Efficient Mesh Deformation Using Radial Basis Functions on Unstructured Meshes

An efficient mesh-deformation algorithm has been developed within an unstructured-grid computational-fluid-dynamics solver framework based on a radial-basis-function volume-interpolation method. The data-transfer problem between fluid and structural solvers is simplified here using a beam structural representation, with surface mesh deformation given directly via translational and rotational deformations. The volume mesh deformation is then performed using a radial-basis-function method, which requires no mesh-connectivity information and allows straightforward implementation in an unstructured computational-fluid-dynamics solver in a parallel fashion. However, the pure method is impractical for large meshes, and a novel "greedy" data-reduction algorithm is presented here to select an optimum reduced set of surface mesh points, which makes the mesh-deformation method extremely efficient. Several two- and three-dimensional test cases are presented to validate the algorithm performance, including a realistic aircraft Bell M427 main rotor. It is shown that the approach can handle effectively very large mesh deformations of complex geometries using unstructured viscous meshes while maintaining good mesh quality and geometric accuracy, and generally requires less than 25% of the computational-fluid-dynamics flow-solver cost.