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

Research output: Contribution to journalArticle


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.


  • Axel Klar
  • Philip Reuterswärd
  • Mohammed Seaid
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Control Engineering


  • Fokker-Planck equations, Computational engineering, Fiber dynamics, Semi-Lagrangian method
Original languageEnglish
Pages (from-to)349-367
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 2009
Publication categoryResearch