Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

The present work is targeted at performing a strong scaling study of the high-order spectral element fluid dynamics solver Nek5000. Prior studies such as [5] indicated a recommendable metric for strong scalability from a theoretical viewpoint, which we test here extensively on three parallel machines with different performance characteristics and interconnect networks, namely Mira (IBM Blue Gene/Q), Beskow (Cray XC40) and Titan (Cray XK7). The test cases considered for the simulations correspond to a turbulent flow in a straight pipe at four different friction Reynolds numbers Reτ = 180, 360, 550 and 1000. Considering the linear model for parallel communication we quantify the machine characteristics in order to better assess the scaling behaviors of the code. Subsequently sampling and profiling tools are used to measure the computation and communication times over a large range of compute cores. We also study the effect of the two coarse grid solvers XXT and AMG on the computational time. Super-linear scaling due to a reduction in cache misses is observed on each computer. The strong scaling limit is attained for roughly 5000 − 10, 000 degrees of freedom per core on Mira, 30, 000 − 50, 0000 on Beskow, with only a small impact of the problem size for both machines, and ranges between 10, 000 and 220, 000 depending on the problem size on Titan. This work aims at being a reference for Nek5000 users and also serves as a basis for potential issues to address as the community heads towards exascale supercomputers.

In this work we report the results of DNSs and LESs of the turbulent flow through hexagonal ducts at friction Reynolds numbers based on centerplane wall shear and duct half-height Reτ,c ≃ 180, 360, and 550. The evolution of the Fanning friction factor f with Re is in very good agreement with experimental measurements. A significant disagreement between the DNS and previous RANS simulations was found in the prediction of the in-plane velocity, and is explained through the inability of the RANS model to properly reproduce the secondary flow present in the hexagon. The kinetic energy of the secondary flow integrated over the cross-sectional area 〈K〉yz decreases with Re in the hexagon, whereas it remains constant with Re in square ducts at comparable Reynolds numbers. Close connection between the values of Reynolds stress uw¯ on the horizontal wall close to the corner and the interaction of bursting events between the horizontal and inclined walls is found. This interaction leads to the formation of the secondary flow, and is less frequent in the hexagon as Re increases due to the 120∘ aperture of its vertex, whereas in the square duct the 90∘ corner leads to the same level of interaction with increasing Re. Analysis of turbulence statistics at the centerplane and the azimuthal variance of the mean flow and the fluctuations shows a close connection between hexagonal ducts and pipe flows, since the hexagon exhibits near-axisymmetric conditions up to a distance of around 0.15DH measured from its center. Spanwise distributions of wall-shear stress show that in square ducts the 90∘ corner sets the location of a high-speed streak at a distance zv+≃50 from it, whereas in hexagons the 120∘ aperture leads to a shorter distance of zv+≃38. At these locations the root mean square of the wall-shear stresses exhibits an inflection point, which further shows the connections between the near-wall structures and the large-scale motions in the outer flow.

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An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts. The goal of the SHARP framework is to perform fully resolved coupled physics analysis of a reactor on heterogeneous geometry, in order to reduce the overall numerical uncertainty while leveraging available computational resources. The coupling methodology and software interfaces of the framework are presented, along with verification studies on two representative fast sodium-cooled reactor demonstration problems to prove the usability of the SHARP framework.