## Publications

88 results found

Giannenas A, Bempedelis N, Schuch F,
et al., 2022, A Cartesian immersed boundary method based on 1D flow reconstructions for high-fidelity simulations of incompressible turbulent flows around moving objects, *Flow, Turbulence and Combustion*, ISSN: 0003-6994

The aim of the present numerical study is to show that the recentlydeveloped Alternating Direction Reconstruction Immersed BoundaryMethod (ADR-IBM) [1] can be used for Fluid-Structure Interaction (FSI)problems and can be combined with an Actuator Line Model (ALM)and a Computer-Aided Design (CAD) interface for high-fidelity simulations of fluid flow problems with rotors and geometrically compleximmersed objects. The method relies on 1D cubic spline interpolations to reconstruct an artificial flow field inside the immersed objectwhile imposing the appropriate boundary conditions on the boundariesof the object. The new capabilities of the method are demonstratedwith the following flow configurations: a turbulent channel flow withthe wall modelled as an immersed boundary, Vortex Induced Vibrations (VIVs) of one-degree-of-freedom (2D) and two-degree-of-freedom(3D) cylinders, a helicopter rotor and a multi-rotor unmanned aerialvehicle in hover and forward motion. These simulations are performed with the high-order fluid flow solver Incompact3d which is based ona 2D domain decomposition in order to exploit modern CPU-basedsupercomputers. It is shown that the ADR-IBM can be used for thestudy of FSI problems and for high-fidelity simulations of incompressible turbulent flows around moving complex objects with rotors.

Giannenas A, Laizet S, Rigas G, 2022, Harmonic forcing of a laminar bluff body wake with rear pitching flaps, *Journal of Fluid Mechanics*, Vol: 945, ISSN: 0022-1120

A numerical study on the response of a 2D bluff body wake subjected to harmonicforcing imposed by two rear pitching flaps is performed. The wake is generated by arectangle at a height-based Reynolds number Re = 100, characterised by laminar vortexshedding. Two forcing strategies are examined corresponding to in-phase “snaking” andout-of-phase “clapping”. The effects of the bluff body aspect ratio (AR = 1, 2, 4), flappingfrequency, flapping amplitude, flap length and Reynolds number are investigated. For thesnaking motion, a strong fundamental resonance of the root mean square (RMS) drag isobserved when the wake is forced near the vortex shedding frequency. For the clappingmotion, a weak subharmonic resonance is observed when the forcing is applied neartwice the vortex shedding frequency resulting in an increase of the lift RMS whereasthe drag RMS remains unaffected. Both resonances intensify the vortex shedding and aconcomitant mean drag increase is observed for the snaking motion. Forcing away fromthe resonant regimes, both motions result in considerable drag reduction through wakesymmetrisation and propulsion mechanisms. The formation of two vortex dipoles peroscillation period due to the flapping motion, which weaken the natural vortex shedding,has been identified as the main symmetrisation mechanism. A single scaling parameter isproposed to collapse the mean drag reduction of the forced flow for both motions over awide range of flapping frequencies, amplitudes and flap lengths. Finally, the assessmentof the performance of the forcing strategies has revealed that clapping is more effectivethan snaking.

Hodgkin A, Laizet S, Deskos G, 2022, Numerical investigation of the influence of shear and thermal stratification on the wind turbine tip-vortex stability, *Wind Energy*, Vol: 25, Pages: 1270-1289, ISSN: 1095-4244

The interaction between wind turbine wakes and atmospheric turbulence is characterisedby complex dynamics. In this study, two major components of the atmospheric boundarylayer dynamics have been isolated, namely, the mean velocity profile shear and the thermalstratification, to examine their impact on the near-wake development by undertaking aseries of highly resolved large-eddy simulations. Subsequently, instantaneous flow fields areextracted from the simulations and used to conduct Fourier analysis and proper orthogonaldecomposition (POD) and compute the mean kinetic energy fluxes by different POD modesto better understand the tip-vortex instability mechanisms. Our findings indicate that shearcan significantly affect the breakup of the wind turbine tip-vortices as well as the shapeand stable length of the wake, whereas thermal stratification seems to only have limitedcontribution to the spatial development of the near-wake field. Finally, our analysis showsthat the applied perturbation frequency determines the tip-vortex breakup location as itcontrols the onset of the mutual inductance instability.

