Affect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation
Numerical simulation of the Richards’ equation in dynamically saturated soils keeps on being a difficult assignment because of its highly non-linear course of action. This is especially evident as soils approach saturation and the conduct of the principal partial differential equation changes from elliptic to parabolic. In this study, we developed a numerical model for solving Richards’ equation with regards to finite element approach in which pressure head-based scheme is proposed to approximate the governing equation, and mass-lumping techniques are used to maintain stability of the numerical simulation. Dynamic adaptive time stepping procedure is implemented in the Picard and Newton linearization schemes. The robustness and accuracy of the numerical model were demonstrated through simulation of two difficult tests, including sharp moisture front that infiltrates into the soil column with time dependent boundary condition and flow into a layered soil with variable initial conditions. The two cases introduced feature various parts of the presentation of the two iterative strategies and the various components that can influence their convergence and efficiency, spatial and temporal discretization, convergence error norm, time weighting, conductivity and moisture content attributes and the degree of completely saturated regions in the soil. Numerical accuracy, mass balance nature and iteration efficiency of Picard and Newton techniquesare compared using different step sizes and spatial resolutions. Results demonstrated that the presented algorithm is vigorous and exact in simulating variably saturated flows and outcomes of some hydrologic process simulations are affected significantly by the spatial and temporal grid scales. Hence it is proposed that the strategy can be adequately actualized and used in numerical models of Richards’ equation.
