非饱和土壤水流问题基于POD 方法的降阶有限体积元格式及外推算法实现

利用特征投影分解(proper orthogonal decomposition, 简记为POD) 方法对非饱和土壤水流问题的经典有限体积元格式做降阶处理, 建立一种具有足够高精度维数较低的降阶有限体积元格式, 并给出这种降阶有限体积元解的误差估计和外推算法的实现, 最后用数值例子说明数值结果与理论结果是相吻合的. 进一步表明了基于POD 方法的降阶有限体积元格式对求解非饱和土壤水流问题数值解是可靠和有效的.

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

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.