Parallel efficient mesh motion using radial basis functions with application to multi-bladed rotors

Radial basis functions are used to provide a solution to the problem of mesh motion for unsteady aerodynamic simulation. The method is independent of connectivity and produces high-quality meshes, but is expensive for large meshes in its full form. Hence, the efficiency of the technique has been greatly improved here by reducing the number of surface points used to define deformations of the surface, and the minor error in position that this implies at other surface points is corrected with a simple decaying perturbation, thus splitting the method into a primary basis function method and a secondary local correction method. This means that the exact surface is retained, but the mesh motion is significantly faster, while splitting the motion into two stages allows both the methods to work on appropriate problems given their relative strengths. An example deformation for a 5×106 cell helicopter rotor mesh with an exaggerated cyclic pitch motion shows excellent mesh quality, thus validating a scheme that is also simple, robust and readily parallelized.