动力学模态分解方法重构及预测流场误差分析

Error analysis of dynamic modal decomposition method reconstruction and prediction for flow field

利用动力学模态分解(dynamic mode decomposition,DMD)方法可以实现非定常流场的分解、重构和预测,但该方法重构和预测流场的误差需要给出定量分析.鉴于此,提出了定量描述动力学模态分解重构和预测流场的误差分析方法,以雷诺数Re=80的圆柱绕流二维流场数值模拟结果为例,研究了非线性流动和周期性流场重构和预测误差的动态变化情况.结果表明:依据能量大小确定的模态反映了流场的主要相干结构;低频、低增长/衰减率和大尺度的相干结构能量占比大,对流场的影响较大;DMD方法可以准确重构非线性和周期性变化流场,重构的误差小于10^-10,预测流场的误差较重构流场出现跳跃增大现象;DMD方法预测非线性变化流场的误差在样本时间区间内较小(小于10^-3),超出样本区间误差的发展急剧增大,变化情况依赖于数据样本;预测周期性流场的误差稳定在10^-4左右.

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 two-dimensional 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 low-frequency,the low-growth decay rate and the large-scale 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 non-linear 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.