Analysis of incompressible massively separated viscous flows using unsteady Navier-Stokes equations.

*(English)*Zbl 0683.76027Summary: The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream-function in generalized curvilinear orthogonal coordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order-accurate wiggle-free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three-dimensionality in the experiment.

##### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |

76M99 | Basic methods in fluid mechanics |

##### Keywords:

backstep channel; incompressible separated flow; unsteady incompressible Navier-Stokes equations; stream-function; generalized curvilinear orthogonal coordinates; direct block Gaussian elimination; One- dimensional stretching functions; optimum grid distribution; finite differenced transport equation
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\textit{K. N. Ghia} et al., Int. J. Numer. Methods Fluids 9, No. 8, 1025--1050 (1989; Zbl 0683.76027)

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