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. 

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.

Rotors play a major role in various applications including ventilation and propulsion systems such as in helicopters, drones, gas turbines and wind turbines. This visualization of instantaneous vortical structures (identified by the k₂ criterion) shows complex flow structures emanating from a twisted drone rotor that is impulsively starting to rotate at 1600 rpm. Initially, a starting vortex is formed as a result of lift generation and shed as a connected vortex tube from the entire surface of the blade, which has a strong connection to the blade tip via the so-called tip vortex. Leading edge separation occurs at span positions of high twist, followed by wave-induced breakdown to turbulence along the whole wing span. This turbulence then sheds as small-scale vortices into the wake and dissipates. Understanding the behaviour of these vortices from such complex blades and how they interact with the other blade is critical to design more efficient and potentially more silent propellers.

The overarching aim of this thesis is to enable accurate simulations of high-Reynolds-number wall-bounded flows, representative of those encountered in realistic engineering applications. Achieving this goal requires progress on several fronts, ranging from methodological developments to computational considerations and the application of simulations to relevant flow configurations.

First, advances are made in numerical techniques for scale-resolving simulations of wall-bounded turbulence. New methods are introduced that allow turbulent boundary layers to be simulated efficiently at arbitrarily high Reynolds numbers and sustained over long physical times. In addition, existing turbulence inflow generation approaches are assessed with particular emphasis on their suitability for aeroacoustic predictions, where a physically consistent representation of turbulent structures is essential.

Second, the ability of scale-resolving simulations to exploit emerging computing architectures is investigated. In particular, the sensitivity of such simulations to reduced-precision arithmetic, a feature increasingly common in modern high-performance computing hardware, is systematically evaluated. This provides insights into the accuracy–efficiency trade-offs that can be expected as computational platforms evolve.

Finally, the methods are applied to canonical but engineering-relevant test cases that combine fundamental physical interest with practical significance. Direct numerical simulations are carried out for flow over the Boeing speed bump and for a drone rotor at moderate Reynolds numbers. For the Boeing speed bump, a detailed analysis of boundary-layer dynamics is performed, providing new insights into the interaction between geometry-induced pressure gradients and turbulent structures. The drone rotor simulations, in turn, represent a first step toward applying scale-resolving methods to realistic aerodynamic configurations where both performance and noise are of interest.

Overall, the contributions of this thesis span algorithmic development, computational assessment, and application to canonical test cases, thereby laying the foundation for scale-resolving simulations of wall-bounded turbulence at conditions directly relevant to engineering design.

Det övergripande målet med denna avhandling är att möjliggöra noggranna simuleringar av väggbundna strömmar vid höga Reynolds-tal, representativa för de förhållanden som återfinns i verkliga ingenjörstillämpningar. För att uppnådetta krävs framsteg på flera områden, från metodutveckling till datoranpassning och tillämpning på relevanta strömningsfall.

För det första presenteras nya numeriska metoder för skalanupplösande simuleringar av väggbunden turbulens. Dessa metoder gör det möjligt att på etteffektivt sätt simulera turbulenta gränsskikt vid godtyckligt höga Reynolds-tal och att upprätthålla simuleringarna under långa tidsperioder. Vidare utvärderas befintliga inflödesmetoder för turbulens med särskilt fokus på deras lämplighet för aeroakustiska prediktioner, där en fysiskt konsekvent representation av turbulenta strukturer är avgörande.

För det andra undersöks skalanupplösande simuleringars förmåga att utnyttjanya beräkningsarkitekturer. I synnerhet analyseras känsligheten hos dessasimuleringar för reducerad numerisk precision, en egenskap som blir allt vanligare i modern högprestandaberäkning. Detta ger viktiga insikter i av vägningen mellan noggrannhet och beräkningseffektivitet vid framtida beräkningsplattformar.

Slutligen tillämpas metoderna på kanoniska men ingenjörsrelevanta fall som kombinerar fundamentalt fysikaliskt intresse med praktisk betydelse. Direkta numeriska simuleringar genomförs för strömning över en Boeing speed bump samt för en drönarrotor vid måttliga Reynolds-tal. För Boeing speed bump analyseras gränsskiktets fysik i detalj, vilket ger nya insikter om samspelet mellan geometriinducerade tryckgradienter och turbulenta strukturer. Simuleringarnaav drönarrotorn utgör i sin tur ett första steg mot att tillämpa skalanupplösande metoder på realistiska aerodynamiska konfigurationer där både prestanda ochbuller är av intresse.

Sammanfattningsvis spänner avhandlingens bidrag från metodutveckling och datorarkitektoniska utvärderingar till tillämpning på kanoniska testfall. Därmed läggs en grund för skalanupplösande simuleringar av väggbunden turbulens under förhållanden som är direkt relevanta för ingenjörsmässig design.

A framework is presented for the spectral-element code Nek5000, which has been, and still is, widely used in the computational fluid dynamics (CFD) community to perform high-fidelity numerical simulations of transitional and high Reynolds number flows. Despite the widespread usage, there is a deficiency in having a comprehensive set of tools specifically designed for conducting simulations using Nek5000. To address this issue, we have created a unique framework that allows, inter alia, to perform stability analysis and compute statistics of a turbulent flow. The framework encapsulates modules that provide tools, run-time parameters and memory structures, defining interfaces and performing different tasks. First, the framework architecture is described, showing its non-intrusive approach. Then, the modules are presented, explaining the main tools that have been implemented and describing some of the test cases. The code is open-source and available online, with proper documentation, to-run instructions and related examples.

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.

With increased computational power through the use of arithmetic in low-precision, a relevant question is how lower precision affects simulation results, especially for chaotic systems where analytical round-off estimates are non-trivial to obtain. In this work, we consider how the uncertainty of the time series of a direct numerical simulation of turbulent channel flow at Ret = 180 is affected when restricted to a reduced-precision representation. We utilize a non-overlapping batch means estimator and find that the mean statistics can, in this case, be obtained with significantly fewer mantissa bits than conventional IEEE-754 double precision, but that the mean values are observed to be more sensitive in the middle of the channel than in the near-wall region. This indicates that using lower precision in the near-wall region, where the majority of the computational efforts are required, may benefit from low-precision floating point units found in upcoming computer hardware.

Rotors play a major role in various applications including ventilation and propulsion systems such as in helicopters, drones, gas turbines, wind turbines and many more. This visualization of instantaneous vortical structures (identified by the λ2 criterion) shows complex flow structures emanating from a twisted drone rotor that is impulsively starting to rotate at 1600 rpm. Initially, a starting vortex is formed as a result of lift generation and shed as a connected vortex tube from the entire surface of the blade, which has a strong connection to the blade tip via the so-called tip vortex. Leading-edge separation occurs at span positions of high twist, followed by wave-induced breakdown to turbulence along the whole wing span. This turbulence then sheds as small-scale vortices into the wake and dissipates. Understanding the behaviour of these vortices from such complex blades and how they interact with the other blade is critical to design more efficient and potentially more silent propellers.

Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. 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 have 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 reduction 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.

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.