High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

The accuracy of large-eddy simulations is limited, among other things, by the quality of the subgrid parametrization and the numerical contamination of the smaller retained flow structures. We characterize the total simulation error in terms of the “subgrid-activity” s, which measures the relative turbulent dissipation rate $\text{(0⩽s⩽1)}$ and the “subgrid resolution” r. This analysis is applied to turbulent mixing of a “Smagorinsky fluid” using a finite volume discretization of fourth order accuracy. On fixed coarse grids, i.e., at constant computational cost, the total simulation error decreases monotonically with filter width $\Delta$ for large s while for smaller s the total error may even increase with decreasing $\mathrm{\Delta .}$ The corresponding modeling- and spatial discretization-error contributions are quantified at various resolutions.

The paper presents a model for particle–particle and particle–wall collisions during interface-resolving numerical simulations of particle-laden flows. The accurate modelling of collisions in this framework is challenging due to methodological problems generated by interface approach and contact as well as due to the greatly different time scales involved. To cope with this situation, multiscale modelling approaches are introduced avoiding excessive local grid refinement during surface approach and time step reduction during the surface contact. A new adaptive model for the normal forces in the phase of ‘dry contact’ is proposed, stretching the collision process in time to match the time step of the fluid solver. This yields a physically sound and robust collision model with modified stiffness and damping determined by an optimization scheme. Furthermore, the model is supplemented with a new approach for modelling the tangential force during oblique collisions which is based on two material parameters: a critical impact angle separating rolling from sliding and the friction coefficient for the sliding motion. The resulting new model is termed the adaptive collision model (ACM). All proposed sub-models only contain physical parameters, and virtually no numerical parameters requiring adjustment or tuning. The new model is implemented in the framework of an immersed boundary method but is applicable with any spatial and temporal discretization. Detailed validation against experimental data was performed so that a general and versatile model for arbitrary collisions of spherical particles in viscous fluids is now available.