Feinstrukturmodellierung und effiziente Finite-Elemente-Simulationen von Fasersuspensionen

• Antragsteller: Professor Dr. Dmitri Kuzmin; Professor Dr. Stefan Turek
• Fachliche Zuordnung: Strömungsmechanik
• Förderung: Förderung von 2014 bis 2020
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 251122961

• Erstellungsjahr: 2019

Zusammenfassung der Projektergebnisse

In summary, this project has greatly advanced the state of the art in the fields of property-preserving numerical methods for tensorial evolution equations, deconvolution-based closures for orientation tensors, and random walk methods for simulating rotary diffusion effects in Lagrangian models of fiber orientation. The developed closures, numerical methods, and extensions of the FEATFLOW package provide a set of well-analyzed and well-tested tools for simulating fiber suspension flows in a robust and efficient manner. Further work will focus on the development of new physics-compatible finite element methods for the Fokker-Planck equation.

Projektbezogene Publikationen (Auswahl)

• Physics-compatible numerical approximations to the Fokker-Planck model of fiber orientation. MultiMat 2015 conference
  C. Lohmann and D. Kuzmin
  
• Efficient algorithms for constraining orientation tensors in Galerkin methods for the Fokker-Planck equation. Computers & Mathematics with Applications 71 (2016) 1059-1073
  C. Lohmann
  
• Galerkin-Spektralverfahren für die Fokker-Planck-Gleichung. Springer Spektrum, Series: BestMasters, 2016
  C. Lohmann
  
• Eigenvalue range limiters for tensors in flux-corrected transport algorithms. MultiMat 2017 conference
  C. Lohmann
  
• Flux-corrected transport algorithms preserving the eigenvalue range of symmetric tensor quantities. J. Comput. Phys. 350 (2017) 907–926
  C. Lohmann
  
• Random walk implementation of rotary diffusion in Lagrangian models of fiber orientation. Ergebnisber. des Instituts für Angew. Math 553, TU Dortmund, 2017
  O. Ahmadi and D. Kuzmin
  
• Algebraic flux correction schemes preserving the eigenvalue range of symmetric tensor fields. Ergebnisber. des Instituts für Angew. Math. 584, TU Dortmund, 2018
  C. Lohmann
  
• Planar and orthotropic closures for orientation tensors in fiber suspension flow models. SIAM Journal on Applied Mathematics 78.6 (2018) 3040–3059
  D. Kuzmin
  
• Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere. Ergebnisber. des Instituts für Angew. Math 595, TU Dortmund, 2019
  A. Novikov, D. Kuzmin and O. Ahmadi