光学学报, 2010, 30 (12): 3367, 网络出版: 2010-12-07
高阶奇异值分解在气动光学效应分析中的应用
High-Order Singular Value Decomposition Applied in Aero-Optical Effects Analysis
气动光学 最佳近似 高阶奇异值分解 湍流 aero-optics optimal approximation high-order singular-value decomposition (HOSVD) turbulence
摘要
提出将湍流三维密度场数据用张量表示,利用高阶奇异值分解得到的较大奇异值及对应特征向量对其进行降秩处理,获得湍流密度场的最佳近似,从而实现了对三维湍流密度场空间大尺度相干结构的提取。降秩近似后的结果保留了原始流场的主要信息,对气动光学效应的仿真结果表明,重构流场能够较好地反映原始流场对光传输的影响。
Abstract
Third-order tensor is introduced to represent 3D density field of turbulence. The third-order tensor is decomposed with high-order singular-value decomposition (HOSVD) method to get singular values and corresponding eigenvector. Several great singular values and corresponding eigenvectors are used to reconstruct the density field which is the optimal approximation of the original flow field and gives the large-scale coherent structure in 3D turbulence. The reconstructed 3D density field involves the dominated information of the original flow field. The simulation results of aero-optical effect give the evidences that light transmission in reconstructed field is similar to original field.
许东, 刘浩伟, 吴琳, 安永泉. 高阶奇异值分解在气动光学效应分析中的应用[J]. 光学学报, 2010, 30(12): 3367. Xu Dong, Liu Haowei, Wu Lin, An Yongquan. High-Order Singular Value Decomposition Applied in Aero-Optical Effects Analysis[J]. Acta Optica Sinica, 2010, 30(12): 3367.