Title: 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:

Corona, Eduardo ^[1]; Greengard, Leslie ^[2]; Rachh, Manas ^[2]; Veerapaneni, Shravan ^[1]

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+ Show Author Affiliations

1. University of Michigan, Ann Arbor, MI (United States)
2. New York University (NYU), NY (United States)

Publication Date:

Fri Dec 16 00:00:00 EST 2016

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