A fast method to compute triply-periodic Brinkman flows

Nguyen, Hoang-Ngan; Olson, Sarah D.; Leiderman, Karin

doi:10.1016/j.compfluid.2016.04.007

Cited by 5 publications

(5 citation statements)

References 71 publications

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“…This blob function was previously derived for a triply periodic Brinkman fluid (Nguyen et al 2016). The resulting functions Gε(r) and Bε(r) are…”

Section: Option 2: Choosing a Blob Functionmentioning

confidence: 99%

“…We note that each approach leads to a slightly different regularization of the forces, which in turn, results in a slightly different flow. Carefully chosen blob functions can reduce error and allow for computationally efficient expressions to calculate regularized Stokes and Brinkman flow (Nguyen & Cortez 2014;Nguyen et al 2016). On the other hand, a particular regularization of the singular solutions may also lead to desired properties.…”

Section: Regularized Coefficient Functionsmentioning

confidence: 99%

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A three-dimensional model of flagellar swimming in a Brinkman fluid

Leiderman

Olson

2019

J. Fluid Mech.

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We investigate 3-dimensional flagellar swimming in a fluid with a sparse network of stationary obstacles or fibers. The Brinkman equation is used to model the average fluid flow where a flow dependent term, including a resistance parameter that is inversely proportional to the permeability, models the resistive effects of the fibers on the fluid. To solve for the local linear and angular velocities that are coupled to the flagellar motion, we extend the method of regularized Brinkmanlets to incorporate a Kirchhoff rod, discretized as point forces and torques along a centerline. Representing a flagellum as a Kirchhoff rod, we investigate emergent emergent waveforms for different preferred strain and twist functions. Since the Kirchhoff rod formulation allows for out-of-plane motion, in addition to studying a preferred planar sine wave configuration, we also study the case with a preferred helical configuration. Our numerical method is validated by comparing results to asymptotic swimming speeds derived for an infinite-length cylinder propagating planar or helical waves. Similar to the asymptotic analysis for both planar and helical bending, we observe that with small amplitude bending, swimming speed is always enhanced relative to the case with no fibers in the fluid (Stokes) as the resistance parameter is increased. For regimes not accounted for with asymptotic analysis, i.e., large amplitude planar and helical bending, our model results show a non-monotonic change in swimming speed with respect to the resistance parameter; a maximum swimming speed is observed when the resistance parameter is near one. The non-monotonic behavior is due to the emergent waveforms; as the resistance parameter increases, the swimmer becomes incapable of achieving the amplitude of its preferred configuration. We also show how simulation results of slower swimming speeds for larger resistance parameters are actually consistent with the asymptotic swimming speeds if work in the system is fixed.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list) †

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“…This blob function was previously derived for a triply periodic Brinkman fluid (Nguyen et al 2016). The resulting functions Gε(r) and Bε(r) are…”

Section: Option 2: Choosing a Blob Functionmentioning

confidence: 99%

Section: Regularized Coefficient Functionsmentioning

confidence: 99%

A three-dimensional model of flagellar swimming in a Brinkman fluid

Leiderman

Olson

2019

J. Fluid Mech.

Self Cite

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“…For the biharmonic kernel B(r) = |r| and the Hasimoto screening function γ H (25), the integral we want to compute is Applying (B.5) for the stokeslet, with A = B and K S given by ( 9), one finds that Q S,1P is symmetric and given by…”

Section: Discussionmentioning

confidence: 99%

“…We have found it useful to let δL ≈ λhP , where the factor λ ≥ 1 depends on the kernel (and thus on the screening function); this naturally connects points (i) and (ii), and furthermore links δL to the window size P , and thus to the overall precision of the method (so that δL becomes larger when more precision is required). Since the Hasimoto screening function (25) decays slower than the Ewald screening function (20), λ is expected to be larger for the stokeslet and stresslet, than for the rotlet.…”

Section: Box Padding and Upsamplingmentioning

confidence: 99%

“…The SE method has also been adapted to related models, such as Brinkman flow [25], and Stokesian dynamics [26]. To facilitate the inclusion of Brownian motion, [27] proposed the Positively Split Ewald (PSE) method for the Rotne-Prager-Yamakawa (RPY) tensor of Stokesian dynamics, thus ensuring that both the short-range and long-range parts are symmetric positive definite.…”

Section: Introductionmentioning

confidence: 99%

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Fast Ewald summation for Stokes flow with arbitrary periodicity

Bagge¹,

Tornberg²

2022

Preprint

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A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stokes flow to periodic boundary conditions in any number (three, two, one, or none) of the spatial directions, in a unified framework. The periodic potential is split into a short-range and a long-range part, where the latter is treated in Fourier space using the fast Fourier transform. A crucial component of the method is the modified kernels used to treat singular integration. We derive new modified kernels, and new improved truncation error estimates for the stokeslet and stresslet. An automated procedure for selecting parameters based on a given error tolerance is designed and tested. Analytical formulas for validation in the doubly and singly periodic cases are presented. We show that the computational time of the method scales like O(N log N ) for N sources and targets, and investigate how the time depends on the error tolerance and window function, i.e. the function used to smoothly spread irregular point data to a uniform grid. The method is fastest in the fully periodic case, while the run time in the free-space case is around three times as large. Furthermore, the highest efficiency is reached when applying the method to a uniform source distribution in a primary cell with low aspect ratio. The work presented in this paper enables efficient and accurate simulations of three-dimensional Stokes flow with arbitrary periodicity using e.g. boundary integral and potential methods.

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