A numerical method for interaction problems between fluid and membranes with arbitrary permeability for fluid

Suguru Miyauchi, Shintaro Takeuchi, Takeo Kajishima

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We develop a numerical method for fluid–membrane interaction accounting for permeation of the fluid using a non-conforming mesh to the membrane shape. To represent the permeation flux correctly, the proposed finite element discretization incorporates the discontinuities in the velocity gradient and pressure on the membrane surface with specially selected base functions. The discontinuities are represented with independent variables and determined to satisfy the governing equations including the interfacial condition on the permeation. The motions of the fluid, membrane and permeation flux are coupled monolithically and time-advanced fully-implicitly. The validity and effectiveness of the proposed method are demonstrated by several two-dimensional fluid–membrane interaction problems of Stokes flows by comparing with the analytical models and numerical results obtained by other methods. The reproduced sharp discontinuities are found to be essential to suppress the non-physical permeation flux. Further, combined with the numerical treatment for the solute concentration across the membrane, the proposed method is applied to a fluid–structure interaction problem including the osmotic pressure difference.

Original languageEnglish
Pages (from-to)33-57
Number of pages25
JournalJournal of Computational Physics
Publication statusPublished - 2017 Sept 15


  • Discontinuity
  • Finite element method
  • Fixed grid method
  • Fluid-membrane interaction
  • Permeation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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