Improved radial basis function fluid–structure coupling via efficient localized implementation

Abstract

SUMMARYPrevious work by the authors has developed a universal interpolation scheme, using radial basis functions (RBFs), which results in a unified formulation for robust fluid-structure interpolation and high-quality mesh motion. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow-solver-type dependence is removed entirely, as all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity requirements are removed from both the coupling and mesh motion problems. Furthermore, only matrix-vector multiplications are required during unsteady simulation because dependence relations are computed once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel and totally independent from the flow-solver. However, the full method is expensive, since the dependence matrix between two sets of points is N points 1 × N points 2 . The fluid-structure coupling behaviour can also be influenced by parameters used in the interpolation. To alleviate these difficulties a more efficient form of the RBF fluid-structure coupling is presented, which also greatly reduces the interpolation parameter influence. A pointwise form of the partition of unity approach is developed that localizes the interpolation, with results presented for static aeroelastic simulations of the Brite-Euram multi-disciplinary optimization wing using a very fine mesh containing 58 000 surface points. It is shown that a 58× reduction in data size is achieved, and equally importantly the interpolation has a much smaller influence on final aeroelastic results.

Doublet-Lattice Method Correction by Means of Linearised Frequency Domain Solver Analysis

“…The first based on radial basis funciton method by Rendall and Allen. 11,12 The second based on the 3D beam and 3D surface available in MSC Nastran using SPLINE6 and SPLINE7.…”

Using Improved Radial Basis Functions Methods for Fluid-Structure Coupling and Mesh Deformation

“…It has been successfully implemented against FSI problems in [17,18] with very promising results. Besides reducing computational cost, it avoids the undesirable influence of support radius into the interpolation process.…”

“…Using the transpose of the global matrix, formed by the local interpolants, assures that the conservation criteria are also met in the PoU approach [17]. A variation of the pre-described method, proposed by Rendall and Allen [18], concerns the application of the PoU method on each boundary flow node separately, instead of decomposing the set of nodes into overlapping patches. Following this strategy, the complex step of decomposing the structural grid into overlapping regions is evaded, and thus the possibility of facing discontinuities between the patches due to the partitioning process is diminished.…”

“…For the alleviation of the aforementioned shortcoming the Partition of Unity (PoU) [17] approach is adopted in data transfer, which regards the decomposition of the interfacing boundary into several smaller regions, where local interpolations are performed independently and hence more efficiently. Although this method ensures energy conservation and offers physical distribution of the forces on the interfacing area [17,18], it is revealed to be inappropriate for mesh deformation, as the dependence matrix takes into account all the flow mesh nodes, entailing significantly increased computational cost . In order to mitigate this inadequacy, a relatively recently developed by the authors methodology is followed, considering agglomeration of the surface nodes, and as such reduction of the dimensions of the pre-mentioned matrix [19]; it is based on the fusion strategy, developed for a corresponding CFD agglomeration multigrid method [20].…”

“…Attention is mainly directed toward the efficient and accurate transfer of predicted displacements (by CSD) and forces (by CFD). Therefore, spatial coupling is obtained by a RBFs interpolation scheme, employing the aforementioned PoU approach [18] to accelerate the exchange procedure. For mesh deformation a corresponding RBFs interpolation process is applied; its efficiency is significantly improved with a surface point reduction technique, based on the agglomeration of adjacent boundary nodes.…”