Hodgkin A, Laizet S, Deskos G, 2022, Do ambient shear and thermal stratification impact wind turbine tip-vortex breakdown?, ISSN: 1742-6588

Modern wind turbines experience uneven inflow conditions across the rotor, due to the ambient flow's shear and thermal stratification. Such conditions alter the shape and length of turbine wakes and thus impact the loads and power generation of downstream turbines. To this end, understanding the spatial evolution of the individual wakes under different atmospheric conditions is key to controlling and optimising turbine arrays. With this numerical study we aim to obtain a better understanding of the fundamental physics governing the near-wake dynamics of wind turbines under shear and thermal stability, by examining their tip-vortex breakup mechanisms. Our approach considers scale-resolving simulations of a single turbine wake under a linear shear profile as well as the application of harmonic tip perturbations to trigger flow instabilities. For the subsequent analysis we use the proper orthogonal decomposition (POD) method to extract coherent structures from the flow, and we also calculate mean kinetic energy fluxes to quantify each coherent structure's contribution to wake recovery. The wake's helical spiral is found to hinder wake recovery for all studied ambient flow conditions, whereas the mutual inductance instability has positive MKE flux leading to an enhanced wake recovery. Finally, the ambient shear has the largest impact on the local MKE flux with respect to downstream location by changing the shape of the curve and location of extrema, whereas thermal stratification has only a minimal impact on the magnitude of the near-wake local MKE flux distribution.

Ozbay A, Laizet S, 2022, Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings, *AIP Advances*, Vol: 12, ISSN: 2158-3226

The usage of neural networks (NNs) for flow reconstruction (FR) tasks from a limited number of sensors is attracting strong research interest owing to NNs’ ability to replicate high-dimensional relationships. Trained on a single flow case for a given Reynolds number or over a reduced range of Reynolds numbers, these models are unfortunately not able to handle flows around different objects without re-training. We propose a new framework called Spatial Multi-Geometry FR (SMGFR) task, capable of reconstructing fluid flows around different two-dimensional objects without re-training, mapping the computational domain as an annulus. Different NNs for different sensor setups (where information about the flow is collected) are trained with high-fidelity simulation data for a Reynolds number equal to ∼300 for 64 objects randomly generated using Bezier curves. The performance of the models and sensor setups is then assessed for the flow around 16 unseen objects. It is shown that our mapping approach improves percentage errors by up to 15% in SMGFR when compared to a more conventional approach where the models are trained on a Cartesian grid and achieves errors under 3%, 10%, and 30% for predictions of pressure, velocity, and vorticity fields, respectively. Finally, SMGFR is extended to predictions of snapshots in the future, introducing the Spatiotemporal MGFR (STMGFR) task. A novel approach is developed for STMGFR involving splitting deep neural networks into a spatial and a temporal component. We demonstrate that this approach is able to reproduce, in time and in space, the main features of flows around arbitrary objects.

Francisco E, Espath LF, Laizet S,
et al., 2022, Direct numerical simulations of intrusive density- and particle-driven gravity currents, *Physics of Fluids*, Vol: 34, Pages: 1-19, ISSN: 1070-6631

