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Insights on using the boundary integral SPH formulations to calculate Laplacians with Dirichlet boundaries.

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Title: Insights on using the boundary integral SPH formulations to calculate Laplacians with Dirichlet boundaries.
Authors: Boregowda, Parikshit1 (AUTHOR) boregopt@mail.uc.edu, Liu, Gui-Rong1 (AUTHOR)
Source: Engineering Analysis with Boundary Elements. Oct2023, Vol. 155, p652-667. 16p.
Subjects: Integrals, Laplacian operator, Hydrodynamics
Abstract: Handling boundary conditions in Smooth Particle Hydrodynamics (SPH) has been known as a challenging problem for a long time, especially when particle approximation is implemented for truncated kernels on the boundary. This work develops a novel particle consistent gradient formulation to impose the Dirichlet boundary condition on a Laplacian with boundary integrals. Boundary integral formulation allows the accurate imposition of boundary conditions without creating virtual particles to extend boundaries, as used in conventional SPH modeling practices. Here, boundary integral formulations are presented for Laplacian operators and the imposition of Dirichlet boundary conditions on arbitrary boundary shapes. We also explore using this particle consistent first-order derivative twice to evaluate the entire Laplacian. Further, the convergence characteristics of different Laplacian formulations with boundary integrals are discussed. Finally, numerical experiments solving explicit thermal and fluid problems are presented to demonstrate the robustness of various Laplacian operators for practical use. [ABSTRACT FROM AUTHOR]
Copyright of Engineering Analysis with Boundary Elements 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: 169929727
AccessLevel: 6
PubType: Periodical
PubTypeId: serialPeriodical
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  Data: Insights on using the boundary integral SPH formulations to calculate Laplacians with Dirichlet boundaries.
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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="%22Engineering+Analysis+with+Boundary+Elements%22">Engineering Analysis with Boundary Elements</searchLink>. Oct2023, Vol. 155, p652-667. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrodynamics%22">Hydrodynamics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Handling boundary conditions in Smooth Particle Hydrodynamics (SPH) has been known as a challenging problem for a long time, especially when particle approximation is implemented for truncated kernels on the boundary. This work develops a novel particle consistent gradient formulation to impose the Dirichlet boundary condition on a Laplacian with boundary integrals. Boundary integral formulation allows the accurate imposition of boundary conditions without creating virtual particles to extend boundaries, as used in conventional SPH modeling practices. Here, boundary integral formulations are presented for Laplacian operators and the imposition of Dirichlet boundary conditions on arbitrary boundary shapes. We also explore using this particle consistent first-order derivative twice to evaluate the entire Laplacian. Further, the convergence characteristics of different Laplacian formulations with boundary integrals are discussed. Finally, numerical experiments solving explicit thermal and fluid problems are presented to demonstrate the robustness of various Laplacian operators for practical use. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Analysis with Boundary Elements 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:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.enganabound.2023.07.011
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 652
    Subjects:
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Laplacian operator
        Type: general
      – SubjectFull: Hydrodynamics
        Type: general
    Titles:
      – TitleFull: Insights on using the boundary integral SPH formulations to calculate Laplacians with Dirichlet boundaries.
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            NameFull: Boregowda, Parikshit
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            NameFull: Liu, Gui-Rong
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          Dates:
            – D: 01
              M: 10
              Text: Oct2023
              Type: published
              Y: 2023
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              Value: 155
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            – TitleFull: Engineering Analysis with Boundary Elements
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