A multivariate interpolation scheme, using radial basis functions, is presented, which results in a completely unified formulation for the fluid–structure interpolation and mesh motion problems. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow-solver type dependence is removed, and all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity and user-input requirements are removed from the computational fluid dynamics–computational structural dynamics (CFD–CSD) coupling problem, as only point clouds are required to determine the coupling. Also, it may equally well be applied to structured and unstructured grids, or structural and aerodynamic grids that intersect, again because no connectivity information is required. Furthermore, no expensive computations are required during an unsteady simulation, just matrix–vector multiplications, since the required dependence relations are computed only once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel, since only the data relevant to each structured block or unstructured partition are required to move those points, and totally independent from the flow solver. Hence, a completely generic ‘black box’ tool can be developed, which is ideal for use in an optimization approach. Aeroelastic behaviour of the Brite–Euram MDO wing is analysed in terms of both static deflection and dynamic responses, and it is demonstrated that responses are strongly dependent on the exact CFD–CSD interpolation used. Mesh quality is also examined during the motion resulting from a large surface deformation. Global grid quality is shown to be preserved well, with local grid orthogonality also being maintained well, particularly at and near the moving surface, where the original orthogonality is retained. Copyright © 2007 John Wiley & Sons, Ltd.

Unified fluid-structure interpolation and mesh motion using radial basis functions

Efficient mesh motion using radial basis functions with data reduction algorithms

Effects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of O(10 3 - 10 4 ) and the reduced frequency of O(1), the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing tip deformation parameter (γ) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for MAV design and performance analysis.

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Effects of Flexibility on the Aerodynamic Performance of Flapping Wings

A fast mesh deformation method using explicit interpolation

https://biblio.ugent.be/publication/940207/file/940246.pdf

Performance of partitioned procedures in fluid-structure interaction

Mesh deformation based on radial basis function interpolation

Fluid-structure interaction computations typically involve moving boundaries for the flow due to the deformation of the structure. Examples can be found in: flutter simulation of wings, blood flow through veins and stability analysis of bridges and tall buildings subjected to windloads. Because of these moving boundaries a fast and reliable method for deforming the computational grid is needed to be able to perform the unsteady flow computations accurately and efficiently. Structured grids can be deformed by fast and accurate algebraic techniques, but for the meshing of complex domains and grid adaptation the greater flexibility of unstructured grids is required.

M. S. van der Schoot

Papers

Mesh deformation based on radial basis function interpolation

Moving Mesh Algorithm for Unstructured Grids Based on Interpolation with Radial Basis Functions