In the present study, mesopycnal flows are investigated using Direct Numerical Simulations (DNS). In particular, intrusive density- and particle-driven gravity currentsin the lock exchange set-up are simulated with the high-order finite-difference framework Xcompact3d. To account for the settling velocity of particles, a customisedFick’s law for the particle-solution species is used with an additional term incorporating a constant settling velocity proportional to the concentration of particles. Ageneral energy budget equation is presented, for which the energy can migrate acrossthe domain’s boundaries. The relevant main features of intrusive gravity currents,such as front velocity, energy exchanges, sedimentation rate, deposit profile, anddeposit map are discussed with comparison between two and three-dimensional simulations. In particular, the influence of the Grashof number, the interface thickness,the energy exchanges, the sedimentation process, and how the presence of more thanone particle fraction may change the flow dynamics are investigated. The results arein good agreement with previous experiments and theoretical work, in particular forthe prediction of the front velocity. For the particle-driven case, the suspended massevolution along with the sedimentation rate suggests the occurrence of three differentstages. In the first stage after the lock release, the particle mixture tends to suspenditself due to gravitational forces. Once most of the particle-mixture mass is suspended, the current intrudes while increases its velocity, reaching its kinetic energypeak. In the last stage, the particles are deposited at a nearly constant sedimentationrate. As a results, the front velocity constantly decelerates.

Hamzehloo A, Lusher DJ, Laizet S, et al., 2022, Direct numerical simulations of shocklet-containing turbulent channel counter-flows, 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)

Counter-flow or counter-current configurations can maintain high turbulence intensities and exhibit a significant level of mixing. We have previously introduced a wall-bounded counter-flow turbulent channel configuration (Physical Review Fluids, 6(9), p.094603.) as an efficient framework to study compressibility effects on turbulence. Here, we extend our previous direct numerical simulation study to a relatively higher Mach number (M = 0.7) to investigate strong compressibility effects (also by reducing the Prandtl number from Pr = 0.7 to 0.2), and the formation and evolution of unsteadyshocklet structures. It is found that the configuration is able to produce highly turbulent flows with embedded shocklets and significant asymmetry in probability density functions of dilatation. A peak turbulent Mach number close to unity is obtained, for which the contribution of the dilatational dissipation to total dissipation is nevertheless found to be limited to 6%.

Khojasteh AR, Laizet S, Heitz D,
et al., 2022, Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900., *Data in Brief*, Vol: 40, Pages: 1-9, ISSN: 2352-3409

The dataset contains Eulerian velocity and pressure fields, and Lagrangian particle trajectories of the wake flow downstream of a smooth cylinder at a Reynolds number equal to 3900. An open source Direct Numerical Simulation (DNS) flow solver named Incompact3d was used to calculate the Eulerian field around the cylinder. The synthetic Lagrangian tracer particles were transported using a fourth-order Runge-Kutta scheme in time and trilinear interpolations in space. Trajectories of roughly 200,000 particles for two 3D sub-domains are available to the public. This dataset can be used as a test case for tracking algorithm assessment, exploring the Lagrangian physics, statistic analyses, machine learning, and data assimilation interests.

Balogh GD, Flynn T, Laizet S,
et al., 2021, Scalable many-core algorithms for tridiagonal solvers, *Computing in Science and Engineering*, Vol: 24, ISSN: 1521-9615

We present a novel distributed memory Tridiagonal solver library, targeting large-scale systems based on modern multi-core and many-core processor architectures. The library uses methods based on both approximate and exact algorithms. Performance comparisons with the state-of-the-art, using both a large Cray EX system and a GPU cluster show the algorithmic trade-offs required at increasing machine scale to achieve good performance, particularly considering the advent of exascale systems.

Giannenas A, Laizet S, 2021, A simple and scalable Immersed Boundary Method for high-fidelity simulations of fixed and moving objects on a Cartesian mesh, *Applied Mathematical Modelling: simulation and computation for engineering and environmental systems*, Vol: 99, Pages: 606-627, ISSN: 0307-904X

A simple and scalable Immersed Boundary Method based on cubic spline reconstructionsis presented for high-fidelity simulations of immersed objects in a turbulent flow on aCartesian mesh. The novelty of the proposed IBM lies in its simplicity, accuracy, scalabilityand its ability to simulate both fixed and moving immersed objects. The new IBM is thoroughly validated against a 1D benchmark, with the 2D flow around a cylinder at Re = 40and 300 and the 3D flow around a sphere at Re = 300 and Re = 3700. Convergence studies and detailed error maps showing the spatial distribution of the velocity L2-Norm errorcompared to a spectral reference solution for the cylinders at Re = 40 show the robustnessof the proposed method. The cost and performance of the method are also presented formulti-billion mesh node simulations with up to 65,536 computational cores. The potentialof the method in handling multiple moving objects for practical applications is demonstrated with the control of a square bluff body wake by two rear pitching flaps.

