A reduced-order finite difference extrapolation algorithm based on POD technique for the non-stationary Navier–Stokes equations

In this paper, a proper orthogonal decomposition (POD) technique is used to establish a reduced-order finite difference (FD) extrapolation algorithm with lower dimensions and sufficiently high accuracy for the non-stationary Navier–Stokes equations, and the error estimates between the reduced-order FD solutions and the classical FD solutions and the implementation for solving the reduced-order FD extrapolation algorithm are provided. Two numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order FD extrapolation algorithm based on POD method is feasible and efficient for solving the non-stationary Navier–Stokes equations.