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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:332

Article

Corona, Eduardo¹  Greengard, Leslie²  Rachh, Manas²  Veerapaneni, Shravan¹ 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] NYU, Courant Inst Math Sci, New York, NY 10003 USA

关键词: Integral equation methods;    Stokes flow;    Particulate flow;    Fast algorithms;   

DOI  :  10.1016/j.jcp.2016.12.018

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free