This research investigates the efficacy of the gradient jump penalisation (GJP) in large-eddy simulations (LES) when coupled with active subgrid-scale models. GJP is a stabilisation method tailored for the continuous Galerkin spectral element method, aiming at mitigating non-physical oscillations induced by discontinuous velocity gradients across element interfaces. We demonstrate that GJP effectively smoothens fields from LES without a salient impact on flow dynamics for the Taylor–Green vortex (TGV) at Re = 1600 , periodic hill flows at bulk Reynolds numbers Re b = 10 , 595 and 37,000, as well as turbulent channel flow at Re τ ≈ 550 . In the TGV case, the application of GJP results in decreased fluctuations at only high wavenumbers compared to simulations without GJP. The periodic hill flow simulations indicate the applicability of GJP in wall-resolved LES involving curved geometries, though it tends to dissipate some of the finer details in the solution. Finally, in the analysis of the canonical turbulent channel flow cases, GJP leads to a higher resolved turbulent kinetic energy than simulations without GJP and direct numerical simulations. GJP’s mechanism is identified as providing enhanced dissipation at high wavenumbers but accompanied with insufficient dissipation at low wavenumbers, leading to a pronounced spectral cut-off. Non-physical oscillations on element interfaces are reflected as spikes in the power spectral density. By evaluating the sharpness of the strongest spike, GJP is shown to smoothen the spectra, however, without completely removing the gradient jumps at low computational resolution.

This study introduces vector autoregression (VAR) as a linear procedure that can be used for synthesizing turbulence time series over an entire plane, allowing them to be imposed as an efficient turbulent inflow condition in simulations requiring stationary and cross-correlated turbulence time series. VAR is a statistical tool for modelling and prediction of multivariate time series through capturing linear correlations between multiple time series. A Fourier-based proper orthogonal decomposition (POD) is performed on the two-dimensional (2-D) velocity slices from a precursor simulation of a turbulent boundary layer at a momentum thickness-based Reynolds number, Re-theta=790. A subset of the most energetic structures in space are then extracted, followed by applying a VAR model to their complex time coefficients. It is observed that VAR models constructed using time coefficients of 5 and 30 most energetic POD modes per wavenumber (corresponding to 66% and 97% of turbulent kinetic energy, respectively) are able to make accurate predictions of the evolution of the velocity field at Re-theta=790 for infinite time. Moreover, the 2-D velocity fields from the POD-VAR when used as a turbulent inflow condition, gave a short development distance when compared with other common inflow methods. Since the VAR model can produce an infinite number of velocity planes in time, this enables reaching statistical stationarity without having to run an extremely long precursor simulation or applying ad hoc methods such as periodic time series.

This study introduces vector autoregression (VAR) as a linear procedure that can be used for synthetizing turbulence time series over an entire plane, allowing them to be imposed as efficient turbulent inflow conditions in simulations requiring stationary and cross-correlated turbulence time series. A VAR model is applied to the complex time coefficients derived from a Fourier-based proper orthogonal decomposition (POD) of the velocity fields of the precursor simulation of a turbulent boundary layer at a momentum thickness based Reynolds number, Re_theta=790. VAR is a statistical tool for modelling and prediction of multivariate time series through capturing linear correlations between multiple time series. By performing POD, firstly a subset of the most energetic structures in space are extracted, and then a VAR model is fitted to their time coefficients. It is observed that VAR models constructed using time coefficients of 5 and 30 most energetic POD modes per wave number (corresponding to >40% and >90% of turbulent kinetic energy across all wave numbers, respectively), are able to make accurate predictions of the evolution of the velocity field at Re_theta=790 for infinite time. Moreover, the two-dimensional velocity fields from the low-order POD-VAR are used as a turbulent inflow condition and compared against other common inflow methods. Since the VAR model can produce an infinite number of velocity planes in time, this enables reaching statistical stationarity without having to run an extremely long precursor simulation or applying ad-hoc methods such as periodic time series. 

Neko is a spectral-element solver for computational fluid dynamics, capable of running on all popular compute backends and distinguished by its excellent parallel performance on both CPUs and GPUs. Here, we present version 1.0 of this software, which represents another milestone in its maturity. Crucial advancements in functionality, such as turbulence modeling, computing statistics, and field interpolation, have been implemented. This is complemented by vastly expanded possibilities for adding custom user code and a C-based API that can also be used for driving Neko simulations using Python or Julia.  We supplement the description of new features with a brief discussion of Neko's overall design, and some key performance figures demonstrating its parallel efficiency.  As of this release, Neko is a full-fledged solver for incompressible fluid flow, ready to be used for advanced research on turbulent flows.