A Highly Efficient Grid Deformation Strategy Based on Proper Orthogonal Decomposition

Abstract

The recent computational progress in multidisciplinary time-domain analysis calls for an efficient grid deformation method which can produce the deformed grid with high quality and can consider the rigid movement and elastic deformation meanwhile. To meet these demands, a highly efficient grid deformation strategy based on the proper orthogonal decomposition (POD) method is developed. In this strategy, the accuracy, efficiency and quality preserving which may contradict with each other in a single grid deformation method are separated and implemented in different methods, such as finite element interpolation (FEI) for accuracy, POD for efficiency and radial basis functions (RBFs) for quality preserving. There are two stages in this strategy: (1) In the pre-processing stage, snapshots, POD basis vectors and RBF coefficients of POD modal weights are calculated in sequence and the focus is quality preserving in this stage; (2) In the simulation stage, the deformed grid is calculated by the weighted summation of POD basis vectors, which is followed by shape preserving process based on the FEI and transfinite interpolation (TFI). The second stage focuses on the efficiency and accuracy. The strategy is then applied to a 2-dimensional biconvex airfoil and a F6 wing-fuselage conjunction. The deformed grid quality is shown to be preserved as well as the RBF’s, while the grid orthogonality is also maintained well, especially at and near the moving surface. As for the efficiency, this strategy is much better than the RBF: 24.3 times for the 2-dimensional biconvex airfoil and 1810 times for the F6 wing-fuselage conjunction.