Proper orthogonal decomposition-Galerkin projection method for quasi-two-dimensional laminar hydraulic transient flow

Abstract

The proper orthogonal decomposition (POD)-Galerkin projection method was applied to the quasi-two-dimensional (quasi-2D) water-hammer problem for achieving a model order reduction. The computation of the axial velocity profile requires a large number of numerical grids that is equal to the number of degrees of freedom (DOFs) in the quasi-2D water-hammer problem. To alleviate the large computational burden, POD was employed to reduce the number of DOFs of the axial velocity. The possibility of expression of the state variable using global basis vectors obtained with POD and the expression of the behavioural characteristics of the POD basis as a function of time were analysed. To verify its accuracy, the proposed method was validated using experimental data. The computational cost was compared for test cases. To estimate the efficiency, the computational complexities of the original model and the reduced-order model were evaluated and compared. Therefore, the overall performance - including the accuracy and efficiency - was proven.