Reviews on numerical method for solving solute transport problems in the saturated porous media

After summarizing a number of literatures around the world about the numerical methods for solving the solute transport equation in the saturated porous media, there have been divided into three types of numerical methods, that is Eulerian method, Lagrangian method and EulerianLagrangian method (ELM), respectively. The essences and features in each type of numerical method are analyzed in detail. Besides, the paper suggests several tendencies in the development of numerical methods to solve advectiondispersion equation, and points out some problems that should be paid much attention in future. It is concluded that, the adaptive EulerianLagrangian method is one of most promising methods to solve advectiondispersion equation. Based upon Modified Method of Characteristics (MMOC), the ELM coupled highorder interpolation calculation in the sharp interface with low order interpolation in the smooth area will be an efficient solution and become popular method for advectiondispersion problems. As to convectiondominated diffusion problems, the most importance and key problem is how to search a new highaccuracy interpolation technique in the threedimensional irregular spatial element. Thus, this new interpolation technique based on irregular element can be used to depict the solute transport in the field studies, rather than limited to ideal model.