A reduced-order finite volume element formulation based on POD method and implementation of its extrapolation algorithm for unsaturated soil water flow equation

Abstract

A proper orthogonal decomposition(POD) method is used to treat a classical finite volume element(FVE) formulation for unsaturated soil water flow problem.A reduced-order FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional unsaturated soil water flow problem is established and the error estimates between the reduced-order FVE solutions and the classical FVE solutions and the implementation of extrapolation algorithm for solving the reduced-order FVE formulation are provided.Some numerical examples illustrate that the results of numerical computation are consistent with theoretical conclusions.Moreover,it is shown that the reduced-order FVE formulation based on POD method is feasible and efficient for solving two-dimensional unsaturated soil water flow problem.