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

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.