Source term estimation in the unsteady flow with dynamic mode decomposition

Abstract

When estimating source parameters in the unsteady flow, the flow information of pollution dispersion is indispensable. It is common practice to save the flow information in the computer in advance but it requires large storage space. Besides, when contaminants are released after a time period of the flow field saved before, calculating the flow field by Computational Fluid Dynamics (CFD) model demands massive computational cost. Dynamic Mode Decomposition (DMD) is thereby proposed to solve the problems mentioned above. Firstly, the fields are decomposed by DMD. Then, the simulated concentrations are acquired by the adjoint equation based on the field synthesized by DMD. Finally, the measured concentrations and the simulated concentrations are taken into Bayesian inference to accomplish source term estimation (STE). The results show that the estimated results with high accuracy are obtained both in the reconstruction stage and in the prediction stage when using the fields obtained by DMD. Also, the efficiency of predicting the future flow by DMD is much higher than that by CFD simulation, suggesting that DMD can improve the efficiency of STE in some cases. As DMD uses a small number of dominant modes to synthesize the approximate fields with minor errors, it reduces the storage demand of flow information in STE. The sampling range and sampling resolution should be properly selected to ensure the accuracy of STE.