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An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

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Název: An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations
Autoři: George C. Bourantas, Benjamin F. Zwick, Grand R. Joldes, Vassilios C. Loukopoulos, Angus C. R. Tavner, Adam Wittek, Karol Miller
Zdroj: Fluids, Vol 4, Iss 3, p 164 (2019)
Informace o vydavateli: MDPI AG
Rok vydání: 2019
Sbírka: Directory of Open Access Journals: DOAJ Articles
Témata: transient incompressible Navier-Stokes, meshless point collocation method, stream function-vorticity formulation, strong form, explicit time integration, Thermodynamics, QC310.15-319, Descriptive and experimental mechanics, QC120-168.85
Popis: We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.
Druh dokumentu: article in journal/newspaper
Jazyk: English
Relation: https://www.mdpi.com/2311-5521/4/3/164; https://doaj.org/toc/2311-5521; https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
DOI: 10.3390/fluids4030164
Dostupnost: https://doi.org/10.3390/fluids4030164
https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
Přístupové číslo: edsbas.77F6352
Databáze: BASE
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  – Url: https://doi.org/10.3390/fluids4030164#
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  Data: An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations
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  Data: <searchLink fieldCode="AR" term="%22George+C%2E+Bourantas%22">George C. Bourantas</searchLink><br /><searchLink fieldCode="AR" term="%22Benjamin+F%2E+Zwick%22">Benjamin F. Zwick</searchLink><br /><searchLink fieldCode="AR" term="%22Grand+R%2E+Joldes%22">Grand R. Joldes</searchLink><br /><searchLink fieldCode="AR" term="%22Vassilios+C%2E+Loukopoulos%22">Vassilios C. Loukopoulos</searchLink><br /><searchLink fieldCode="AR" term="%22Angus+C%2E+R%2E+Tavner%22">Angus C. R. Tavner</searchLink><br /><searchLink fieldCode="AR" term="%22Adam+Wittek%22">Adam Wittek</searchLink><br /><searchLink fieldCode="AR" term="%22Karol+Miller%22">Karol Miller</searchLink>
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  Data: Fluids, Vol 4, Iss 3, p 164 (2019)
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  Data: MDPI AG
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  Label: Publication Year
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  Data: 2019
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  Data: <searchLink fieldCode="DE" term="%22transient+incompressible+Navier-Stokes%22">transient incompressible Navier-Stokes</searchLink><br /><searchLink fieldCode="DE" term="%22meshless+point+collocation+method%22">meshless point collocation method</searchLink><br /><searchLink fieldCode="DE" term="%22stream+function-vorticity+formulation%22">stream function-vorticity formulation</searchLink><br /><searchLink fieldCode="DE" term="%22strong+form%22">strong form</searchLink><br /><searchLink fieldCode="DE" term="%22explicit+time+integration%22">explicit time integration</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamics%22">Thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22QC310%2E15-319%22">QC310.15-319</searchLink><br /><searchLink fieldCode="DE" term="%22Descriptive+and+experimental+mechanics%22">Descriptive and experimental mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22QC120-168%2E85%22">QC120-168.85</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.
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  Data: https://www.mdpi.com/2311-5521/4/3/164; https://doaj.org/toc/2311-5521; https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
– Name: DOI
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  Data: 10.3390/fluids4030164
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  Data: https://doi.org/10.3390/fluids4030164<br />https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
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        Value: 10.3390/fluids4030164
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: transient incompressible Navier-Stokes
        Type: general
      – SubjectFull: meshless point collocation method
        Type: general
      – SubjectFull: stream function-vorticity formulation
        Type: general
      – SubjectFull: strong form
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      – SubjectFull: explicit time integration
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      – SubjectFull: Thermodynamics
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      – SubjectFull: QC310.15-319
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      – SubjectFull: Descriptive and experimental mechanics
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      – SubjectFull: QC120-168.85
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      – TitleFull: An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations
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