Mahfoze O, Laizet S, 2021, Non-explicit Large Eddy Simulations of turbulent channel flows from Reτ= 180 up to Reτ= 5,200, *Computers and Fluids*, Vol: 228, Pages: 1-19, ISSN: 0045-7930

This numerical study based on high-order finite-difference schemes presents LES-NWR (Large Eddy Simulation with near-wall resolution) of turbulent channel flows up to Reτ = 5200 using non-explicit approaches for which numerical dissipation is introduced via the discretisation of viscous terms of the Navier-Stokes equations. These models are cheaper than explicit LES models as no extra terms are needed in the equations toaccount for the contribution of the unresolved scales. The Approximate Deconvolution Method with Relaxation Term (ADM-RT) approach is also assessed and the present LES data are compared with reference Direct Numerical Simulations (DNS) data for first and second order moments as well as for the turbulent kinetic energy budget. Even if the viscous sublayer is not resolved, the proposed non-explicit LES approaches are in excellent agreement with the reference DNS data and to a certain extent with the ADM-RT model, for a fraction of the cost of the DNS. The proposed non-explicit models, for which the possibility to locally adjust the added numerical dissipation is investigated, are straightforward to implement and come with a negligible additional computational cost while the ADM-RT model is 30% more expensive than the non-explicit models.The parameters of the models are defined before the simulations and no modifications of the parameters are needed when the Reynolds number and the mesh resolution are changed. It is shown that a modulation of the magnitude of the numerical dissipation in time and in space is not necessarily needed, at least for the mesh resolutions and Reynolds numbers considered in the present study. The main conclusion is that non-explicit models can replace advantageously explicit models when high-order finite-difference methods are used. They can generate accurate LES-NWR of turbulent channel flows over a wide range of Reynolds numbers at a fraction of a cost of DNS.

Khojasteh AR, Yang Y, Heitz D,
et al., 2021, Lagrangian coherent track initialisation, *Physics of Fluids*, Vol: 33, Pages: 1-13, ISSN: 1070-6631

Advances in time-resolved three-dimensional Particle Tracking Velocimetry (4D-PTV)techniques have been consistently revealed more accurate Lagrangian particle motions.A novel track initialisation technique as a complementary part of 4D-PTV, based on localtemporal and spatial coherency of neighbour trajectories, is proposed. The proposed Lagrangian Coherent Track Initialisation (LCTI) applies physics-based Finite Time LyapunovExponent (FTLE) to build four frame coherent tracks. We locally determine LagrangianCoherent Structures (LCS) among neighbour trajectories by using the FTLE boundaries(i.e., ridges) to distinguish clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wakedownstream of a smooth cylinder at a Reynolds number equal to 3900 obtained fromthree-dimensional (3D) Direct Numerical Simulation (DNS). Performance of the proposedmethod based on three characteristic parameters, temporal scale, particle concentration(i.e., density), and noise ratio, showed robust behaviour in finding true tracks compared tothe recent initialisation algorithms. Sensitivity of LCTI to the number of untracked andwrong tracks are also discussed. We address the capability of using the proposed methodas a function of a 4D-PTV scheme in the Lagrangian Particle Tracking (LPT) challenge.We showed that LCTI prevents 4D-PTV divergence in flows with high particle concentrations. Finally, the LCTI behaviour was demonstrated in a jet impingement experiment.LCTI was found to be a reliable tracking tool in complex flow motions, with a strengthrevealed for flows with high velocity and acceleration gradients.

