High-performance computational homogenization of Stokes–Brinkman flow with an Anderson-accelerated FFT method

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Fluid flow problems in bi-porous media have strong implications in a variety of industrial applications, such as nuclear waste disposal and composites manufacturing. Despite various numerical solutions proposed in the literature, the prediction of dual-scale flow remains a challenging task due to the requirement of fine meshes to resolve the complex microstructures of bi-porous media. This paper introduces a new numerical solver based on fast Fourier transform (FFT) for the Stokes–Brinkman problem to predict fluid flow in bi-porous media with local anisotropy. The novel FFT solver is derived from a velocity-form of the problem, in contrast to the stress-form proposed by a recent work. The Anderson acceleration technique is applied for the first time to the Stokes–Brinkman problem, leading to a substantial (orders of magnitude) improvement of the convergence rate. A range of detailed numerical examples are provided to validate the method against the analytical and literature results. Parametric studies are also demonstrated to aid in the selection of model parameters to achieve optimum numerical performance. With a 3D unit cell of a woven textile fabric, we demonstrate that the proposed method is capable of handling high-resolution simulations with strongly heterogeneous microstructures. Combined with a parallelized implementation over high-performance computing systems, our method demonstrates a new state-of-the-art in numerical solvers for the Stokes-Brinkman problem, in terms of computation capacity.

Original languageEnglish
JournalInternational Journal for Numerical Methods in Fluids
Early online date30 Apr 2023
Publication statusE-pub ahead of print - 30 Apr 2023

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council (grant number EP/P006701/1), as part of the EPSRC Future Composites Manufacturing Research Hub, for which the author holds the Innovation Research Fellowship. The ARCHER2 UK National Supercomputing Service ( https://www.archer2.ac.uk ) was used for the woven fabric example. The author would like to acknowledge Dr. Lionel Gélébart for his help on the improvement of the algorithms and the implementation with AMITEX, Profs. Richard Butler and Chris Bowen for their help in preparing the manuscript. Acknowledgement also must go to the anonymous reviewers for their careful reading and in‐depth comments, which have led to a significant improvement of the work.


  • Anderson acceleration
  • anisotropy
  • Bi-porous media
  • FFT method
  • stokes-Brinkman equation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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