A POD-based reduced-order finite difference extrapolating model with fully second-order accuracy for non-stationary Stokes equations

A proper orthogonal decomposition (POD) reduced-order finite difference (FD) extrapolating model is established for the channel flow with local expansion denoted by non-stationary Stokes equations. The POD-based reduced-order numerical model to produce the solutions on the time span [T0, T] (T0 ≪ T) are obtained by extrapolation and iteration from the very short time span [0, T0] information. The guides to choose the number of POD basis and renew POD basis are provided, and an implementation for solving the POD-based reduced-order FD extrapolating model is given. Some numerical experiments are used to show that the POD-based reduced-order FD extrapolating model is feasible and efficient for simulating the channel flow with local expansion.