Error analysis of dynamic modal decomposition method reconstruction and prediction for flow field
(1. College of Water Resources and Architectural Engineering， Northwest A&F University， Yangling， Shaanxi 712100， China； 2. State Key Laboratory of Water Resources and Hydropower Engineering， Wuhan University， Wuhan， Hubei 430072， China)
Abstract：The dynamic modal decomposition（DMD） method can be used to decompose, reconstruct and predict the unsteady flow field, but the error of the reconstruction and prediction of flow field needs quantitative analysis. To solve the problem, an error analysis method for describing the reconstruction and prediction quantitatively of flow field was proposed for the dynamic modal decomposition. Taking the twodimensional numerical simulation results of cylinder flow with Re of 80 as example, the dynamic changes of reconstruction and prediction errors of the nonlinear and periodic flow fields were investigated. The results show that the mode determined according to the energy size can reflect the main coherent structure of flow field. The lowfrequency, the lowgrowth decay rate and the largescale coherent structures have large energy proportion, which has great impact on flow field. The nonlinear and periodic changing flow field can be accurately reconstructed by DMD method with reconstruction error less than 10-10, and the error of the predicted flow field are larger than that of the reconstructed flow field. The error of the DMD method for predicting the nonlinear changing flow field is less than 10-3 within the sample time interval. The development of errors is increased sharply beyond the sample interval, and the change depends on the data sample. The error for predicting the periodic flow field is stable at about 10-4.