Hamzehloo A, Lusher D, Laizet S,
et al., 2021, Direct numerical simulation of compressible turbulence in acounter-flow channel configuration, *Physical Review Fluids*, Vol: 6, Pages: 1-21, ISSN: 2469-990X

Counter-flow configurations, whereby two streams of fluid are brought together from oppositedirections, are highly efficient mixers due to the high turbulence intensities that can be maintained.In this paper, a simplified version of the problem is introduced that is amenable to direct numericalsimulation. The resulting turbulent flow problem is confined between two walls, with one non-zeromean velocity component varying in the space direction normal to the wall, corresponding to asimple shear flow. Compared to conventional channel flows, the mean flow is inflectional and themaximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The numerical requirements and turbulence properties of this configuration are firstdetermined. The Reynolds shear stress is required to vary linearly by the imposed forcing, witha peak at the channel centreline. A similar behaviour is observed for the streamwise Reynoldsstress, the budget of which shows an approximately uniform distribution of dissipation, with largecontributions from production, pressure-strain and turbulent diffusion. A viscous sublayer is obtained near the walls and with increasing Reynolds number small-scale streaks in the streamwisemomentum are observed, superimposed on the large-scale structures that buffet this region. Whenthe peak local mean Mach number reaches 0.55, turbulent Mach numbers of 0.6 are obtained,indicating that this flow configuration can be useful to study compressibility effects on turbulence.

Özbay AG, Hamzehloo A, Laizet S,
et al., 2021, Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh, *Data-Centric Engineering*, Vol: 2, Pages: 1-31, ISSN: 2632-6736

<jats:title>Abstract</jats:title> <jats:p>The Poisson equation is commonly encountered in engineering, for instance, in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right-hand side term, arbitrary boundary conditions, and grid parameters. It provides unprecedented versatility for a CNN approach dealing with partial differential equations. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace subproblems. The model is trained using a novel loss function approximating the continuous <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2632673621000071_inline1.png" /> <jats:tex-math>$ {L}^p $</jats:tex-math> </jats:alternatives> </jats:inline-formula> norm between the prediction and the target. Even when predicting on grids denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile. The proposed model, which outperforms well-known neural network models, can be included in a CFD solver to help with solving the Poisson equation. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors below 10%, an improvement by comparison to the first step of conventional iterative methods. Predictions from our model, used as the initial guess to iterative algorithms like Multigrid, can reduce the root mean square error af

Hamzehloo A, Bartholomew P, Laizet S, 2021, Direct numerical simulations of incompressible Rayleigh–Taylor instabilities at low and medium Atwood numbers, *Physics of Fluids*, Vol: 33, Pages: 1-23, ISSN: 1070-6631

Direct numerical simulations of two-dimensional (2D) and three-dimensional (3D), single-mode and multi-mode, incompressible immiscible Rayleigh–Taylor (RT) instabilities are performed using a phase-field approach and high-order finite-difference schemes. Various combinations of Atwood number, Reynolds number, surface tension, and initial perturbation amplitude are investigated. It is found that at high Reynolds numbers, the surface tension, if significant, could prevent the formation of Kelvin–Helmholtz type instabilities within the bubble region. A relationship is proposed for the vertical distance of the bubble and spike vs the Atwood number. The spike and bubble reaccelerate after reaching a temporary plateau due to the reduction of the friction drag as a result of the formation of the spike vortices and also the formation of a momentum jet traveling upward within the bubble region. The interface for a 3D single-mode instability grows exponentially; however, a higher Reynolds number and/or a lower Atwood number could result in a noticeably larger surface area after the initial growth. It is also shown that a 3D multi-mode RT instability initially displays an exponential interface growth rate similar to single-mode RT instabilities. Due to the collapse and merging of individual single-mode instabilities, the interface area for a multi-mode RT instability is strongly dependent to the mesh resolution after the exponential growth rate. However, the ratio of kinetic energy over released potential energy exhibits an almost steady state after the initial exponential growth, with values around 0.4, independently of the mesh resolution.

