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Hermite radial basis collocation method for unsaturated soil water movement equation. (English) Zbl 1427.74176

Summary: 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.

MSC:

74S25 Spectral and related methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Software:

HYDRUS
PDFBibTeX XMLCite
Full Text: DOI

References:

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