Computation of a regularized Brinkmanlet near a plane wall

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

doi:10.1007/s10665-018-9980-8

Cited by 4 publications

(4 citation statements)

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“…A related, widely applied numerical approach in the low Reynolds number regime is to abstract the swimmer into a one-dimensional collection of regularized singularities, which yields good approximations the swimmer’s far field ( 6 , 38 , 61 – 64 ). However, this method requires specialization when the near field is of prime importance, such as swimming in crowded or confined environments ( 65 , 66 ). We now use the RMT to simulate a finite-size swimmer in a small no-slip box, showing the method naturally resolves the near field.…”

Section: Resultsmentioning

confidence: 99%

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Lin

Derr

Rycroft

2021

Proc. Natl. Acad. Sci. U.S.A.

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We present a numerical method specifically designed for simulating three-dimensional fluid–structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method’s suitability in investigating many-body and active systems, as well as its accuracy and convergence. The examples include settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

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Section: Resultsmentioning

confidence: 99%

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Lin

Derr

Rycroft

2021

Proc. Natl. Acad. Sci. U.S.A.

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“…In addition to revealing physical properties and limitations of the regularised stokeslet representation, our work creates avenues for future explorations and optimisations of regularised stokeslets. Similar investigations are needed to understand the flows from regularised point forces near boundaries [55,56], regularised higher-order singularities [56] or in Brinkman fluids [57]. The identification of the flow could also help with the design of regularised stokeslets for specific purposes, such as optimal regularisations for densely packed systems, or regularisations to reflect inherent geometric asymmetries.…”

Section: Discussionmentioning

confidence: 99%

“…These results typically compare favourably with exact solutions and experiments. The method has also been extended to consider slender-filaments [30,[50][51][52][53][54], flows near walls [55,56] and Brinkman fluids [57].…”

Section: Introductionmentioning

confidence: 99%

Method of regularized stokeslets: Flow analysis and improvement of convergence

2019

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Since their development in 2001, regularised stokeslets have become a popular numerical tool for low-Reynolds number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with flow singularities , SIAM J. Sci. Comput. 23, 1204. The physical changes to the flow resulting from this process are, however, unclear. In this paper, we analyse the flow induced by general regularised stokeslets. An explicit formula for the flow from any regularised stokeslet is first derived, which is shown to simplify for spherically symmetric blobs. Far from the centre of any regularised stokeslet we show that the flow can be written in terms of an infinite number of singularity solutions provided the blob decays sufficiently rapidly. This infinite number of singularities reduces to a point force and source dipole for spherically symmetric blobs. Slowly-decaying blobs induce additional flow resulting from the non-zero body forces acting on the fluid. We also show that near the centre of spherically symmetric regularised stokeslets the flow becomes isotropic, which contrasts with the flow anisotropy fundamental to viscous systems. The concepts developed are used to identify blobs that reduce regularisation errors. These blobs contain regions of negative force in order to counter the flows produced in the regularisation process, but still retain a form convenient for computations. a

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“…In the case of a Stokesian fluid, an image system can be utilized [49,51,52]. However, in the case of a Brinkman fluid, the image system can not be truncated and alternate approaches have been developed that can be utilized in future simulation studies [53]. In this work, we utilized an elastic wall as in [41], where future work can also investigate walls that exhibit a time dependent configuration, corresponding to peristaltic contractions in the oviduct [5].…”

Section: Discussionmentioning

confidence: 99%

Dynamics of Swimmers in Fluids with Resistance

Jeznach

Olson

2020

Fluids

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Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter.

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Computation of a regularized Brinkmanlet near a plane wall

Cited by 4 publications

References 50 publications

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Method of regularized stokeslets: Flow analysis and improvement of convergence

Dynamics of Swimmers in Fluids with Resistance

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