Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils

Simulations of transient, unsaturated vertical flow in different initially dry homogeneous soils using Richards' equation suggest that, for a relatively coarse numerical grid, there is no universal weighting scheme to estimate interblock conductivities capable of giving an accurate resolution of the resulting steep wetting fronts, except for the scheme associated with the Kirchhoff transformation (KT). The principal drawback of KT is that it can hardly be applied to heterogeneous soils. A new asymptotic weighting (AW) scheme, based on the asymptotic behavior of the hydraulic conductivity function in the vicinity of residual saturation, is proposed. Numerical tests demonstrate that the AW scheme describes wetting fronts in homogeneous soils nearly as accurately as a scheme based on KT. Applicability and robustness of the AW scheme for simulating water infiltration into heterogeneous soils having substantial vertical variation of hydraulic properties are also demonstrated. Extension of the proposed scheme to higher dimensions is straightforward.