Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall

Yan, Wen; Shelley, Michael

doi:10.1016/j.jcp.2018.08.041

Cited by 20 publications

(19 citation statements)

References 33 publications

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“…In the application example below, we employ the fast multi-pole boundary element method fastBEM [39,40], available for download at [64]. The open-source implementation of the fast boundary element method STKFMM directly incorporates the fundamental solution of the Stokes equation close to a no-slip boundary wall [65] and thus relieves the need for an explicit representation of the boundary as a triangulated mesh, yet currently only supports the computation of velocity fields from force distributions [66,67].…”

Section: Multi-scale Modeling: Numerical Implementationmentioning

confidence: 99%

Lagrangian mechanics of active systems

Соловьев

Friedrich

2021

Eur. Phys. J. E

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We present a multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics of shape-changing immersed objects, e.g., biological microswimmers and active surfaces. The key idea is to consider principal shape changes as generalized coordinates and define conjugate generalized hydrodynamic friction forces. Conveniently, the corresponding generalized friction coefficients can be pre-computed and subsequently reused to solve dynamic equations of motion fast. This framework extends Lagrangian mechanics of dissipative systems to active surfaces and active microswimmers, whose shape dynamics is driven by internal forces. As an application case, we predict in-phase and anti-phase synchronization in pairs of cilia for an experimentally measured cilia beat pattern. Graphic Abstract

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Section: Multi-scale Modeling: Numerical Implementationmentioning

confidence: 99%

Lagrangian mechanics of active systems

Соловьев

Friedrich

2021

Eur. Phys. J. E

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“…Ewald methods for Stokes flow based on image constructions have been developed for a single bottom wall using Fourier transforms in all directions [35] or FMMs [36,37]. However, the image construction for a no-slip wall for Stokes flow involves several types of image singularities [38], and this leads to substantial complexity and inefficiency compared to the approach we developed here for the Poisson equation.…”

Section: Discussionmentioning

confidence: 99%

A fast spectral method for electrostatics in doubly-periodic slit channels

Maxian,

Peláez,

Greengard

et al. 2021

Preprint

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We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using Ewald splitting to replace the original Poisson equation for nearly-singular sources with a smooth far-field Poisson equation, combined with a localized near-field correction.Unlike existing spectral Ewald methods, which make use of the Fourier transform in the aperiodic direction, we recast the problem as a two-point boundary value problem in the aperiodic direction for each transverse Fourier mode, for which exact analytic boundary conditions are available. We solve each of these boundary value problems using a fast, well-conditioned Chebyshev method. In the presence of dielectric jumps, combining Ewald splitting with the classical method of images results in smoothed charge distributions which overlap the dielectric boundaries themselves.We show how to preserve high order accuracy in this case through the use of a harmonic correction which involves solving a simple Laplace equation with smooth boundary data. We implement our method on Graphical Processing Units, and combine our doubly-periodic Poisson solver with Brownian Dynamics to study the equilibrium structure of double layers in binary electrolytes confined by dielectric boundaries. Consistent with prior studies, we find strong charge depletion near the interfaces due to repulsive interactions with image charges, which points to the need for incorporating polarization effects in understanding confined electrolytes, both theoretically and computationally.

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“…It follows that the constant k = 0 basis function makes no contribution to K, and so we exclude it from the matrix. Note that two clamped ends cannot straightforwardly be fit into our approach, since it is difficult to write a basis like (69) when there is a constraint on L 0 τ (s) ds.…”

Section: Spectral Discretizationmentioning

confidence: 99%

“…We chose an Ewald approach because we are interested in triply-periodic systems; in free space a fast multipole method[24] is likely the best choice, and systems with mixed periodicity are an avenue of active research[37,69].…”

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confidence: 99%

The hydrodynamics of a twisting, bending, inextensible fiber in Stokes flow

Maxian¹,

Sprinkle²,

Peskin³

et al. 2022

Preprint

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In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid motion.In this paper, we develop a novel numerical method for the simulation of cylindrical fibers by extending our previous work on inextensible bending fibers [Maxian et al., Phys. Rev. Fluids 6 (1), 014102] to fibers with twist elasticity. In our "Euler" model, twist is a scalar function that measures the deviation of the fiber cross section relative to a twist-free frame, the fiber exerts only torque parallel to the centerline on the fluid, and the perpendicular components of the rotational fluid velocity are discarded in favor of the translational velocity. In the first part of this paper, we justify this model by comparing it to another commonly-used "Kirchhoff" formulation where the fiber exerts both perpendicular and parallel torque on the fluid, and the perpendicular angular fluid velocity is required to be consistent with the translational fluid velocity. Through asymptotics and numerics, we show that the perpendicular torques in the Kirchhoff model are small, thereby establishing the asymptotic equivalence of the two models for slender fibers. We then develop a spectral numerical method for the hydrodynamics of the Euler model. We define hydrodynamic mobility operators using integrals of the Rotne-Prager-Yamakawa tensor, and evaluate these integrals through a novel slender-body quadrature, which requires on the order of 10 points along the fiber to obtain several digits of accuracy. We demonstrate that this choice of mobility removes the unphysical negative eigenvalues in the translation-translation mobility associated with asymptotic slender body theories, and ensures strong convergence of the fiber velocity and weak convergence of the fiber constraint forces. We pair the spatial discretization with a semi-implicit temporal integrator to confirm the negligible contribution of twist elasticity to the relaxation dynamics of a bent fiber. We also study the 1

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Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall

Cited by 20 publications

References 33 publications

Lagrangian mechanics of active systems

Lagrangian mechanics of active systems

A fast spectral method for electrostatics in doubly-periodic slit channels

The hydrodynamics of a twisting, bending, inextensible fiber in Stokes flow

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