地下水模型的Neumann展开Monte-Carlo随机有限元法

NEUMANN EXPANSIONS MONTE-CARLO STOCHASIC FINITE ELEMENT METHOD FOR GROUNDWATER MODELS

讨论了求解地下水模型（水流模型和水质模型）的Ｎｅｕｍａｎｎ展开Ｍｏｎｔｅ－Ｃａｒｌｏ随机有限元法。从基本的随机变量入手，避免了过程中随机变量的增多问题，给出结点水头（浓度）的均值、方差和水头在某区间的概率计算方法；改进了矩阵求逆的效率，对输入随机变量较多、随机变量变异较大的非稳定地下水问题特别有效。同时选取二维承压地下水水流问题（有解析解）作为例子，进行了随机数值模拟实验。

Neumann Expansions Monte Carlo stochastic finite element method(NMCSFEM) for ground water models is discussed .The computing methods of the mean value 、the variance and probability in some interval of water head at each node are given.Neumann expansions is introduced into the research field of groudwater to improve computational efficiency.When number of input stochastic variables is large,and the variances of input stochastic variables are big,NMCSFEM is best choice .The 2 D confined groundwater flow example (with an analytical solution) is used for stochastic numerical test.