三维地下水流随机分析的配点法

The collocation method for stochastic analysis of three-dimensional groundwater flow

提出三维地下水不确定分析的随机配点法,比较了张量积配点法(TPCM)、Smolyak配点法(SmCM)、Stroud-2配点法(StCM)和概率配点法(PCM)等4种配点法的基本原理。其渗透系数场和水头场分别被表示为Karhunen-Loeve展开和多项式展开的形式;初始随机偏微分方程被转化为在相应配点上的确定性方程。进一步建立了基于Modflow-2000的随机模型,讨论了以上不同算法的计算精度及计算成本。分析结果表明,配点法可充分继承现有模拟软件或代码的求解功能,配点的选取方法决定了其计算成本,SmCM具有最高的计算精度,但StCM具有最好的性价比。

The stochastic collocation method is used to qualify the uncertainty of the three-dimensional groundwater flow. The basic ideas about the tensor product collocation method（TPCM）, Smolyak collocation method （SmCM） , Stround-2 collocation method （StCm） , and probability collocation method （PCM）are compared. The conductivity field and hydraulic field are represented by Karhunen-Loeve expansion and polynomial expansion, respectively. The original stochastic partial differential equation is transformed into a series of deterministic equation at the collocation points. The numerical model based on the Modflow-2000 is established, and the accuracy and computational cost are analyzed. The results show that the collocation capitalizes the numerical functionality of the existing codes or software. The computational cost differs for different types of collocation method. The SmCM has highest accuracy, while the StCM own the best cost performance ratio.