### 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 language | English (US) |
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Pages (from-to) | 504-519 |

Number of pages | 16 |

Journal | Journal of Computational Physics |

Volume | 332 |

DOIs | |

State | Published - Mar 1 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Computer Science Applications

### Cite this

*Journal of Computational Physics*,

*332*, 504-519. https://doi.org/10.1016/j.jcp.2016.12.018

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

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 332, pp. 504-519. https://doi.org/10.1016/j.jcp.2016.12.018

}

TY - JOUR

T1 - An integral equation formulation for rigid bodies in Stokes flow in three dimensions

AU - Corona, Eduardo

AU - Greengard, Leslie

AU - Rachh, Manas

AU - Veerapaneni, Shravan

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Fast algorithms

KW - Integral equation methods

KW - Particulate flow

KW - Stokes flow

UR - http://www.scopus.com/inward/record.url?scp=85007388002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007388002&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2016.12.018

DO - 10.1016/j.jcp.2016.12.018

M3 - Article

VL - 332

SP - 504

EP - 519

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -