International audienceThe present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter -R < r < R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectral convergence that reduces the number of grid points with respect to lower-order numerical methods. The grid-points distribution densifies the mesh only near the boundaries that makes the algorithm well-suited to simulate rotating cavity flows where thin layers develop along the walls. Comparisons with reliable experimental and numerical results of the literature show good quantitative agreements for flows driven by rotating discs in tall cylinders and thin inter-disc cavities. Associated to a spectral vanishing viscosity [E. Séverac, E. Serre, A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities, J. Comp. Phys. 226 (2007) 1234-1255], the method provides very promising LES results of turbulent cavity flows

International audienceA simple model of synthetic (zero-net mass-flux) micro-jet is proposed and implemented in a large-eddysimulation spectral solver of the incompressible Navier–Stokes equations. Essentially, it is simplyrequired to introduce a penalty like term in the momentum equation, with a variable penalty coefficientthat culminates during the expulsion phase. Examples of applications are considered for the control ofseveral turbulent wake flows, the backward facing step, the D-shaped body and the square backAhmed body

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