Affect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation
richards equation; finite element; variably saturated flow; spatial discretization; temporal discretization
Abstract
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.
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2020-11-23
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