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A multiscale probabilistic collocation method for subsurface flow in heterogeneous media.

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Title: A multiscale probabilistic collocation method for subsurface flow in heterogeneous media.
Authors: Shi, Liangsheng, Zhang, Dongxiao, Lin, Lin, Yang, Jinzhong
Source: Water Resources Research; 2010, Vol. 46 Issue 11, pn/a-n/a, 18p
Subject Terms: MULTISCALE modeling, COLLOCATION methods, UNDERGROUND areas, STOCHASTIC analysis, PROBABILISTIC inference, STOCHASTIC differential equations, FINITE element method, HETEROGENEITY
Abstract: Owing to the spatial variability of the media properties, uncertainty quantification for subsurface flow and solute transport usually requires high-resolution simulations. In this work, a multiscale probabilistic collocation method (MSPCM) is developed for solving such problems in a computationally efficient manner. The subsurface flow problem is cast in a stochastic framework, and probabilistic collocation strategy is used to represent the original stochastic differential equation. The resulting equations are a set of decoupled deterministic equations with respect to collocation points. A multiscale finite element method is utilized to solve these deterministic problems on a coarse mesh. Coarse-scale basis functions are constructed on a field in which the conductivity varies spatially at each set of stochastic collocation points. The coarse-scale solution is then obtained by solving a modified coarse formulation that takes into account the fine-scale heterogeneity. The fine-scale solution is reconstructed after the coarse-scale solution is available. Since the PCM and multiscale finite element method are implemented at different levels, the MSPCM inherits their respective advantages, in which a stochastic problem is decomposed by fewer realizations and is solved on a coarser grid. The performance of the proposed method is demonstrated with numerical examples. The capability of MSPCM in reproducing the probability density functions (PDFs) of head and velocity is investigated. The numerical results show that the MSPCM with proper coarsening level is able to capture small-scale heterogeneity with a coarse mesh and to generate satisfactory probability density functions of head and velocity. [ABSTRACT FROM AUTHOR]
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  Data: A multiscale probabilistic collocation method for subsurface flow in heterogeneous media.
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  Data: <searchLink fieldCode="AR" term="%22Shi%2C+Liangsheng%22">Shi, Liangsheng</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Dongxiao%22">Zhang, Dongxiao</searchLink><br /><searchLink fieldCode="AR" term="%22Lin%2C+Lin%22">Lin, Lin</searchLink><br /><searchLink fieldCode="AR" term="%22Yang%2C+Jinzhong%22">Yang, Jinzhong</searchLink>
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  Data: Water Resources Research; 2010, Vol. 46 Issue 11, pn/a-n/a, 18p
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  Group: Su
  Data: <searchLink fieldCode="DE" term="%22MULTISCALE+modeling%22">MULTISCALE modeling</searchLink><br /><searchLink fieldCode="DE" term="%22COLLOCATION+methods%22">COLLOCATION methods</searchLink><br /><searchLink fieldCode="DE" term="%22UNDERGROUND+areas%22">UNDERGROUND areas</searchLink><br /><searchLink fieldCode="DE" term="%22STOCHASTIC+analysis%22">STOCHASTIC analysis</searchLink><br /><searchLink fieldCode="DE" term="%22PROBABILISTIC+inference%22">PROBABILISTIC inference</searchLink><br /><searchLink fieldCode="DE" term="%22STOCHASTIC+differential+equations%22">STOCHASTIC differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22FINITE+element+method%22">FINITE element method</searchLink><br /><searchLink fieldCode="DE" term="%22HETEROGENEITY%22">HETEROGENEITY</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Owing to the spatial variability of the media properties, uncertainty quantification for subsurface flow and solute transport usually requires high-resolution simulations. In this work, a multiscale probabilistic collocation method (MSPCM) is developed for solving such problems in a computationally efficient manner. The subsurface flow problem is cast in a stochastic framework, and probabilistic collocation strategy is used to represent the original stochastic differential equation. The resulting equations are a set of decoupled deterministic equations with respect to collocation points. A multiscale finite element method is utilized to solve these deterministic problems on a coarse mesh. Coarse-scale basis functions are constructed on a field in which the conductivity varies spatially at each set of stochastic collocation points. The coarse-scale solution is then obtained by solving a modified coarse formulation that takes into account the fine-scale heterogeneity. The fine-scale solution is reconstructed after the coarse-scale solution is available. Since the PCM and multiscale finite element method are implemented at different levels, the MSPCM inherits their respective advantages, in which a stochastic problem is decomposed by fewer realizations and is solved on a coarser grid. The performance of the proposed method is demonstrated with numerical examples. The capability of MSPCM in reproducing the probability density functions (PDFs) of head and velocity is investigated. The numerical results show that the MSPCM with proper coarsening level is able to capture small-scale heterogeneity with a coarse mesh and to generate satisfactory probability density functions of head and velocity. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Water Resources Research is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1029/2010WR009066
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: n/a
    Subjects:
      – SubjectFull: MULTISCALE modeling
        Type: general
      – SubjectFull: COLLOCATION methods
        Type: general
      – SubjectFull: UNDERGROUND areas
        Type: general
      – SubjectFull: STOCHASTIC analysis
        Type: general
      – SubjectFull: PROBABILISTIC inference
        Type: general
      – SubjectFull: STOCHASTIC differential equations
        Type: general
      – SubjectFull: FINITE element method
        Type: general
      – SubjectFull: HETEROGENEITY
        Type: general
    Titles:
      – TitleFull: A multiscale probabilistic collocation method for subsurface flow in heterogeneous media.
        Type: main
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          Name:
            NameFull: Shi, Liangsheng
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            NameFull: Zhang, Dongxiao
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            NameFull: Lin, Lin
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            NameFull: Yang, Jinzhong
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          Dates:
            – D: 01
              M: 11
              Text: 2010
              Type: published
              Y: 2010
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              Value: 00431397
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              Value: 46
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            – TitleFull: Water Resources Research
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