Frantz R, Deskos G, Laizet S,
et al., 2021, High-fidelity simulations of gravity currents using a high-order finite-difference spectral vanishing viscosity approach, *Computers and Fluids*, Vol: 221, Pages: 1-18, ISSN: 0045-7930

This numerical work investigates the potential of a high-order finite-difference spectralvanishing viscosity approach to simulate gravity currents at high Reynolds numbers.The method introduces targeted numerical dissipation at small scales through alteringthe discretisation of the second derivatives of the viscous terms in the incompressibleNavier-Stokes equations to mimic the spectral vanishing viscosity (SVV) operator, originally designed for the regularisation of spectral element method (SEM) solutions of pureadvection problems. Using a sixth-order accurate finite-difference scheme, the adoption ofthe SVV method is straightforward and comes with a negligible additional computationalcost. In order to assess the ability of this high-order finite-difference spectral vanishingviscosity approach, we performed large-eddy simulations (LES) of a gravity current ina channelised lock-exchange set-up with our SVV model and with the well-known explicit static and dynamic Smagorinsky sub-grid scale (SGS) models. The obtained dataare compared with a direct numerical simulation (DNS) based on more than 800 millionmesh nodes, and with experimental measurements. A framework for the energy budgetis introduced to investigate the behaviour of the gravity current. First, it is found thatthe DNS is in good agreement with the experimental data for the evolution of the frontlocation and velocity field as well as for the stirring and mixing inside the gravity current. Secondly, the LES performed with less than 0.4% of the total number of mesh nodescompared to the DNS, can reproduce the main features of the gravity currents, with theSVV model yielding slightly more accurate results. It is also found that the dynamicSmagorinsky model performs better than its static version. For the present study, thestatic and dynamic Smagorinsky models are 1.8 and 2.5 times more expensive than theSVV model, because the latter does not require the calculation of explicit SGS terms inthe Navier-Stokes equa

Mays MD, Laizet S, Lardeau S, 2021, Performance of Various Turbulence Models for Simulating Sub-critical High-Reynolds Number Flows over a Smooth Cylinder

Simulating the flow over a smooth cylinder with low-level inlet turbulence for a Reynolds number equal to 140,000 remains a robust test case to evaluate the performance of turbulence closure models and numerical methods. This study considers a variety of closure levels, Reynolds-Averaged Navier-Stokes (RANS), Detached and Large Eddy Simulations (DES/LES) and hybrid RANS/LES, to determine their applicability to this case, with consideration given to their sensitivities to the spatial resolution and to the numerical schemes used. Neither the RANS nor DES closures selected in this study are able to capture the correct physical behavior of the flow, largely due to weaknesses in the model formulations that prevent the formation of instabilities in the free shear layer. The LES Wall-Adapting Local Eddy-viscosity (WALE) model performs well with a sufficiently well refined mesh but it remains a computationally demanding method. A novel Scale Resolving Hybrid (SRH) model, formally derived from temporal filtering of the Navier-Stokes equations, shows an excellent agreement with experiment for the quantities of interest. The SRH model performs far better on a coarse mesh by comparison to other RANS and hybrid RANS/LES models and can produce results similar to the LES WALE model. The main conclusion of this work is that the robust behaviour of the SRH model, coupled with its potentially substantial reduction in computational demand, makes it an excellent candidate to study highly-separated external flows at high Reynolds numbers.

Hamzehloo A, Lusher D, Laizet S,
et al., 2021, On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high-speed compressible flows, *International Journal for Numerical Methods in Fluids*, Vol: 93, Pages: 176-196, ISSN: 0271-2091

High‐speed compressible turbulent flows typically contain discontinuities and have been widely modelled using Weighted Essentially Non‐Oscillatory (WENO) schemes due to their high‐order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence, and result in inaccurate solutions in the context of turbulence‐resolving simulations. In this connection, the recently‐developed Targeted Essentially Non‐Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully‐turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1: 5 and Re τ = 222 is conducted using OpenSBLI, a high‐order finite difference CFD framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high‐order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against theWALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three‐dimensional vortical structures. The 6th order adaptive TENO scheme is found to produce comparable results to those obtained with non‐dissipative 4th and 6th order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.

