A semi-Lagrangian method for a Fokker-Planck equation describing fiber dynamics

Klar, A.; Reuterswärd, P.; Seaid, M.

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.

Citation

Klar, A., Reuterswärd, P., & Seaid, M. (2009). A semi-Lagrangian method for a Fokker-Planck equation describing fiber dynamics. Journal of Scientific Computing, 38(3), 349-367. https://doi.org/10.1007/s10915-008-9244-2

• Journal Article Type: Article
• Publication Date: Mar 1, 2009
• Deposit Date: Oct 20, 2009
• Journal: Journal of Scientific Computing
• Print ISSN: 0885-7474
• Electronic ISSN: 1573-7691
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 3
• Pages: 349-367
• DOI: https://doi.org/10.1007/s10915-008-9244-2
• Keywords: Fiber dynamics, Fokker-Planck equations, Semi-Lagrangian method, Computational engineering.
• Public URL: https://durham-repository.worktribe.com/output/1547382