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

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• 作者：Eduardo Corona^a ; Leslie Greengard^b ; Manas Rachh^b ; Shravan Veerapaneni^a ; ^{shravan@umich.edu}
• 关键词：Integral equation methods ; Stokes flow ; Particulate flow ; Fast algorithms
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：332
• 期：Complete
• 页码：504-519
• 全文大小：1392 K
• 卷排序：332

文摘

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)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.