Voet L, Ahlfeld R, Gaymann A,
et al., 2021, A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling, *Applied Mathematical Modelling: simulation and computation for engineering and environmental systems*, Vol: 89, Pages: 885-906, ISSN: 0307-904X

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

Wang C, Muñóz-Simon A, Deskos G,
et al., 2020, Code-to-code-to-experiment validation of LES-ALM wind farm simulators, *Journal of Physics: Conference Series*, Vol: 1618, Pages: 1-8, ISSN: 1742-6588

The aim of this work is to present a detailed code-to-code comparison of two Large-Eddy Simulation (LES) solvers. Corresponding experimental measurements are used as a reference to validate the quality of the CFD simulations. The comparison highlights the effects of solver order on the solutions, and it tries to answer the question of whether a high order solver is necessary to capture the main characteristics of a wind farm. Both solvers were used on different grids to study their convergence behavior. While both solvers show a good match with experimental measurements, it appears that the low order solver is more accurate and substantially cheaper in terms of computational cost.

Bartholomew P, Deskos G, Frantz R,
et al., 2020, Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh, *SoftwareX*, Vol: 12, ISSN: 2352-7110

Xcompact3D is a Fortran 90–95 open-source framework designed for fast and accurate simulations of turbulent flows, targeting CPU-based supercomputers. It is an evolution of the flow solver Incompact3D which was initially designed in France in the mid-90’s for serial processors to solve the incompressible Navier–Stokes equations. Incompact3D was then ported to parallel High Performance Computing (HPC) systems in the early 2010’s. Very recently the capabilities of Incompact3D have been extended so that it can now tackle more flow regimes (from incompressible flows to compressible flows at low Mach numbers), resulting in the design of a new user-friendly framework called Xcompact3D. The present manuscript presents an overview of Xcompact3D with a particular focus on its functionalities, its ready-to-run simulations and a few case studies to demonstrate its impact.

Xiao H, Wu J-L, Laizet S,
et al., 2020, Flows over periodic hills of parameterized geometries: a dataset for data-driven turbulence modeling from direct simulations, *Computers and Fluids*, Vol: 200, ISSN: 0045-7930

Computational fluid dynamics models based on Reynolds-averaged Navier–Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.

Deskos G, Laizet S, Palacios R, 2020, WInc3D: a novel framework for turbulence-resolving simulations of wind farm wake interactions, *Wind Energy*, Vol: 23, Pages: 779-794, ISSN: 1095-4244

A fast and efficient turbulence‐resolving computational framework, dubbed as WInc3D (Wind Incompressible 3‐Dimensional solver), is presented and validated in this paper. WInc3D offers a unified, highly scalable, high‐fidelity framework for the study of the flow structures and turbulence of wind farm wakes and their impact on the individual turbines' power and loads. Its unique properties lie on the use of higher‐order numerical schemes with “spectral‐like” accuracy, a highly efficient parallelisation strategy which allows the code to scale up to O(104) computing processors and software compactness (use of only native solvers/models) with virtually no dependence to external libraries. The work presents an overview of the current modelling capabilities along with model validation. The presented applications demonstrate the ability of WInc3D to be used for testing farm‐level optimal control strategies using turbine wakes under yawed conditions. Examples are provided for two turbines operating in‐line as well as a small array of 16 turbines operating under “Greedy” and “Co‐operative” yaw angle settings. These large‐scale simulations were performed with up to 8192 computational cores for under 24 hours, for a computational domain discretised with O(109) mesh nodes.

Mahfoze O, Moody A, Wynn A,
et al., 2019, Reducing the skin-friction drag of a turbulent boundary-layer flow with low-amplitude wall-normal blowing within a Bayesian optimisation framework, *Physical Review Fluids*, Vol: 4, Pages: 094601-1-094601-23, ISSN: 2469-990X

