非饱和水流问题的迎风差分法及其数值模拟  

Upwind Finite Difference Methods and Numerical Simulations for the Unsaturated Water Flow Problem

作　　者：张志娟[1] 袁益让[2] 

机构地区：[1]中国工程物理研究院研究生部,北京100088 [2]山东大学数学与系统科学学院,济南250100

出　　处：《应用数学学报》2009年第3期385-399,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家重点基础研究发展规划项目(1999032803);国家自然科学基金(10370252;10271066);教育部博士点基金资助项目(20030422047)

摘　　要：本文考察了非饱和水流问题模型方程的守恒型迎风差分法.我们基于有限体积方法建立的非饱和流动的守恒形式,分别提出了一阶和二阶迎风差分格式,并对差分格式进行了误差估计,给出了收敛性定理.最后,数值模拟验证了计算格式的有效性.Abstract In this paper, the conservative upwind finite difference methods for an unsaturated soil water flow equation are studied. Based on the conservative form of the flow equation, both one-order and two-order upwind finite difference scheme error estimates of the schemes are numerical simulations are shown to are proposed. The analyzed and convergence results are given. Finally, verify the efficiency of the proposed schemes.

关 键 词：非饱和水流 迎风 有限差分 误差估计 数值模拟 

分 类 号：O241.82[理学—计算数学]