| 孟广伟,李霄琳,周立明.裂隙岩体渗流的光滑多尺度随机配点法[J].水利学报,2015,46(1): |
| 裂隙岩体渗流的光滑多尺度随机配点法 |
| Smoothed multiscale stochastic collocation method for flow in fractured rocks |
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| DOI： |
| 中文关键词: 光滑多尺度随机配点法 双重介质模型 多尺度有限元法 梯度光滑技术 随机配点法 |
| 英文关键词: smoothed multiscale stochastic collocation method dual porosity model multiscale finite element method gradient smoothing technique stochastic collocation method |
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| 中文摘要: |
| 针对非均质裂隙岩体的随机渗流问题，提出光滑多尺度随机配点法。其基本思想是基于稀疏网格随机配点法将随机问题简化为相应配点处的非耦合确定性问题，利用有限全局信息构造多尺度基函数，捕捉材料的非均质性和流体流动的耦合关系，引入梯度光滑技术组装粗网格单元相关矩阵，将小尺度非均质信息体现到大尺度上，由此在粗网格上对问题进行求解。同传统多尺度随机配点法相比，光滑多尺度随机配点法在组装粗网格单元相关矩阵时将研究区域的内积分转化为边界积分，无需求解基函数的连续形式及导数，简化了程序，并且使有限元系统得到一定程度的“软化”。数值算例结果表明：光滑多尺度随机配点法比传统多尺度随机配点法具有更高的精度和效率。 |
| 英文摘要: |
| A smoothed multiscale stochastic collocation method （SMsSCM） was proposed to solve stochastic problems of fluid flow in heterogeneous fractured rocks. The basic idea of this method is to simplify the stochastic problem into a series of deterministic problems at the collocation points based on the sparse grid stochastic collocation method， then construct multiscale basis functions using limited global information to demonstrate material heterogeneity and coupled relationship of fluid flow in porous and fractured media，and finally solve the coarse scale problem by reflecting the small scale heterogeneity on large scale material， with the adoption of gradient smoothing technique when assembling the coarse element correlation matrix. Comparing with the traditional multiscale stochastic collocation method， SMsSCM transforms inner integral of the interest domain into boundary integral without solving the continuous form and derivatives of the basis functions when assembling the correlation matrix of coarse element. Correspondingly， the programming has been simplified and the finite element system is fairly softened. The results indicate that SMsSCM is more accurate and efficient than the traditional multiscale stochastic collocation method. |
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