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The LES of a 3D mixing layer spatially developing downstream of a flat plate has been conducted for a high Reynolds number (Reh ¼ 2835). To overcome the problem of the pressure condition on the free boundaries,use of the ( v–x) formulation of the Navier–Stokes equations has been preferred over the primitive (v–p) formulation. To deal with the difficult problem of the divergence free constraint on both the velocity and the vorticity field,a new and efficient numerical algorithm has been devised which turns out to be very attractive. The velocity components are computed as a solution of a Cauchy–Riemann problem using a fractional step method. As one of the main advantages of the vorticity-based formulation is the treatment of the free flow boundary conditions,special care has been devoted to these boundary conditions. An optimum approximation of the outflow boundary condition has been carried out which satisfies the conservation of mass,making the long time integration easier and more accurate. The numerical results are compared to a reference experiment [Appl. Sci. Res. 53 (1994) 263; J. Delville,PhD thesis,University of Poitiers,1995] for a rather high Reynolds number. Using inlet perturbations and the mixed scale model,the LES results agree very well with the reference experiments. The validation of the numerical procedure is reviewed on the mean and fluctuating quantities. Good prediction of the spatial evolution is demonstrated for the distribution of the vorticity thickness as well as for the Reynolds stress profiles and spatial correlations. In order to estimate the quality of the spatio-temporal development,a spectral analysis is also reported on the space and time spectra,pointing out a highly 3D arrangement with length scales and frequencies in rather good agreement with the ones generally admitted. � 2004 Elsevier Ltd. All rights reserved.

A comparative assessment of six subgrid-scale models is presented in the case of a compressible plane channel flow over isothermal walls, four of which are based on the recent mixed-scale model. A supersonic and a subsonic case in temporal development at Mach 1.5 and 0.5, respectively, are considered for a Reynolds number equal to 3000, with comparison to the direct numerical simulations (DNS) of Coleman et al. in the first case, and the incompressible DNS of Kim et al. in the second case. For each Mach number, two grids are considered, with about 20 and 5 times less grid points as in the reference DNS, and the results are globally satisfactory, although not excellent. In particular, the wall friction is globally underestimated by about 10%, both in the subsonic and the supersonic cases. Among the models tested are several original combinations, which vanish at the wall without requiring any damping function

Large eddy simulation (LES) of compressible periodic channel flow is performed using a fourth-order finite difference scheme for a Reynolds number based on bulk density, bulk velocity and channel half-width equal to 3000. Two configurations are studied: a subsonic case (M0=0.5) that corresponds to the experiments of Niederschulte et al. [‘Measurements of turbulent flow in a channel at low Reynolds numbers’, Exp. Fluids, 9, 222–230 (1990)] and a supersonic case (M0=1.5) that corresponds to the direct numerical simulation (DNS) results by Coleman et al. [‘A numerical study of turbulent supersonic isothermal-wall channel flow’, J. Fluid Mech., 305, 159–183 (1995); ‘Compressible turbulent channel flows: DNS results and modeling’, J. Fluid Mech., 305, 185–218 (1995)]. In order to determine the influence of the discretization, two cases are computed using two different meshes, a coarse one and a fine one. Two subgrid-scale models are tested: the first one is an extension to compressible flows of the Smagorinsky model, while the second one is a model based both on large and small scales of turbulence, a hybrid Bardina–selective mixed scale model. Various statistical comparisons are made with experimental and DNS data at similar Reynolds numbers, including higher-order statistics. Copyright © 2000 John Wiley & Sons, Ltd.

The spatial development of a 3D plane mixing layer in incompressible flow has been performed using a L.E.S. approach. The resolutions of the Navier-Stokes equations, written in velocity-vorticity formulation, is based on an original fractional step algorithm (Bertagnolio et al. (1996)). The results presented are obtained through the use of two subgrid scale models (a vorticity model and a mixed scale model). To validate the L.E.S. approach, a comparison with the experiments is provided. The main statistical values, expansion factor, Reynolds stress tensor and 3D arrangement are well predicted.

Multigrid and ADI methods were used to solve unsteady 3D Navier-Stokes equations in Velocity-Vorticity formulation, for the lid-driven cavity test case of spanwise aspect ratio equal to 3:1, at a Reynolds number Re equal to 3200. Results are given for the characteristic times T=50,100,200.

Unsteady viscous flow around a large-amplitude and high-frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth-order Hermitian finite difference scheme for the stream function equation and a classical second-order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 103 and 104. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.

Unsteady fully three-dimensional Navier-Stokes equations of viscous incompressible flow around finite length circular cylinder placed between two circular plates is studied using finite difference numerical scheme. The algorithm uses iterative correction processes of the velocity and the vorticity fields in order to satisfy the two divergence free conditions. In order to study the three-dimensional effects, results are presented for this external flow with Re=800 for different cylinder lengths.