Reduced-order finite difference extrapolation model based on proper orthogonal decomposition for two-dimensional shallow water equations including sediment concentration

In this study, we employ a proper orthogonal decomposition (POD) method to establish a POD-based reduced-order finite difference (FD) extrapolating model with very few degrees of freedom for two-dimensional shallow water equations that include the sediment concentration. We provide estimates of the error between the accurate solution and classical FD solutions, as well as those between the accurate solution and the POD-based reduced-order FD solutions. Moreover, we present two numerical simulation experiments to demonstrate that the POD-based reduced-order FD extrapolating model can greatly reduce the computational load. Thus, we validate both the feasibility and efficiency of the POD-based reduced-order FD extrapolating model.