High-order singular value decomposition applied in aero-optical effects analysis

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.