An integral equation formulation for rigid bodies in Stokes flow in three dimensions
Abstract
We present a new derivation of a boundary integral equation (BIE) for simulating the threedimensional dynamics of arbitrarilyshaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a singlelayer representation and leads to a simple secondkind 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 highorder timestepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.
 Publication:

Journal of Computational Physics
 Pub Date:
 March 2017
 DOI:
 10.1016/j.jcp.2016.12.018
 arXiv:
 arXiv:1606.07428
 Bibcode:
 2017JCoPh.332..504C
 Keywords:

 Integral equation methods;
 Stokes flow;
 Particulate flow;
 Fast algorithms;
 Mathematics  Numerical Analysis
 EPrint:
 doi:10.1016/j.jcp.2016.12.018