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.

Computational fluid dynamics (CFD) and direct numerical simulations (DNS),when applied to the study of turbulence, have traditionally been treated as acompute bound discipline, where the size of problems of interest is limited bythe capacity of supercomputers. While this remains true, the relatively recentadoption of specialized hardware such as graphics processing units (GPUs) hasallowed researchers to start studying problems that were not thought possiblebefore. This trend brings benefits for scientific discovery, however, it alsoaccentuates the importance of robust methodologies to manage and processthe increasing amount of data that is being produced by the simulations. Thepresent thesis explores techniques to process large scale data sets produced,mainly, by the spectral element method (SEM).This study explores the possibility to exploit the computational resourcesused by the simulations to perform data analysis and transformations in whatis termed, in-situ data processing. It is shown that it is viable to apply amultitude of processing tasks, such as data compression and image visualizationefficiently, as long as the hardware being used is taken into consideration, whichis relevant for modern heterogeneous systems. Furthermore it is shown that datacompression is an efficient technique to reduce storage requirements while keepingaccuracy, even for turbulence research. On this note, this thesis introduces amethod that incorporates uncertainty quantification (UQ) techniques for datacompression to facilitate the data quality evaluation.Data compression is a large focus in the present work, however, methodsto facilitate data analysis are also studied. Streaming and parallel modaldecompositions, in particular proper orthogonal decomposition (POD), aredeveloped and made available to the turbulence community with the additionof uncertainty quantification studies to ease its adoption. It is found thatthis sort of technique is excellent at increasing the interpretability of the data,while being able to exploit computational resources with in-situ execution.Additionally, parallel high-order interpolation techniques are introduced, whichbecome essential to reduce the memory footprint of large data sets whenperforming post-processing tasks, while aiding to simplify the data distributionof traditional SEM meshes.

Beräkningsvätskedynamik (CFD) och direkta numeriska simuleringar (DNS)har, när de tillämpas på studien av turbulens, traditionellt behandlats som enberäkningsbegränsad disciplin där storleken på intressanta problem begränsas avsuperdatorers kapacitet. Även om detta fortfarande stämmer har den relativt nyaanvändningen av specialiserad hårdvara, såsom grafikprocessorer (GPU:er), gjortdet möjligt för forskare att börja studera problem som tidigare betraktades somoåtkomliga. Denna utveckling gynnar den vetenskapliga kunskapsutvecklingen,men den betonar också behovet av robusta metoder för att hantera och bear-beta den växande datamängd som genereras av simuleringarna. Föreliggandeavhandling undersöker tekniker för att bearbeta storskaliga datamängder somhuvudsakligen produceras med spektralelementmetoden (SEM).Denna studie utforskar möjligheten att utnyttja de beräkningsresurser somanvänds av simuleringarna för att utföra dataanalys och transformationer inomså kallad in situ-databehandling. Den belyser att det är möjligt att effektivtgenomföra en rad bearbetningsuppgifter, såsom datakomprimering och visualise-ring, under förutsättning att den använda hårdvaran beaktas, vilket är särskiltrelevant för moderna heterogena system. Vidare åskådliggörs att datakomprime-ring är en effektiv metod för att minska lagringsbehovet samtidigt som noggrann-heten bibehåll, även inom turbulensforskning. I detta sammanhang introduceraravhandlingen en metod som integrerar tekniker för osäkerhetskvantifiering (UQ)i datakomprimering för att underlätta bedömningen av datakvalitet.Datakomprimering är ett centralt fokus i arbetet, men även metodersom underlättar dataanalys studeras. Strömmande och parallella modalned-brytningar, i synnerhet Proper Orthogonal Decomposition (POD), utveck-las och görs tillgängliga för turbulensfältet, kompletterade med studier avosäkerhetskvantifiering för att underlätta införandet. Det konstateras att dennatyp av teknik i hög grad ökar datans tolkbarhet samtidigt som den kan utnyttjaberäkningsresurser genom in situ. Dessutom introduceras parallella interpola-tionsmetoder av hög ordning, vilka är avgörande för att minska minnesavtryckethos stora datamängder vid efterbehandling och som samtidigt bidrar till attförenkla datadistributionen i traditionella SEM-nät.

The computational power of High-Performance Computing (HPC) systems increases continuously and rapidly. Data-intensive applications are designed to leverage the high computational capacity of HPC resources and typically generate a large amount of data for traditional post-processing data analytics. However, the HPC systems' in-/output (IO) subsystem develops relatively slowly, and the storage capacity is limited. This could lead to limited actual performance and scientific discovery. In-situ techniques are a partial remedy to these problems by reducing or avoiding the data flow through the IO subsystem to/from the storage. However, in current practice, asynchronous in-situ techniques with static resource management often allocate separate computing resources for executing in-situ task(s), which remain idle if no in-situ work is at hand. In the present work, we target improving the efficiency of computing resource usage by launching and releasing necessary additional computing resources for in-situ task(s). Our approach is based on extensions for MPI Sessions that enable the required dynamic resource management. In this paper, we propose a basic and an advanced in-situ techniques with dynamic resource management enabled by MPI Sessions, their implementations on two real-world use cases, and a critical analysis of the experimental results.

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.

