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 journalArticle

Abstract

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
Volume332
DOIs
StatePublished - Mar 1 2017

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Stokes flow
Boundary integral equations
rigid structures
Integral equations
integral equations
Torque
formulations
Fluids
conditioning
quadratures
multipoles
torque
derivation
scaling
fluids

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

An integral equation formulation for rigid bodies in Stokes flow in three dimensions. / Corona, Eduardo; Greengard, Leslie; Rachh, Manas; Veerapaneni, Shravan.

In: Journal of Computational Physics, Vol. 332, 01.03.2017, p. 504-519.

Research output: Contribution to journalArticle

Corona, Eduardo ; Greengard, Leslie ; Rachh, Manas ; Veerapaneni, Shravan. / An integral equation formulation for rigid bodies in Stokes flow in three dimensions. In: Journal of Computational Physics. 2017 ; Vol. 332. pp. 504-519.
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