The flow past a circular cylinder at critical and supercritical Reynolds number combines flow separation, turbulence transition, reattachment of the flow and further turbulent separation of the boundary layer. The transition to turbulence causes the delaying of the separation point and, an important reduction of the drag force on the cylinder surface. In the present work, large-eddy simulations of the flow past a circular cylinder at Reynolds numbers in the range 2.5 × 10 5 -8.5 × 10 5 are performed. In this range, major changes in the pressure distribution occur, the pressure minimum gets more negative as its location moves towards the cylinder rear, whereas the base pressure increases. These changes are shown to take place first on one side of the cylinder and then on the other side as the drag completes its drop up to a minimum value of ∼0.23, registered at Re = 6.5 × 10 5 in this work. After that, the flow enters in the supercritical regime, with little changes in the wake configuration. Furthermore, these changes in the wake topology as the Reynolds number increases are also shown to be related to the increase in the vortex shedding frequency.

The analysis of the resulting spectrum showed the footprint of Kelvin-Helmholtz instabilities in the whole range. It is found that the ratio of these instabilities frequency to the primary vortex shedding frequency matches quite well the scaling proposed by Prasad and Williamson (f KH /f vs ∝ Re 0.67 ).

In this paper a parallel adaptive mesh refinement (AMR) strategy for large and accuracy of our methodology is shown on the numerical simulation of the turbulent flow around a square cylinder at Re = 22000 and the turbulent flow around two side-by-side square cylinders at Re = 21000.

Summary Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell‐centred velocity reconstructions, the standard first‐order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd–even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable‐density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy‐preserving scheme is applied to the momentum equations, namely, the symmetry‐preserving scheme. Furthermore, a new approach to define the far‐neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self‐igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable‐density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second‐order behaviour on unstructured meshes, and the symmetry‐preserving is reliably used in all computations. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the e↵ects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k{D " 0.02 are performed