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.

Turbulence data sets produced from computational fluid dynamics (CFD), especially from fine-resolved direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent flows, tend to be very large due to high resolutions adopted to accurately resolve the smallest scales. While the computational capacity of high-performance computing (HPC) platforms has kept increasing, storage capacity has lagged to the point that more data is being produced than what can be efficiently managed. Among the several methods emerged to deal with this problem, an efficient technique is data compression. In this study, we present a proof of concept of a novel data compression approach that relies on Gaussian process regression (GPR) within a Bayesian framework to handle data sets in such a way that initially discarded information can be recovered a posteriori. The approach can be used to supplement existing compression algorithms with measures of uncertainty and we show that it can be applied to compress not only the 3D spatial fields of turbulence but also the discrete sets of time series data. The compression algorithm has been designed for data from spectral element method (SEM) simulations but can be extended to spatiotemporal fields obtained from other methods arising in engineering and physics. Our investigation shows that it is possible to use Gaussian process regression for data compression, however also highlights several of its limitations, in particular, that efficient implementations of GPR are crucial for its adoption, and that, while it is unlikely that the method can compete in terms of throughput with state of the art methods, given the cost of GPR, there is potential in terms of compression performance, as long as efficient bit-plane coding is integrated.

Proper orthogonal decomposition (POD) is a quintessential tool in the analysis of flow fields in experimental and computational fluid dynamics as a whole and turbulence in particular. It is a data driven technique that can be used to extract coherent structures in the flow and to create reduced-order dynamical systems that represent the most energetic flow structures. While extremely useful, its main drawback is that, at least traditionally, the POD algorithm is executed in serial using all the available data at once, while the original full-order system (simulation or experiment) is typically conducted and concluded before, either using a parallel simulation code or an (optical field-based) experiment. This can potentially limit its applications, in particular for large-scale data sets, e.g., from three-dimensional turbulent flows. In this article, we collect and review some of the more flexible methods for calculation of the POD (in particular, based on singular value decomposition, SVD) that have appeared over the years in order to tackle these limitations. We summarize an implementation that combines the characteristics of the (distributed-memory) parallel and streaming methods and conduct detailed uncertainty quantification studies to address the effect of the hyper-parameters that typically appear with the introduction of streaming and parallel computations. We find that in general, the number of parallel processes used to compute the POD has no significant effect. On the other hand, the accuracy of the results depends on the number of updated modes and the number of snapshots treated simultaneously, with 60% and 30% of global sensitivity, respectively, in the error in the obtained POD modes. Given these findings, we formulate the recommendation that it is beneficial that more POD modes than those desired for later analysis are continuously updated. We find that the errors introduced by using streaming and parallel algorithms are minimal in all cases, including extended implementations such as the novel Hilbert-POD, which incorporates a spatial Hilbert transform. Therefore, the use of these algorithms for either computation on smaller memory systems, or online (in-situ) computation of POD modes as simulations advance is a reliable and robust way forward to increase the rate of scientific discovery in large-scale fluid-mechanics problems.

Modern computing clusters offer specialized hardware for reduced-precision arithmetic, which can significantly speed up the time to solution. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases has not been explored in detail, and limits the optimal utilization of new high-performance computing systems. In this work, the effect of reduced precision is studied using four diverse computational fluid dynamics (CFD) solvers (two incompressible, Neko and Simson, and two compressible, PadeLibs and SSDC) using four test cases: turbulent channel flow at Reτ=550 and higher, forced transition in a channel, flow over a cylinder at ReD=3900, and compressible flow over a wing section at Rec=50000. We observe that the flow physics are remarkably robust with respect to reductions in lower floating-point precision, and that often other forms of uncertainty, due to, for example, time averaging, often have a much larger impact on the computed result. Our results indicate that different terms in the Navier–Stokes equations can be computed to a lower floating-point accuracy without affecting the results. In particular, standard IEEE single precision can be used effectively for the entirety of the simulation, showing no significant discrepancies from double-precision results across the solvers and cases considered. Potential pitfalls are also discussed. 

One of the main challenges in simulating high Reynolds number (italic Re Re) turbulent boundary layers (TBLs) is the long streamwise distance required for large-scale outer-layer structures to develop, making such simulations prohibitively expensive. We propose an inflow generation method for high italic Re Re wall turbulence that leverages the known structure and scaling laws of TBLs. Pre-multiplied spectra of streamwise velocity show that with an increase in italic Re Re the outer region grows and occupies more of the spanwise wavenumber space in proportion to the increase in italic Re Re, while the inner region remains approximately the same. Exploiting this behaviour, we generate inflow conditions for a target italic Re Re by starting from cross-stream velocity slices at a lower base italic Re Re. In spectral space, we identify the inner- and outer-region wavenumbers, and shift the outer-region components proportionally to the desired italic Re Re increase. We examine the capability of this method by scaling velocity slices at italic Re Subscript theta Baseline equals 2240 Reθ=2240 and 4430 to italic Re Subscript theta Baseline equals 8000 Reθ=8000, and using them as inflow conditions for direct numerical simulations of TBLs growing in the range italic Re Subscript theta Baseline equals 8000 minus 9000 Reθ=8000-9000, with italic Re Subscript theta Reθ being the Reynolds number based on the momentum-loss thickness theta θ. The predicted skin friction coefficient and shape factor, regardless of the base italic Re Subscript theta Reθ tested, lie within plus or minus 3.5 percent sign ±3.5% and plus or minus 0.5 percent sign ±0.5%, respectively, of that of a precursor simulation right from the inlet. Reynolds stresses match very well after approximately 8 delta Subscript 99 Sub Subscript 0 8δ990. The development length in terms of the Reynolds stresses is approximately 8 delta Subscript 99 Sub Subscript 0 8δ990, where delta Subscript 99 Sub Subscript 0 δ990 is the boundary layer thickness at the inlet. This gives an order of magnitude reduction in development length compared with other methods proposed in the literature.

