土壤水流与溶质耦合运移问题的混合元-迎风广义差分法研究

MIXED FINITE ELEMENT AND UPWIND GENERALIZED DIFFERENCE METHOD FOR COUPLED TRANSPORT MODELS OF UNSATURATED SOIL WATER FLOW AND SOLUTE

本文研究了一维非饱和土壤水流与溶质耦合运移问题的数学模型,建立了求其数值解的守恒混合元-迎风广义差分格式.对非线性土壤水分入渗方程,采用守恒混合元法进行离散模拟,同时得到了土壤含水量和水分通量;而对对流-扩散形式的溶质运移方程,利用迎风的广义差分法离散求解.且分析了解的存在唯一性,并讨论了误差估计.最后给出数值算例,模拟结果表明利用本文格式来求解非饱和土壤水流与溶质耦合运移问题是可靠的,且该格式具有稳定性和可实用性.

In this paper, we study a mathematical model for one-dimensional coupled transport problem of unsaturated soil water flow and solute and establish its numerical formulation. The paper develops the mixed finite element method for the approximation of unsaturated soil water flow equation and simultaneously products both the content and flux of soil moisture, and analyzes upwind generalized difference approximation of solute transport equation. The existence and uniqueness of its numerical solution are proved, and the error estimates are discussed. Finally, a numerical example is given. Moreover, it is also shown by numerical example that our numerical method to solve the unsaturated soil water problem is reliable, stable and practical.