Mesh deformation based on radial basis function interpolation

Boer, A. de; Schoot, M. S. van der; Bijl, H.

doi:10.1016/j.compstruc.2007.01.013

Cited by 609 publications

(306 citation statements)

References 18 publications

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“…The geometric conservation law [37] is satisfied [38]. We use the radial basis function interpolation method to deform the computational mesh at each time step [39]. The spatial and temporal sensitivity studies as well as computational set-up are shown in appendix A.…”

Section: Numerical Modelsmentioning

confidence: 99%

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Kang

Shyy

2013

J. R. Soc. Interface.

159

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We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier-Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid-structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing-wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.

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Section: Numerical Modelsmentioning

confidence: 99%

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Kang

Shyy

2013

J. R. Soc. Interface.

159

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“…In this case the RBF morphing field is interpolated using a cloud of points with given displacements. Even if there is interesting research demonstrating that RBF can be successfully adopted for the deformation of CFD meshes (Jakobsson, 2007;de Boer, 2007), their numerical cost has limited their application in the past (direct solution grows by N 3 where N is the number of RBF centres). Recent efforts have been devoted to the acceleration of the method to deal with large RBF dataset.…”

Section: Mesh Morphingmentioning

confidence: 99%

Sails trim optimisation using CFD and RBF mesh morphing

2014

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The study is focused on the use of mesh morphing to explore different trims of yachts sails. In particular, four trims of the fore and aft sail of a model-scale sailing yacht were modelled leading to 16 configurations in total. Sail pressure distributions were validated with wind-tunnel measurements for all the 16 configurations, and full verification and validation was performed for one of these conditions. The 16 configurations were modelled with two different approaches: generating a new mesh for each trim condition (standard method) and using a morphed version of the baseline condition. This second novel method, based on the use of radial basis functions to morph the mesh, allows the computational time of exploring different geometries with computational fluid dynamics to be significantly decreased. Good agreement is observed between the pressure distributions computed with new meshes and morphed meshes. In order to show an example of trim optimisation, a metamodel approach is defined for the estimation of the response surface using radial basis function interpolation in the parameter space. Thanks to the continuum nature of morphing approach, the optimal trim angles for the given flow condition could be verified using new full computational fluid dynamic simulations. The original full factorial map of 16 points was replaced with a new map of 9 points with an optimal space filling approach to understand the faithfulness of a reduced metamodel. In both cases optimal point is evaluated using a fine Design Of Experiment table built using the metamodel (41 levels for each parameter). The maximum thrust is achieved at the same trim for both metamodels.Proposed method can be easily extended to a wide number of parameters. Such flexibility is demonstrated in the present paper showing the sensitivity of results with respect to apparent wind angle and heeling angle.

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“…RBF interpolation is currently one of the more popular mesh movement methods available, as it results in comparably good quality meshes, at relatively cheap computational costs. For the sake of brevity, we wont discuss the RBF method in detail, but for more information refer to de Boer et al [5] or Rendall et al [6]. RBF interpolation moves the internal mesh nodal coordinates according to an interpolation function based on the motion of the boundary nodes.…”

Section: Test Problemmentioning

confidence: 99%

“…This is referred to as mesh movement, examples of which include the spring analogy [3], solving a set of Laplacian or Bi-harmonic equations [4], radial basis function (RBF) interpolation [5,6] or through mesh optimization [7,8].…”

Section: Introductionmentioning

confidence: 99%

Highly efficient optimization mesh movement method based on proper orthogonal decomposition

Bogaers¹,

Kok²,

Malan³

2010

Numerical Meth Engineering

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In this paper, we implement the method of Proper Orthogonal Decomposition (POD) to generate a reduced order model (ROM) of an optimization based mesh movement scheme. In the study it is shown that POD can be used effectively to generate a ROM, that accurately reproduces the full order mesh movement algorithm, with a decrease in computational time of over 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme.

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Mesh deformation based on radial basis function interpolation

Cited by 609 publications

References 18 publications

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Sails trim optimisation using CFD and RBF mesh morphing

Highly efficient optimization mesh movement method based on proper orthogonal decomposition

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