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Analysis of transient free surface seepage flow using numerical manifold method.

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Title: Analysis of transient free surface seepage flow using numerical manifold method.
Authors: Jia, Zhen1 (AUTHOR), Zheng, Hong1 (AUTHOR) hzheng@whrsm.ac.cn
Source: Computers & Mathematics with Applications. Jul2025, Vol. 189, p129-143. 15p.
Subjects: Partition of unity method, Free surfaces, Finite element method, Transient analysis, Degrees of freedom
Abstract: In the analysis of transient seepage flow with free surfaces, not only the free surfaces but also the boundary conditions vary with time, introducing significant challenges to those traditional mesh-based numerical methods. Although the numerical manifold method (NMM) has shown great advantages in tracking time-independent free surface seepage flow due to its dual cover systems – the mathematical cover and the physical cover, in the analysis of transient free surface seepage flow it will encounter the inheritance issue of degrees of freedom between two consecutive time steps, which is still an open issue for all the partition of unity based methods such as the extended finite element method (XFEM) and the generalized finite element method (GFEM). It is shown in this study that the issue can be easily overcome if a different discretization order from the classical discretization order is adopted, i.e. , time discretization is carried out before to spatial discretization. By analyzing typical transient seepage examples, the positions of the transient free surfaces predicted by the proposed method are excellently consistent with analytical solutions or experimental results. At the same time, it also points out the errors and possible consequences of some literature concerning the handling of sudden drops in upstream water level. The results demonstrate that the proposed procedure not only effectively predicts the evolution of free surfaces but also accurately addresses transient seepage problems, including those with complex drainage systems. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 185077196
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  Data: Analysis of transient free surface seepage flow using numerical manifold method.
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  Data: <searchLink fieldCode="AR" term="%22Jia%2C+Zhen%22">Jia, Zhen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zheng%2C+Hong%22">Zheng, Hong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hzheng@whrsm.ac.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Jul2025, Vol. 189, p129-143. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Free+surfaces%22">Free surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Transient+analysis%22">Transient analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In the analysis of transient seepage flow with free surfaces, not only the free surfaces but also the boundary conditions vary with time, introducing significant challenges to those traditional mesh-based numerical methods. Although the numerical manifold method (NMM) has shown great advantages in tracking time-independent free surface seepage flow due to its dual cover systems – the mathematical cover and the physical cover, in the analysis of transient free surface seepage flow it will encounter the inheritance issue of degrees of freedom between two consecutive time steps, which is still an open issue for all the partition of unity based methods such as the extended finite element method (XFEM) and the generalized finite element method (GFEM). It is shown in this study that the issue can be easily overcome if a different discretization order from the classical discretization order is adopted, i.e. , time discretization is carried out before to spatial discretization. By analyzing typical transient seepage examples, the positions of the transient free surfaces predicted by the proposed method are excellently consistent with analytical solutions or experimental results. At the same time, it also points out the errors and possible consequences of some literature concerning the handling of sudden drops in upstream water level. The results demonstrate that the proposed procedure not only effectively predicts the evolution of free surfaces but also accurately addresses transient seepage problems, including those with complex drainage systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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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    Identifiers:
      – Type: doi
        Value: 10.1016/j.camwa.2025.04.011
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 129
    Subjects:
      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Free surfaces
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Transient analysis
        Type: general
      – SubjectFull: Degrees of freedom
        Type: general
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      – TitleFull: Analysis of transient free surface seepage flow using numerical manifold method.
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            NameFull: Jia, Zhen
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            NameFull: Zheng, Hong
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          Dates:
            – D: 01
              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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            – Type: issn-print
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              Value: 189
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            – TitleFull: Computers & Mathematics with Applications
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