Modeling and simulation of fish-like swimming

In this paper, we propose a second order penalized direct forcing method to deal with fluidstructure interaction problems involving complex static or time-varying geometries. As this work constitutes a first step toward more complicated problems, our developments are restricted to Dirichlet boundary condition in purely hydraulic context. The proposed method belongs to the class of immersed boundary techniques and consists in immersing the physical domain in a Cartesian fictitious one of simpler geometry on fixed grids. A penalized forcing term is added to the momentum equation to take the boundary conditions around/inside the obstacles into account. This approach avoids the tedious task of re-meshing and allows us to use fast and accurate numerical schemes. In contrary, as the immersed boundary is described by a set of Lagrangian points that does not generally coincide with those of the Eulerian grid, numerical procedures are required to reconstruct the velocity field near the immersed boundary. Here, we develop a second order linear interpolation scheme and we compare it to a simpler model of order one. As far as the governing equations are concerned, we use a particular fractional-step method in which the penalized forcing term is distributed both in prediction and correction equations. The accuracy of the proposed method is assessed through 2-D numerical experiments involving static and rotating solids. We show in particular that the numerical rate of convergence of our method is quasi-quadratic.

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“…Furthermore, it could be extended to computational grids that can be mapped into Cartesian ones or to deformable bodies as in [22].…”

Section: Immersed Boundary Methodsmentioning

confidence: 99%

“…Links can be found with the works of Sarthou & al. [21] and those of Bergmann & Iollo [22]. As for the DF method, the unknowns are locally enforced on the grid nodes nearest the immersed interface.…”

Section: Introductionmentioning

confidence: 99%

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

Introini¹,

Belliard²,

Fournier³

2014

Computers & Fluids

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“…However, it does not exactly preserve length and volume consistency, as the authors mentioned themselves. These consistencies should be fulfilled especially when calculating forces and torques [1] or using the digital surface models for CFD simulations. However, the error in length as well as volume conservation is not given in any of the studies.…”

Section: Introductionmentioning

confidence: 99%

Size does matter: The use of fish motion for improving human swimming simulations

Pacholak

Brücker

2017

Applied Mathematical Modelling

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In this study we evaluated the length and volume inconsistencies that occur when applying simple motion functions onto surface models of swimming fish and human, respectively. The larger the size (diameter and length) of the body, the larger are theses inconsistencies. To eliminate these errors, different surface correction algorithms are introduced. Additional terms are implemented to overcome structural insufficiencies through over-stretching and overlapping in sensible body parts. For human undulatory swimming these models combine the motion of rigid extremities with the smooth surface bending at joints. The advantages of this hybrid model can be crucial for Computational Fluid Dynamics, where deviation from natural behaviour results in unrealistic surface pressures and artificial vortex structures. The structural improvements are also promising for computational graphic programming, where skin-like stretching surfaces mediate a natural impression.

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“…Similar results were obtained numerically by Eldredge & Pisani (2008) modelling a poly-articulated † Email address for correspondence: fabien.candelier@univ-amu.fr Elongated body swimming in a weakly non-uniform flow 617 fish-like system. Hydrodynamic interaction effects are also expected to be significant during school swimming (see for instance the pioneering investigations by Weihs (1973), or the recent numerical investigations by Bergmann & Iollo (2011)). …”

Section: Introductionmentioning

confidence: 99%

Note on the swimming of an elongated body in a non-uniform flow

Candelier¹,

Porez²,

Boyer³

2013

J. Fluid Mech.

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International audienceThis paper presents an extension of Lighthill's large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann's boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street

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Modeling and simulation of fish-like swimming

Cited by 107 publications

References 44 publications

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

Size does matter: The use of fish motion for improving human swimming simulations

Note on the swimming of an elongated body in a non-uniform flow

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