Improved Radial Basis Function Fluid-Structure Coupling via Efficient Localised Implementation

Abstract

SUMMARY Previous 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 Npoints1 ×Npoints2 . 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 58000 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. Copyright q 2009 John Wiley & Sons, Ltd.