A Semi-Lagrangian Method for a Fokker-Planck Equation Describing Fiber Dynamics

Authors:
Axel Klar;Philip Reuterswärd;Mohammed Seaïd
Affiliations:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany 67663 and Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany 67663;Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany 67663;School of Engineering, University of Durham, Durham, UK DH1 3LE
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

A simplified Fokker-Planck model for the lay-down of fibers on a conveyor belt in the production process of nonwovens is investigated. It takes into account the motion of the fiber under the influence of turbulence. The emphasis in this paper is on the development of a numerical procedure to solve the model. We present a semi-Lagrangian scheme that accurately captures the fiber dynamics and conserves the mass. The scheme allows large time steps to be taken in numerical simulations and requires moderate computing times to obtain steady state solutions. Numerical results and examples are presented and compared for several selection of fiber parameters. The obtained results show that the semi-Lagrangian method is able to reproduce accurately the time development of functionals of the process that are important for the quality assessment of industrial fibers.