SUMMARYIn the present paper, a comparative study of numerical solutions for Newtonian uids based on the lattice-Boltzmann method (LBM) and the classical ÿnite volume method (FVM) is presented for the laminar ow through a 4:1 planar contraction at a Reynolds number of value one, Re = 1. In this study, the stress ÿeld for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM-data use the evaluations of velocity gradients with ÿnite di erences. The stress ÿeld for both LBM and FVM is expressed in the present study in terms of the shear stress and the ÿrst normal stress di erence. The lateral and axial proÿles of the velocity, the shear stress and the ÿrst normal stress di erence for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results.

We consider the case of transient three-dimensional, incompressible and isothermal channel flow of a newtonian fluid past a symmetrically confined obstacle of square cross section at zero incidence. The blockage ratio (ratio of cylinder diameter to channel width) is fixed at 1/4. Results from both Laser Doppler (LDV) experiments and direct simulations upto Reynolds numbers (Re ≤ 250) have been reported.Starting from the onset of instability (Re cr ≈ 58), close examination of the apparent region of influence that envelopes the cylinder reveals a clear vortex shedding signature which extends up to about three diameters upstream. While the fundamental vortex shedding frequency displays a fairly steady monotonic increase with Reynolds number, the Strouhal number (St) shows an inflexion point around Re ≈ 115. No signs of hysteresis were detected around this region. Furthermore, incommensurate harmonics observed for Reynolds numbers in the range 127 ≤ Re ≤ 175 suggest a quasi-periodic transition to three-dimensionality. This is shown to be followed by an intermediate periodic window starting around Re ≈ 180. Results from direct simulations performed using OpenFOAM (the Open Source CFD Toolbox) are used not only to enhance confidence in the accuracy of the reported LDV measurements, but also to help explain the observed phenomena through frequency power spectra and spanwise velocity correlations. Finally, it is concluded that only a parametric variation of transverse and spanwise blockage ratios can bring closure to the subject of bluff-body wake transitions.