An integral equation formulation for rigid bodies in Stokes flow in three dimensions

Eduardo Corona, Leslie Greengard, Manas Rachh, Shravan Veerapaneni

Research output: Contribution to journalArticlepeer-review


We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O(n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.

Original languageEnglish (US)
Pages (from-to)504-519
Number of pages16
JournalJournal of Computational Physics
StatePublished - Mar 1 2017


  • Fast algorithms
  • Integral equation methods
  • Particulate flow
  • Stokes flow

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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