Subgrid Scale Modeling and Efficient Finite Element Simulation of Fiber Suspension Flows

• Applicants: Professor Dr. Dmitri Kuzmin; Professor Dr. Stefan Turek
• Subject Area: Fluid Mechanics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 251122961

• Final Report Year: 2019

Final Report Abstract

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.

Publications

• 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
  (See online at https://doi.org/10.1016/j.camwa.2016.01.012)
• Galerkin-Spektralverfahren für die Fokker-Planck-Gleichung. Springer Spektrum, Series: BestMasters, 2016
  C. Lohmann
  (See online at https://doi.org/10.1007/978-3-658-13311-5)
• 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
  (See online at https://doi.org/10.1016/j.jcp.2017.09.009)
• 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
  (See online at https://doi.org/10.1137/18M1175665)
• 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