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.

Keywords:

• Variably saturated flow
• Nonlinear parabolic equation
• Convection dominant diffusion
• Characteristics based method
• MMOCAA

Acknowledgements

The author wishes to thank the referees for their useful comments. The author also thanks Professor J. Vigo-Aguiar for his encouragement.