Hermite Radial Basis Collocation Method for Unsaturated Soil Water Movement Equation

Jiao Wang,Xinqiang Qin,Lijun Su

doi:10.1155/2018/8298915

Jiao Wang, Xinqiang Qin + Show 1 more

Open Access

https://doi.org/10.1155/2018/8298915

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Abstract

Due to the nonlinear diffusion term, it is hard to use the collocation method to solve the unsaturated soil water movement equation directly. In this paper, a nonmesh Hermite collocation method with radial basis functions was proposed to solve the nonlinear unsaturated soil water movement equation with the Neumann boundary condition. By preprocessing the nonlinear diffusion term and using the Hermite radial basis function to deal with the Neumann boundary, the phenomenon that the collocation method cannot be used directly is avoided. The numerical results of unsaturated soil moisture movement with Neumann boundary conditions on the regular and nonregular regions show that the new method improved the accuracy significantly, which can be used to solve the low precision problem for the traditional collocation method when simulating the Neumann boundary condition problem. Moreover, the effectiveness and reliability of the algorithm are proved by the one-dimensional and two-dimensional engineering problem of soil water infiltration in arid area. It can be applied to engineering problems.

Highlights

Unsaturated soil moisture movement [1] referring to the water in the soil is not filled with all the pores of the water movement, and it is an important fluid movement form of porous media
The numerical results of unsaturated soil moisture movement with Neumann boundary conditions on the regular and nonregular regions show that the new method improved the accuracy significantly, which can be used to solve the low precision problem for the traditional collocation method when simulating the Neumann boundary condition problem
Since soil water movement equation is a nonlinear partial differential equation, the existence of nonlinear diffusion terms often leads to the collocation method is hard to be used in discreting partial differential equations directly

Summary

Introduction

Unsaturated soil moisture movement [1] referring to the water in the soil is not filled with all the pores of the water movement, and it is an important fluid movement form of porous media. The Hermite radial basis function combined with the collocation method was used to solve the unsaturated soil water movement equation with Neumann boundary condition. Hermite interpolation of the field quantity function u(x) in the local support region near the point x(x, z) is approximated by the RBFs and its derivative at the Neumann boundary which can be expressed as [22]. The nonlinear equations about the initial-boundary value problem of differential equation are obtained

Hermite Radial Basis Collocation Scheme

Results and Discussion

Conclusions