viscous Fibers

S. Panda, N. Marheineke, Raimund Wegener. Technical Report, Berichte des Fraunhofer ITWM, Nr. 86, 2006