Abstract
In [15], the authors propose an accurate method, namely the correction method, for computing hydrodynamic interaction between very closed spherical particles in a Stokes fluid. The accuracy of this method depends on two truncation parameters for approximating the Neumann to Dirichlet matrix and the velocity correction respectively. In this paper, we establish a numerical determination to estimate these parameters. We perform some numerical experiments to present our method. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Highlights
We consider N non intersecting particles immersed in a viscous uid
On the surfaces of the particles, we consider a no-slip boundary condition, In recent papers, many mathematicians have studied the hydro dynamic interactions between close particles immersed in a Stokes uid to simulate the motions of nano scale swimmers robots which is designed from nano-sized medical devices
The total force and total torque exerted by the particle Bi on the uid are given by the following formulas, Fi =
Summary
Let us rst introduce a cut-o distance δ > 0. (7) solves the Stokes equations (6) in the original domain but with modied boundary conditions c 2017 Journal of Advanced Engineering and Computation (JAEC). Where B±dc denotes the solid sphere with unit radius and center ±(1 + dc/2)ez The dierence between these problems comes from the specic boundary conditions, uZ = wZ on ∂B+dc ∪ ∂B−dc , where wZ are dened as follows, for x ∈ ∂B±dc , deduced from the former. It is of the same nature as the original problem: solve the Stokes equations in the uid domain surrounding the particles. As a consequence, applying standard numerical methods to problem (6), we can compute approximations of (u0, p0) with an accuracy that does not depend on the distance dc between close particles.
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