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 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.
- 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
- E-Print:
- doi:10.1016/j.jcp.2016.12.018