A POD-based Reduced-order Finite Difference Extrapolating Scheme For Double-diffusive Natural Convection In Porous Medium

Proper orthogonal decomposition(POD)method is an effective reduction method.In this paper,we use POD method to reduce the order of the classical finite difference scheme for double-diffusive natural convection in porous medium,and we establish a POD-based reduced-order finite difference extrapolating scheme containing very few unknowns but holding sufficient high accuracy for the double-diffusive natural convection in porous medium.First,the POD method is used to extract the snapshot matrix formed from the first few instantaneous finite difference solutions as a set of POD base by means of singular value decomposition based on the classical finite difference scheme for the double-diffusive natural convection in porous medium.Next,we can establish a reduced-order extrapolation finite difference iterative scheme for the double-diffusive natural convection in porous medium with the POD basis.Then,we analyze the stability and convergence of the reduced-order extrapolation finite difference iterative format.Furthermore,we introduce the algorithm steps of POD-based reduced-order finite difference scheme for the double-diffusive natural convection in porous medium.Finally,some numerical examples are used to demonstrate that the results of numerical calculation accord with the theoretical analysis result.Further,the feasibility and effectiveness of the reduced-order extrapolation finite difference iterative scheme for the double-diffusive natural convection in porous medium is verified.