Unsaturated-Flow Simulation with Green Element Models

Flows in variably saturated media are of profound interest to numerical analysts, engineers, and scientists because of not only the challenge they pose as a result of their highly nonlinear constitutive relations but also their importance in many fields of engineering such as drainage, irrigation, hydrology, environmental, soil, and petroleum engineering. In this paper, the Picard and NewtonRaphson (N-R) algorithms are incorporated into the Green element method (GEM) to simulate these flows. The GEM offers a viable means of implementing the singular boundary integral theory so that the theory is more generally applicable and computationally efficient. Here GEM discretizes the integro-differential equation in space with suitable polygonal elements and in time with a difference scheme, and the system of nonlinear discretized element equations are linearized by the Picard and N-R algorithms. Calculations carried on three numerical examples of infiltration into unsaturated soils in two spatial dimensions indicate better convergence of the N-R algorithm than the Picard algorithm at comparable computational cost.