饱和水流溶质运移问题数值解法综述

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

本文总结了饱和水流中溶质运移方程求解的各种数值方法,分析各种方法的本质特征以及各自的优缺点,并指出了求解对流 弥散方程的各种数值方法的研究进展和值得重视的问题。研究结果表明,自适应欧拉 拉格朗日法(ELM)是溶质运移问题中,求解对流 弥散方程是比较有发展潜力的方法之一。以MMOC法为基础在陡峰值高价插值和其它区域低价插值相结合的ELM法,将是未来发展的趋势。而寻求非规则网格上高精度的空间单元插值模式,已开始成为求解对流问题数值方法研究的重点和关键问题。

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.