Retrieval Of Initial Condition For Navier-Stokes Equations Via DEIM-based PC-EnKF Method

The parameter retrieval,as an important study direction,has already attracted much more attention in science and engineering.The parameter estimation intends to reduce the uncertainty of input parameter of physical system by using the existing observation data with the suitable method.However,the ill-posed essence of the parameter retrieval generally make it much more difficult to study,some limitations for further research are thus encountered.Aiming to the retrieval of initial conditions,this thesis introduces the discrete empirical interpolation method in the framework of the polynomial chaos ensemble Kalman filter data assimilation,and proposes a new idea to make a reconstruction for the initial conditions.The detailed procedure includes: the determination of the spatial interpolation point,the estimation of the initial value on the interpolation locations using the optimal observations,and the reconstruction of initial conditions in the full space.The method proposed here not only extends the further application of DEIM in solving inverse problem,and also contributes to the development for the existing theory of ensemble Kalman filter data assimilation.The current study takes the reconstruction of the initial field of the Navier-Stokes equations as an example to illustrate the effectness of our method.The experimental results show that the DEIM-based PC-EnKF interpolation data assimilation method is feasible and effective,and a better reconstruction for the initial field is arrived at.Comparing with the initial guess for the initial field,the uncertainty has a substantial reduction.When running the numerical model,the prediction result with the reconstructed initial field is almost the same as that with the original reference(or true)initial field.