A predictor-corrector second-order time-stepping schemes for solving water flow and solute transport in unsaturated porous media

Abstract

The objective of this study is to numerically solve the coupled system of water flow and solute transport in unsaturated porous media using a noniterative predictor-corrector temporal scheme for the Richards equation and a semi-implicit temporal scheme for the advection dispersion equation (ADE). The standard and non-standard Galerkin finite element methods are used for spatial discretization. Three different techniques are proposed to calculate the pressure head in the Levrett equation. These techniques are different in terms of the chosen shape functions in the finite element space. The proposed schemes offer distinct advantages due to the linear nature of the resulting system, facilitating easy implementation and avoiding the issues associated with the divergence of iterative schemes. We evaluated the robustness and efficacy of the suggested methods using a computational experiment to simulate soil salinity and water flow in loamy soil. We compared it with data found in the literature. The results provide compelling evidence confirming the proposed methods’ effectiveness and stability.