An integral equation formulation for rigid bodies in Stokes flow in three dimensions
Abstract
Here 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 $$\mathscr{O}(n)$$ 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.
- Authors:
-
- University of Michigan, Ann Arbor, MI (United States)
- New York University (NYU), NY (United States)
- Publication Date:
- Research Org.:
- New York Univ. (NYU), NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); Simons Collaboration
- OSTI Identifier:
- 1532878
- Alternate Identifier(s):
- OSTI ID: 1416826
- Grant/Contract Number:
- FG02-88ER25053; FA9550-10-1-0180; DMS-1224656; DMS-1454010; DMS-1418964; 317933; DEFGO288ER25053
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 332; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; integral equation methods; Stokes flow; particulate flow; fast algorithms
Citation Formats
Corona, Eduardo, Greengard, Leslie, Rachh, Manas, and Veerapaneni, Shravan. An integral equation formulation for rigid bodies in Stokes flow in three dimensions. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.12.018.
Corona, Eduardo, Greengard, Leslie, Rachh, Manas, & Veerapaneni, Shravan. An integral equation formulation for rigid bodies in Stokes flow in three dimensions. United States. https://doi.org/10.1016/j.jcp.2016.12.018
Corona, Eduardo, Greengard, Leslie, Rachh, Manas, and Veerapaneni, Shravan. Fri .
"An integral equation formulation for rigid bodies in Stokes flow in three dimensions". United States. https://doi.org/10.1016/j.jcp.2016.12.018. https://www.osti.gov/servlets/purl/1532878.
@article{osti_1532878,
title = {An integral equation formulation for rigid bodies in Stokes flow in three dimensions},
author = {Corona, Eduardo and Greengard, Leslie and Rachh, Manas and Veerapaneni, Shravan},
abstractNote = {Here 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 $\mathscr{O}(n)$ 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.},
doi = {10.1016/j.jcp.2016.12.018},
journal = {Journal of Computational Physics},
number = C,
volume = 332,
place = {United States},
year = {Fri Dec 16 00:00:00 EST 2016},
month = {Fri Dec 16 00:00:00 EST 2016}
}
Web of Science
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