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Fluid Flow Computation: Incompressible Flows

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The Finite Volume Method in Computational Fluid Dynamics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 113))

Abstract

In previous chapters the procedure for discretizing and solving the general transport equation for the variable \( \phi \) in the presence of a known velocity field was formulated. In general, the velocity field is not known and has to be computed by solving the set of Navier-Stokes equations. For incompressible flows this task is complicated by the strong coupling that exist between pressure and velocity and by the fact that pressure does not appear as a primary variable in either the momentum or continuity equations. The focus of this chapter is on presenting a method that addresses these two issues, and computes the flow field for incompressible fluid flows. This is accomplished initially on a one dimensional staggered grid, then on a collocated one dimensional grid and finally on a collocated three dimensional unstructured grid. In addition to fully deriving the SIMPLE, SIMPLEC, PRIME and PISO algorithms, the Rhie-Chow interpolation and its extension to transient, relaxation and body force terms are clearly formulated. Finally, the implementation details for a number of frequently encountered boundary conditions are presented.

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Author information

Authors and Affiliations

  1. Mechanical Engineering, American University of Beirut, Beirut, Lebanon

    F. Moukalled

  2. Engineering and Architecture, Lucerne University of Applied Science and Arts, Horw, Switzerland

    L. Mangani

  3. Department of Mechanical Engineering, American University of Beirut, Beirut, Lebanon

    M. Darwish

Authors
  1. F. Moukalled
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  2. L. Mangani
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  3. M. Darwish
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Corresponding author

Correspondence to F. Moukalled .

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Moukalled, F., Mangani, L., Darwish, M. (2016). Fluid Flow Computation: Incompressible Flows. In: The Finite Volume Method in Computational Fluid Dynamics. Fluid Mechanics and Its Applications, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-16874-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-16874-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16873-9

  • Online ISBN: 978-3-319-16874-6

  • eBook Packages: EngineeringEngineering (R0)

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