Boundary integral method for the flow of vesicles with viscosity contrast in three dimensions

Abtin Rahimian, Shravan K. Veerapaneni, Denis Zorin, George Biros

Research output: Contribution to journalArticlepeer-review


We propose numerical algorithms for the simulation of the dynamics of three-dimensional vesicles suspended in viscous Stokesian fluid. Our method is an extension of our previous work (S.K. Veerapaneni et al., 2011) [37] to flows with viscosity contrast. This generalization requires a change in the boundary integral formulation of the solution, in which a double-layer Stokes integral is introduced, and leads to changes in the fluid dynamics due to the viscosity contrast of the vesicles, which can no longer be efficiently resolved with existing algorithms. In this paper we describe the algorithms needed to handle flows with viscosity contrast accurately and efficiently. We show that a globally semi-implicit method does not have any time-step stability constraint for flows with single and multiple vesicles with moderate viscosity contrast and the computational cost per simulation unit time is comparable to or less than that of an explicit scheme. Automatic oversampling adaptation enables us to achieve high accuracy with very low spectral resolution. We conduct numerical experiments to investigate the stability, accuracy, and the computational cost of the algorithms. Overall, our method achieves several orders of magnitude speed-up compared to the standard explicit schemes.

Original languageEnglish (US)
Pages (from-to)766-786
Number of pages21
JournalJournal of Computational Physics
StatePublished - 2015


  • Boundary integral
  • Galerkin method
  • Implicit time stepping
  • Stokes flow
  • Viscosity contrast

ASJC Scopus subject areas

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


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