Analysis of Galerkin-characteristics algorithm for variably saturated flow in porous media

Abstract

A nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow in porous media is considered. The numerical scheme consists of combining the Galerkin-characteristics with adjusted advection algorithm and an efficient linearization algorithm. The convergence of the numerical scheme is shown to be the weak solution. Computational experiments are carried out to illustrate and validate the behaviour and the capability of the schemes. The numerical results demonstrate that the proposed scheme gives good performance in convergence and accuracy.