Finite element formulation for filling a thin section cavity

David T. Gethin, Shahrir Abdullah

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Presents a quasi three-dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no-slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air-filled (empty) surfaces. The formulation was developed to analyze the sections which lie in the xy-plane or may be oriented arbitrarily in three-dimensional space. Solves the discretized thickness-integrated finite element flow equations by using the implicit mixed velocity-pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three-dimensional thin section cavities of irregular shape.

Original languageEnglish
Pages (from-to)344-366
Number of pages23
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume7
Issue number4
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Cavity
Finite Element
Slip Condition
Formulation
Three-dimensional
Fluids
Volume of Fluid Method
Free Surface
Irregular
Transverse
Air
Fluid
Numerical Examples
Demonstrate
Model

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Applied Mathematics

Cite this

Finite element formulation for filling a thin section cavity. / Gethin, David T.; Abdullah, Shahrir.

In: International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 7, No. 4, 1997, p. 344-366.

Research output: Contribution to journalArticle

@article{aa3379bf60e34792a560252d92d84473,
title = "Finite element formulation for filling a thin section cavity",
abstract = "Presents a quasi three-dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no-slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air-filled (empty) surfaces. The formulation was developed to analyze the sections which lie in the xy-plane or may be oriented arbitrarily in three-dimensional space. Solves the discretized thickness-integrated finite element flow equations by using the implicit mixed velocity-pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three-dimensional thin section cavities of irregular shape.",
author = "Gethin, {David T.} and Shahrir Abdullah",
year = "1997",
language = "English",
volume = "7",
pages = "344--366",
journal = "International Journal of Numerical Methods for Heat and Fluid Flow",
issn = "0961-5539",
publisher = "Emerald Group Publishing Ltd.",
number = "4",

}

TY - JOUR

T1 - Finite element formulation for filling a thin section cavity

AU - Gethin, David T.

AU - Abdullah, Shahrir

PY - 1997

Y1 - 1997

N2 - Presents a quasi three-dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no-slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air-filled (empty) surfaces. The formulation was developed to analyze the sections which lie in the xy-plane or may be oriented arbitrarily in three-dimensional space. Solves the discretized thickness-integrated finite element flow equations by using the implicit mixed velocity-pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three-dimensional thin section cavities of irregular shape.

AB - Presents a quasi three-dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no-slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air-filled (empty) surfaces. The formulation was developed to analyze the sections which lie in the xy-plane or may be oriented arbitrarily in three-dimensional space. Solves the discretized thickness-integrated finite element flow equations by using the implicit mixed velocity-pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three-dimensional thin section cavities of irregular shape.

UR - http://www.scopus.com/inward/record.url?scp=0030644078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030644078&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030644078

VL - 7

SP - 344

EP - 366

JO - International Journal of Numerical Methods for Heat and Fluid Flow

JF - International Journal of Numerical Methods for Heat and Fluid Flow

SN - 0961-5539

IS - 4

ER -