A scale-resolving simulation of a turbulent boundary layer (TBL) requires an inflow condition that introduces turbulence into the domain. The boundary values must accurately approximate real turbulent structures in order to minimize the inflow adaption and to allow for sustained growth of the TBL. In practice, all inflow conditions incur an error on the flow field directly downstream. This error is typically quantified as the distance from the inlet at which the velocity statistics recover correct values. However, this measure is insufficient for simulations where evaluating acoustic pressure is an important outcome, necessitating a quantification of the error in the pressure field. This aspect of inflow generation is currently not addressed in the literature and constitutes the main topic of this article. We show that violation of the continuity equation near the inflow region generates spurious pressure fluctuations over the entire domain, leading to poor sound prediction results in low Mach number regimes. In particular, we look at three known inflow generation methods (namely, precursor simulations, the synthetic eddy method, and recycling using an upstream open channel flow) and evaluate how silent they are. For evaluation, the sensitive case of a TBL developing over a flat plate is used as the test case. The recycling method satisfies the divergence-free condition and introduces the least amount of spurious numerical noise to the sound field while giving reasonably good agreement in terms of the overall development of the TBL.

We detail our work on improving the performance and scalability of key numerical methods in the high-fidelity spectral element code Neko on accelerated exascale machines. Eifficient preconditioners are essential in incompressible fluid dynamics; however, the most eifficient method (with respect to convergence) might be challenging to implement with good performance on an accelerator. We present our development of a GPU-optimised preconditioner with task overlapping for the pressure-Poisson equation, improving the preconditioner's throughput (in TDoF/s) by close to 60%. The new preconditioner is explained in detail, together with detailed performance studies on accelerated Cray EX platforms, including strong scalability studies on LUMI and Frontier.

The computational capacity of High-Performance Computing (HPC) systems increases continuously with the rapid development of central processing units (CPUs) and graphic processing units (GPUs), while the in-/output (IO) subsystem develops relatively slowly and storage capacity is also limited. Data-intensive applications, which are designed to leverage the high computational capacity of HPC resources, typically generate a considerable amount of data for post-processing visualizations and data analytics. The limited IO speed and storage space could lead to constraints in the actual performance of these applications and, therefore, scientific discovery. In-situ techniques, where data is visualized/analysed while still in memory rather than through disk, can contribute to alleviating these problems as they can reduce or even fully avoid data writing/reading through the IO subsystem to/from storage. However, the overall efficiency of insitu techniques crucially depends on the characteristics of both the in-situ tasks and the applications, and the resource distribution among them. Therefore, choosing the right in-situ approach (synchronous, asynchronous, or hybrid) and resource allocation is essential to minimize overhead and maximize the benefits of concurrent execution. In this paper, we present a performance model of in-situ techniques to find the most beneficial in-situ approach and the preferred resource configuration. We verify the high accuracy of our approach with over 6800 measurements and provide use cases with different applications.

In this work, we introduce a novel application of the adaptive mesh refinement (AMR) technique for the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial since an inadequate resolution might introduce numerical noise that triggers premature transition to turbulence. With AMR, we enable the design of three different and independent meshes for the non-linear base flow and the linear direct and adjoint solutions. Each of these is designed to reduce the truncation and quadrature errors for its respective solution, based on the spectral error indicator. We provide details about the workflow and the refining procedure. The numerical framework is validated for the two-dimensional flow past a circular cylinder, computing a portion of the spectrum for the linearised direct and adjoint Navier–Stokes operators.

Recent trends and advancements in including more diverse and heterogeneous hardware in High-Performance Computing (HPC) are challenging scientific software developers in their pursuit of efficient numerical methods with sustained performance across a diverse set of platforms. As a result, researchers are today forced to re-factor their codes to leverage these powerful new heterogeneous systems. We present our design considerations of Neko—a portable framework for high-fidelity spectral element flow simulations. Unlike prior works, Neko adopts a modern object-oriented Fortran 2008 approach, allowing multi-tier abstractions of the solver stack and facilitating various hardware backends ranging from general-purpose processors, accelerators down to exotic vector processors and Field-Programmable Gate Arrays (FPGAs). Focusing on the performance and portability of Neko, we describe the framework's device abstraction layer managing device memory, data transfer and kernel launches from Fortran, allowing for a solver written in a hardware-neutral yet performant way. Accelerator-specific optimizations are also discussed, with auto-tuning of key kernels and various communication strategies using device-aware MPI. Finally, we present performance measurements on a wide range of computing platforms, including the EuroHPC pre-exascale system LUMI, where Neko achieves excellent parallel efficiency for a large direct numerical simulation (DNS) of turbulent fluid flow using up to 80% of the entire LUMI supercomputer.