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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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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