论文部分内容阅读
The proper orthogonal decomposition(POD)was introduced by Lumley in 1967 as an objective definition of coherent structures.The POD is also known as the Method of Snapshots,the Karhunen-Loeve expansion,principal component analysis(PCA),singular value decomposition(SVD)and other names.The main objective in proper orthogonal decomposition(POD)is to obtain an optimal low dimensional basis for representing an ensemble of high-dimensional experimental or simulation data.This basis is optimal in the sense that a truncated series expansion of the data in this basis has a smaller mean square truncation error than a representation by any other basis.A number of practical engineering problems require the repeated simulation of Navier-Stokes equation for a large number of parameter values.To make many of these problems tractable,reduced-order modelling has been used to minimize the simulation requirements.The proper orthogonal decomposition(POD)coupling with Galerkin projection is the prevailing method in the model reduction of Navier-Stokes equation.However,the reduced order model may lose its accuracy as some parameters changed.A global POD reduced order model is proposed in this paper which is valid as Reynolds number changed in a certain region.This is accomplished by generating several numerical simulations at various values of the parameter range and assembling all data into a larger snapshot matrix.The POD method is then applied to the identification of a basis that minimizes the error across all solution samples in the snapshot matrix.The Navier-Stokes equation is first numerically solved by characteristic-based-split(CBS)algorithm,obtaining some numerical results by the snapshot method.Then a global optimal basis is constructed using proper orthogonal decomposition method in Reynolds number from 500 to 3500.The global reduced order model is derived by projection the Navier-Stokes equation to the global pod basis.Some Numerical experiments performed on the flow around an airfoil over the region of Reynolds numbers demonstrate the effectiveness of this global ROM method.