A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D

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

Research output: Contribution to journalArticlepeer-review


We present a new method for the evolution of inextensible vesicles immersed in a Stokesian fluid. We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the non-local hydrodynamic forces with the elastic forces due to bending and tension. Numerical simulations of such vesicle motions are quite challenging. On one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives and a milder constraint due to a transport-like stability condition. On the other hand, an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step. We present two semi-implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme. We discretize the equations by using a spectral method in space, and a multistep third-order accurate scheme in time. We use the fast multipole method (FMM) to efficiently compute vesicle-vesicle interaction forces in a suspension with a large number of vesicles. We report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme.

Original languageEnglish (US)
Pages (from-to)2334-2353
Number of pages20
JournalJournal of Computational Physics
Issue number7
StatePublished - Apr 20 2009


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

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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