An efficient mode shape-based RBF mesh deformation approach via forward-backward greedy algorithm in CFD/CSD coupled simulation

Mesh deformation is an important element of CFD/CSD coupled time marching simulation. A mode shape-based Radial Basis Functions interpolation (M-RBF) approach is proposed to improve the efficiency of mesh deformation in the time marching simulation. Inspired by the modal expansion theorem in vibration theory, a set of interpolation nodes is pre-selected according to the mode shapes, rather than the physical displacements at each individual time step. The data reduction scheme of the forward-backward greedy algorithm is developed to select an optimum set of interpolation nodes. The AGARD 445.6 wing, a benchmark model for transonic flutter prediction, and the Goland+ wing with a tip store, which presents complexities in both aerodynamic configuration and mode shapes, are employed to validate the accuracy, efficiency, and capability of the M-RBF approach. The results show that the optimum set of interpolation nodes can achieve the desired interpolation accuracy while having little effect on the mesh quality at all time steps. The traditional RBF mesh deformation (T-RBF) and the RBF mesh deformation method via forward greedy algorithm (G-RBF) method spent majority of CPU time on the linear system solution (approximately 99% and 77.6%, respectively) and the selection of interpolation nodes (about 87.7% and 91.9%, respectively) in the case of AGARD 445.6 and Goland+ wing. However, by eliminating the need for repeated node selections, our M-RBF approach can improve the efficiency of mesh deformation by 2 to 3 orders of magnitude compared to the T-RBF method and 1 to 2 orders of magnitude compared to the G-RBF approach. The comparison of selected interpolation nodes by the M-RBF approach to the structural grid and CFD mesh indicates that the importance of nodes on the deforming boundary may be related to their distances from the structural grid.