WSEAS Transactions on Heat and Mass Transfer
Print ISSN: 1790-5044, E-ISSN: 2224-3461
Volume 14, 2019
A Spectral Element Method for Unsaturated Flow in Porous Soils
Authors: , , , ,
Abstract: A spectral element method for one-dimensional transient water flow in unsaturated soils considering the pressure head form of the Richards flow equation is developed. The analyses were performed for pressure head flow in horizontal, upward and downward vertical unsaturated soils and for various hydraulic characteristics. The spectral element method combines the flexibility of the finite element method with the accuracy of spectral techniques. The spatial discretized equation was performed using the Galerkin weighted formulation combined with Legendre Gauss-Lobatto quadrature sets, whereas the temporal discretization is achieved by the Picard iteration procedure for soil moisture linearization combines with fully implicit time three-level scheme and two-level scheme with/without standard chord slope. The spectral element predictions compare well with exact results for pressure head flow in horizontal, upward and downward vertical unsaturated soils. The spectral element method results also compare favorably with the finite element method with mass-lumped approximation. Numerical experiments indicated that the spectral element method with standard chord slope schemes is mass conservative: the mass balance error is zero for different soil types considered. The numerical experiments also show that the spectral element method with three level scheme is more efficient that if using standard two-level scheme. Finally, it is found that the spectral element method is a convergent algorithm, which maintains high accuracy and less computational times. The present formulation of the spectral element method for unsaturated flow problem is original and it is of special importance for soil hydrology and groundwater management.
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Keywords: Hydraulic characteristics, numerical experiments, Richards flow equation, soil moisture prediction, spectral element method, unsaturated soils
Pages: 21-37
WSEAS Transactions on Heat and Mass Transfer, ISSN / E-ISSN: 1790-5044 / 2224-3461, Volume 14, 2019, Art. #3