The laminar separation bubble on an SD7003 aerofoil at a Reynolds numberRe= 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble. The measurements were performed with a high-resolution time-resolved particle image velocimetry (TR-PIV) system. Contrary to typical measurements performed through conventional PIV, the different modes can be identified by applying TR-PIV. The interaction between the shed vortices is analysed, and their significance for the production of turbulence is presented. In the shear layer above the bubble the generation and amplification of vortices due to Kelvin–Helmholtz instabilities is observed. It is found that these instabilities have a weak coherence in the spanwise direction. In a later stage of transition these vortices lead to a three-dimensional breakdown to turbulence.

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We consider the steady-state equations for a compressible uid. For low-speed ow, the system is sti because the ratio of the convective speed to the speed of sound is quite small. To overcome this di culty, we alter the time evolution of the equations but retain the same steady-state analytic equations. To achieve high numerical resolution, we also alter the articial viscosity of the numerical scheme, which is implemented conveniently by using other sets of variables in addition to the conservative variables. We investigate the e ect of the articial dissipation within this preconditioned system. We consider both the nonconservative and conservative formulations for arti cial viscosity and examine their e ect on the accuracy and convergence of the numerical solutions. The numerical results for viscous three-dimensional wing ows and two-dimensional multi-element airfoil ows indicate that e cient multigrid computations of ows with arbitrarily low Mach numbers are now possible with only minor modi cations to existing compressible Navier-Stokes codes. The conservative formulation for arti cial viscosity, coupled with the preconditioning, o ers a viable computational uid dynamics (CFD) tool for analyzing problems that contain both incompressible and compressible ow regimes.

Several schemes for introducing an arti cial dissipation into a central di erence approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective u p wind and split pressure CUSP s c heme, which is designed to support single interior point discrete shock w aves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation MATD s c hemes. Resolution capability i s determined by solving subsonic, transonic, and hypersonic ow problems. A nite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the ow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil ows the best accuracy on coarse meshes for aerodynamic coe cients is obtained with a simple MATD scheme. The coarsegrid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modi cations reduce the background dissipation and provide control over the regions where the scheme can become rst order.

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