THE OPTIMAL TRUNCATED LOW-DIMENSIONAL DYNAMICAL SYSTEMS BASED ON FLOW DATABASES

摘要

A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems(LDDSs)with different physical meanings has beendeveloped.The physical properties of the optimal bases are reflected in the user-defined optimal conditions.Through the analysis of linear and nonlinear examples,itis shown that the LDDSs constructed by using the Proper Orthogonal Decomposition(POD)method are not the optimum.After comparing the errors of LDDSs based onthe new theory,POD and Fourier methods,it is concluded that the LDDSs based onthe new theory are optimally truncated and catch the desired physical properties ofthe systems.