A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

Shravan K. Veerapaneni, Denis Gueyffier, George Biros, Denis Zorin

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55 Citations (Scopus)


We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case-spectral approximation in space, semi-implicit time-stepping scheme-the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

Original languageEnglish
Pages (from-to)7233-7249
Number of pages17
JournalJournal of Computational Physics
Issue number19
Publication statusPublished - 20 Oct 2009
Externally publishedYes


  • Axisymmetric flows
  • Fluid membranes
  • Inextensible vesicles
  • Integral equations
  • Moving boundaries
  • Numerical methods
  • Particulate flows


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