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首页> 外文期刊>Water resources research >Stochastic finite element method for probabilistic analysis of flow and transport in a three-dimensional heterogeneous porous formation
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Stochastic finite element method for probabilistic analysis of flow and transport in a three-dimensional heterogeneous porous formation

机译：三维非均质多孔地层中流动和输运概率分析的随机有限元方法

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摘要

A probabilistic study is attempted to analyze the flow and transport in a three-dimensional (3-D) porous formation where the governing parameters are varying randomly in space. It is assumed that the soil parameters, namely, hydraulic conductivity, dispersivity, molecular diffusion, porosity, sorption coefficient, and decay rate, are random fields. A stochastic finite element method (SFEM), which is based on perturbation technique, is developed. The method developed here uses an alternate approach for obtaining improved computational efficiency. The derivatives of the concentration with respect to random parameters are obtained by using the derivatives of local matrices instead of global matrices. This approach increases the computational efficiency of the present method by several orders with respect to standard SFEM. Both accuracy and computational efficiency of this method are compared with that of commonly used Monte Carlo simulation method (MCSM). It is observed that for moderate values of coefficient of variations of the random parameters the mean and standard deviation match reasonably well with MCSM results. Using this method the excessive computational effort required by MCSM can be avoided. In the present study both 1-D as well as 3-D problems are solved to show the advantages of SFEM over MCSM. The correlation scale of the random field is found to be an important parameter. For the range of this parameter studied here it is found that as correlation scale increases, the standard deviation increases. The results obtained for two particular problems in this study show that the coefficient of variation of concentration is higher for the 1-D problem than the 3-D problem.
机译：尝试进行概率研究来分析三维（3-D）多孔地层中的流动和输运，其中控制参数在空间中随机变化。假定土壤参数，即水力传导率，分散性，分子扩散，孔隙度，吸附系数和衰减率是随机场。提出了一种基于摄动技术的随机有限元方法。此处开发的方法使用另一种方法来获得改进的计算效率。相对于随机参数的浓度的导数是通过使用局部矩阵的导数而不是全局矩阵来获得的。这种方法相对于标准SFEM，将本方法的计算效率提高了几个数量级。将这种方法的准确性和计算效率与常用的蒙特卡洛模拟方法（MCSM）进行了比较。可以看出，对于适度的随机参数变化系数，平均值和标准偏差与MCSM结果相当吻合。使用这种方法可以避免MCSM所需的过多计算工作量。在本研究中，一维和3-D问题都得到解决，以显示SFEM优于MCSM。发现随机场的相关标度是重要的参数。对于这里研究的该参数的范围，发现随着相关标度的增加，标准偏差也增加。在此研究中，针对两个特定问题获得的结果表明，一维问题的浓度变化系数高于三维问题。

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