二维非饱和土壤水分运动问题的半离散有限体积元模拟  

SELF-DISCRETE FINITE VOLUME ELEMENT SIMULATION FOR TWO-DIMENSION UNSATURATED SOIL WATER FLOW PROBLEM

作　　者：李焕荣[1] 罗振东[2] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]华北电力大学数理学院,北京102206

出　　处：《计算数学》2011年第1期57-68,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10871217);重庆市科委自然科学基金(2010BB9252);重庆市教委科技基金(2011年)资助课题

摘　　要：本文利用基于重心对偶剖分的有限体积元法建立了二维非饱和土壤水分运动问题的数值逼近格式,讨论了离散有限体积元解的存在唯一性,并给出了最优误差估计的证明.最后给出数值算例,模拟结果表明,利用有限体积元格式来求解二维非饱和土壤水分运动问题是可靠的,且该格式具有稳定性和可实用性.A numerical model for a two-dimension unsaturated soil water flow equation is estab- lished with a finite volume element method. The existence and uniqueness of its discrete finite volume element solutions are proved, and the error estimates of the discrete finite volume element solutions are analyzed. And finally, a numerical example is given. More- over, it is also shown by numerical example that the finite volume element method to solve two-dimensional unsaturated soil water problem is reliable, stable and practical.

关 键 词：有限体积元法 数值模拟 误差估计 二维非饱和水流问题 

分 类 号：O241.82[理学—计算数学]