Summary
A velocity-vorticity formulation of the unsteady three dimensional Navier-Stokes equations has been used to solve for the incompressible viscous flow within a driven cavity of spanwise aspect ratio 3:1 at a Reynolds number Re = 3200 on a non-uniform (65 × 65 × 49) grid covering one half of the span. An efficient Alternating-DirectionImplicit method which treats all cross derivative terms implicitly and which requires only six scalar tridiagonal sweeps has been developed for the vorticity transport equation. The divergence-curl formulation for the elliptic velocity problem is solved at each time step by a Multi-Grid Distributive Gauss-Seidel iterative scheme. The pressure is solved, only when desired, from the three-dimensional Pressure Poisson problem using a Multi-Grid Gauss-Seidel iterative scheme. Velocity, vorticity and pressure results are given for a characteristic time t = 50 after the upper surface of the cavity is impulsively started from rest.
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References
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© 1992 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Huang, Y., Ghia, U., Osswald, G.A., Ghia, K.N. (1992). Velocity-Vorticity Simulation of Unsteady 3-D Viscous Flow within a Driven Cavity. In: Deville, M., Lê, TH., Morchoisne, Y. (eds) Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-00221-5_7
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DOI: https://doi.org/10.1007/978-3-663-00221-5_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-663-00071-6
Online ISBN: 978-3-663-00221-5
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