A new finite element formulation for incompressible flow

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A basic objective in computational fluid dynamics is the efficient solution of nonlinear systems of equations that arise in finite element modeling of convective-diffusive flow. The use of implicit Newton-like schemes to solve the coupled system of Navier-Stokes and continuity equations enables rapid convergence, although the well-known difficulty of indirect pressure linkage requires attention when forming the Jacobian matrices. Traditional approaches for overcoming this obstacle include reordering strategies, modification of diagonal terms, and changes of variables. In contrast, the author develops a primitive variable finite element formulation which employs an auxiliary pressure equation derived from the Navier-Stokes and continuity equations. ... continued below

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27 p.

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Curfman, L.V. February 1, 1995.

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Description

A basic objective in computational fluid dynamics is the efficient solution of nonlinear systems of equations that arise in finite element modeling of convective-diffusive flow. The use of implicit Newton-like schemes to solve the coupled system of Navier-Stokes and continuity equations enables rapid convergence, although the well-known difficulty of indirect pressure linkage requires attention when forming the Jacobian matrices. Traditional approaches for overcoming this obstacle include reordering strategies, modification of diagonal terms, and changes of variables. In contrast, the author develops a primitive variable finite element formulation which employs an auxiliary pressure equation derived from the Navier-Stokes and continuity equations. This formulation extends the work of Rice and Schnipke, where a similar equation was developed in the context of a segregated solution method. Approximate Newton methods using the new finite element formulation are evaluated in terms of accuracy, convergence rate, and overall efficiency for flow problems with varying degrees of nonlinearity.

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27 p.

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OSTI as DE95007141

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  • Other Information: PBD: [1995]

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  • Other: DE95007141
  • Report No.: ANL/MCS/PP--80304
  • Grant Number: W-31109-ENG-38
  • DOI: 10.2172/26516 | External Link
  • Office of Scientific & Technical Information Report Number: 26516
  • Archival Resource Key: ark:/67531/metadc669207

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  • February 1, 1995

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • Dec. 16, 2015, 12:59 p.m.

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Curfman, L.V. A new finite element formulation for incompressible flow, report, February 1, 1995; Illinois. (digital.library.unt.edu/ark:/67531/metadc669207/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.