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Estimating finite difference block equivalent hydraulic conductivity for numerically solving the Richards' equation

Feng, Chih-Yung, Lee, Tim Hau, Lee, Wen Sen, Chen, Chu-Hui
Hydrological processes 2007 v.21 no.26 pp. 3587-3600
Richards' equation, hydraulic conductivity, hydrologic models, infiltration (hydrology), simulation models
A method is proposed for calculating the equivalent hydraulic conductivity (EHC) within a finite difference block (FDB). Application of the constant-flux assumption of Darcy's Law, the EHC equals to the integration of effective hydraulic conductivity (Kw) as a function of pressure head (hw) divided by the head difference at the ends of the FDB. Error analysis show that the constant-flux (CF) EHC estimates are better than those computed by the commonly used arithmetic-mean (AM), geometric-mean (GM), and harmonic-mean (HM) techniques. CF EHC results are even more superior at larger interblock head difference situations.Simulations of water infiltration experiments show that simulations using the CF EHC or AM or GM weighting technique have only slight difference while applying the Neumann type boundary condition at the ground surface. In case of the Dirichlet type boundary condition, however, the CF EHC is superior to the other two in correctly estimating the depth of infiltration while enlarging the grid size. Therefore, it is recommended to adopt the CF EHC with a larger grid size to the more stable and more efficient results.