(A) study on the mass conservative numerical solutions of water flow and radionuclide transport in unsaturated porous media

Abstract

A theoretical model for soil water characteristic curves based on the effective pore radius distribution of the soil medium and capillarity law, was derived. Using this new curve and Mualem``s model, the evolution of unsaturated hydraulic conductivity and soil water diffusivity functions was explored. The equations for these three parameters are not expressed in analytic forms but as integrals. However, it was found that they reveal realistically the characteristics of unsaturated soils. Results of the new soil water characteristic and relative hydraulic conductivity relationship were compared with observed data of four soils with a wide range of soil physical properties. A fairly good agreement between the calculated curves and observed data was obtained irrespective of the scale of effective pore radius. The Galerkin finite element formulation is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solute in unsaturated porous media. Numerical approximations based on different forms of governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in unsaturated flow problem. Solutions given by simple Picard iteration method based on the h-based Richards equation yields large mass balance error and underestimation of infiltration depth. Usually the $\theta$-based form of Richards equation has not been used for unsaturated flow analysis because of the restriction in convergence. With the employment of ROMV (Restoration of Main Variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. When the ROMV concept is used, the discretized equations based on the standard h-based and $\theta$-based Richards equation can also be used for flow analysis in unsaturated soil media. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV me...