We detail our developments in the high-fidelity spectral-element code Neko that are essential for unprecedented large-scale direct numerical simulations of fully developed turbulence. Major inno- vations are modular multi-backend design enabling performance portability across a wide range of GPUs and CPUs, a GPU-optimized preconditioner with task overlapping for the pressure-Poisson equation and in-situ data compression. We carry out initial runs of Rayleigh–Bénard Convection (RBC) at extreme scale on the LUMI and Leonardo supercomputers. We show how Neko is able to strongly scale to 16,384 GPUs and obtain results that are not pos- sible without careful consideration and optimization of the entire simulation workflow. These developments in Neko will help resolv- ing the long-standing question regarding the ultimate regime in RBC. 

The computational power of High-Performance Computing (HPC) systems is constantly increasing, however, their input/output (IO) performance grows relatively slowly, and their storage capacity is also limited. This unbalance presents significant challenges for applications such as Molecular Dynamics (MD) and Computational Fluid Dynamics (CFD), which generate massive amounts of data for further visualization or analysis. At the same time, checkpointing is crucial for long runs on HPC clusters, due to limited walltimes and/or failures of system components, and typically requires the storage of large amount of data. Thus, restricted IO performance and storage capacity can lead to bottlenecks for the performance of full application workflows (as compared to computational kernels without IO). In-situ techniques, where data is further processed while still in memory rather to write it out over the I/O subsystem, can help to tackle these problems. In contrast to traditional post-processing methods, in-situ techniques can reduce or avoid the need to write or read data via the IO subsystem. They offer a promising approach for applications aiming to leverage the full power of large scale HPC systems. In-situ techniques can also be applied to hybrid computational nodes on HPC systems consisting of graphics processing units (GPUs) and central processing units (CPUs). On one node, the GPUs would have significant performance advantages over the CPUs. Therefore, current approaches for GPU-accelerated applications often focus on maximizing GPU usage, leaving CPUs underutilized. In-situ tasks using CPUs to perform data analysis or preprocess data concurrently to the running simulation, offer a possibility to improve this underutilization.

Flush-mounted cavity hot-wire probes have emerged as an alternative to classical hot-wire probes mounted several diameters above the surface for wall-shear stress measurements. They aim at increasing the frequency response and accuracy by circumventing the well-known issue of heat transfer to the substrate that hot-wire and hot-film probes possess. Their use, however, depends on the assumption that the cavity does not influence the flow field. In this study, we show that this assumption does not hold, and that turbulence statistics are modified by the presence of the cavity with sizes that are practically in use. The mean velocity and fluctuations increase near the cavity while the shear stress decreases in its surroundings, all seemingly stemming from the fact that the no-slip condition is not present anymore and that flow reversal occurs. Overall, the energy spectra and the probability density function of the wall shear stress fluctuations indicate a change of nature of turbulence by the presence of the cavity.

High-Performance Computing (HPC) systems provide input/output (IO) performance growing relatively slowly compared to peak computational performance and have limited storage capacity. Computational Fluid Dynamics (CFD) applications aiming to leverage the full power of Exascale HPC systems, such as the solver Nek5000, will generate massive data for further processing. These data need to be efficiently stored via the IO subsystem. However, limited IO performance and storage capacity may result in performance, and thus scientific discovery, bottlenecks. In comparison to traditional post-processing methods, in-situ techniques can reduce or avoid writing and reading the data through the IO subsystem, promising to be a solution to these problems. In this paper, we study the performance and resource usage of three in-situ use cases: data compression, image generation, and uncertainty quantification. We furthermore analyze three approaches when these in-situ tasks and the simulation are executed synchronously, asynchronously, or in a hybrid manner. In-situ compression can be used to reduce the IO time and storage requirements while maintaining data accuracy. Furthermore, in-situ visualization and analysis can save Terabytes of data from being routed through the IO subsystem to storage. However, the overall efficiency is crucially dependent on the characteristics of both, the in-situ task and the simulation. In some cases, the overhead introduced by the in-situ tasks can be substantial. Therefore, it is essential to choose the proper in-situ approach, synchronous, asynchronous, or hybrid, to minimize overhead and maximize the benefits of concurrent execution.

Rayleigh–Bénard convection (RBC) is the canonical flow case in the studyof natural convection. Due to the search for numerical data approaching theso-called ultimate regime, simulations on narrow cells have been performedin the past in order to reach the Rayleigh number (Ra) range where such aphenomenon is expected to appear. While it can be argued that narrow cellsare not optimal for the study of such a regime, it is still an interesting flow caseto study given that the constrained domain introduces certain simplifications tothe flow, namely, only one large circulation structure (LCS) can appear. Thisprovides ample opportunity to understand the effect of such structure in theheat transfer and to isolate production mechanisms for turbulence. In this studywe perform direct numerical simulations of RBC in the Ra range of 109 to1014. We perform a detailed statistical analysis and uncertainty quantificationof time series of the non-dimensional heat transfer, i.e., the Nusselt number N u,and validate the results obtained by Iyer et al. (2020) using slightly differentnumerical methods and different meshes. Furthermore, we identify that thedissipation of turbulent kinetic energy in the domain is balanced mostly by thesource term associated with temperature fluctuations and do not find a strongindication that shear is one of the dominating mechanisms in this range. Furtherinvestigation on the shear dominated regions indicate that less than 50% of thein-plane cross sections present evidence of a shear layer forming. Our studiesof the dominant structures with the use of proper orthogonal decompositionalso indicate that most of the dynamics in this geometry stem from the largecirculation structure.