1. An integral equation formulation for rigid bodies in Stokes flow in three dimensions.
- Author
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Corona, Eduardo, Greengard, Leslie, Rachh, Manas, and Veerapaneni, Shravan
- Subjects
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RIGID bodies , *INTEGRAL equations , *STOKES flow , *THREE-dimensional imaging , *DISCRETIZATION methods - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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