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On the accuracy of SPH formulations with boundary integral terms.

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Title: On the accuracy of SPH formulations with boundary integral terms.
Authors: Boregowda, Parikshit1 (AUTHOR) boregopt@mail.uc.edu, Liu, Gui-Rong1 (AUTHOR)
Source: Mathematics & Computers in Simulation. Aug2023, Vol. 210, p320-345. 26p.
Subjects: Correction factors, Integrals, Numerical analysis, Hydrodynamics
Abstract: Handling boundaries in smoothed particle hydrodynamics (SPH) is believed to be one of the most critical problems in studies and applications of SPH. In the last two decades, excellent progress has been made in exploring the evaluation of the boundary integral terms directly to improve SPH approximation on the boundary. However, because of the fundamental difficulties, formulations in this regard are difficult to be made consistent when using SPH particle approximations, which significantly affect the solution accuracy. In this work, an intensive investigation is made in carefully analyzing the order of accuracy of the SPH approximation when boundary integral terms are included. Both kernel consistent and particle consistent boundary integral formulations of SPH are examined in great detail. Notably, a novel particle consistent boundary integral formulation for first-order derivatives is derived. An approximation of this new formulation, which is weakly consistent, is also discussed. The theoretical analysis and numerical experiments show that the SPH with particle consistent boundary integral formulation outperforms significantly in terms of accuracy compared to the correction factors used in traditional SPH implementations. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. 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.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 163423827
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  Data: On the accuracy of SPH formulations with boundary integral terms.
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  Data: <searchLink fieldCode="AR" term="%22Boregowda%2C+Parikshit%22">Boregowda, Parikshit</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> boregopt@mail.uc.edu</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Gui-Rong%22">Liu, Gui-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Aug2023, Vol. 210, p320-345. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Correction+factors%22">Correction factors</searchLink><br /><searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrodynamics%22">Hydrodynamics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Handling boundaries in smoothed particle hydrodynamics (SPH) is believed to be one of the most critical problems in studies and applications of SPH. In the last two decades, excellent progress has been made in exploring the evaluation of the boundary integral terms directly to improve SPH approximation on the boundary. However, because of the fundamental difficulties, formulations in this regard are difficult to be made consistent when using SPH particle approximations, which significantly affect the solution accuracy. In this work, an intensive investigation is made in carefully analyzing the order of accuracy of the SPH approximation when boundary integral terms are included. Both kernel consistent and particle consistent boundary integral formulations of SPH are examined in great detail. Notably, a novel particle consistent boundary integral formulation for first-order derivatives is derived. An approximation of this new formulation, which is weakly consistent, is also discussed. The theoretical analysis and numerical experiments show that the SPH with particle consistent boundary integral formulation outperforms significantly in terms of accuracy compared to the correction factors used in traditional SPH implementations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. 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: 10.1016/j.matcom.2023.03.018
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 26
        StartPage: 320
    Subjects:
      – SubjectFull: Correction factors
        Type: general
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Hydrodynamics
        Type: general
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      – TitleFull: On the accuracy of SPH formulations with boundary integral terms.
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            NameFull: Boregowda, Parikshit
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            NameFull: Liu, Gui-Rong
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            – D: 01
              M: 08
              Text: Aug2023
              Type: published
              Y: 2023
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              Value: 210
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            – TitleFull: Mathematics & Computers in Simulation
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