A Bayesian optimisation framework is developed to optimise low-amplitude wall-normal blowing control of a turbulent boundary-layer flow. The Bayesian optimisation framework determines the optimum blowing amplitude and blowing coverage to achieve up to a 5% net-power saving solution within 20 optimisation iterations, requiring 20 Direct Numerical Simulations (DNS). The power input required to generate the low-amplitude wall-normal blowing is measured experimentally for two different types of blowing device, and is used in the simulations to assess control performance. Wall-normal blowing with amplitudes of less than 1% of the free-stream velocity generate a skin-friction drag reduction of up to 76% over the control region, with a drag reduction which persists for up to 650δ0 downstream of actuation (where δ0 is the boundary-layer thickness at the start of the simulation domain). It is shown that it is the slow spatial recovery of the turbulent boundary-layer flow downstream of control which generates the net-power savings in this study. The downstream recovery of the skin-friction drag force is decomposed using the Fukagata-Iwamoto-Kasagi (FIK) identity, which shows that the generation of the net-power savings is due to changes in contributions to both the convection and streamwise development terms of the turbulent boundary-layer flow.

Bartholomew P, Laizet S, 2019, A new highly scalable, high-order accurate framework for variable-density flows: application to non-Boussinesq gravity currents, *Computer Physics Communications*, Vol: 242, Pages: 83-94, ISSN: 0010-4655

This paper introduces a new code “QuasIncompact3D” for solving the variabledensity Navier-Stokes equations in the low-Mach number limit. It is derived from the Incompact3D framework which is designed for incompressible flows [1]. QuasIncompact3D is based on high-order accurate compact finite-differences [2], an efficient 2D domain decomposition [3] and a spectral Poisson solver. The first half of the paper focuses on introducing the low-Mach number governing equations, the numerical methods and the algorithm employed by QuasIncompact3D to solve them. Two approaches to forming the pressure-Poisson equation are presented: one based on an extrapolation that is efficient but limited to low density ratios and another one using an iterative approach suitable for higher density ratios. The scalability of QuasIncompact3D is demonstrated on several TIER-1/0 supercomputers using both approaches, showing good scaling up to 65k cores. Validations for incompressible and variable-density low-Mach number flows us-ing the Taylor-Green vortex and a non-isothermal mixing layer, respectively, as test cases are then presented, followed by simulations of non-Boussinesq gravity currents in two- and three-dimensions. To the authors’ knowledge this is the first investigation of 3D non-Boussinesq gravity currents by means of Direct Numerical Simulation over a relatively long time evolution. It is found that 2D and 3D simulations of gravity currents show differences in the locations of the fronts, specifically that the fronts travel faster in three dimensions, but that it only becomes apparent after the initial stages. Our results also show that the difference in terms of front location decreases the further the flow is from Boussinesq conditions.

Pinier B, Mémin E, Laizet S,
et al., 2019, Stochastic flow approach to model the mean velocity profile of wall-bounded flows, *Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*, Vol: 99, ISSN: 1539-3755

There is no satisfactory model to explain the mean velocity profile of the whole turbulent layer in canonical wall-bounded flows. In this paper, a mean velocity profile expression is proposed for wall-bounded turbulent flows based on a recently proposed stochastic representation of fluid flows dynamics. This original approach, called modeling under location uncertainty, introduces in a rigorous way a subgrid term generalizing the eddy-viscosity assumption and an eddy-induced advection term resulting from turbulence inhomogeneity. This latter term gives rise to a theoretically well-grounded model for the transitional zone between the viscous sublayer and the turbulent sublayer. An expression of the small-scale velocity component is also provided in the viscous zone. Numerical assessments of the results are provided for turbulent boundary layer flows, pipe flows and channel flows at various Reynolds numbers.

Wu J, Sun R, Laizet S,
et al., 2019, Representation of stress tensor perturbations with application in machine-learning-assisted turbulence modeling, *Computer Methods in Applied Mechanics and Engineering*, Vol: 346, Pages: 707-726, ISSN: 0045-7825

Numerical simulations based on Reynolds-Averaged Navier–Stokes (RANS) equations are widely used in engineering design and analysis involving turbulent flows. However, RANS simulations are known to be unreliable in many flows of engineering relevance, which is largely caused by model-form uncertainties associated with the Reynolds stresses. Recently, a machine-learning approach has been proposed to quantify the discrepancies between RANS modeled Reynolds stress and the true Reynolds stress. However, it remains a challenge to represent discrepancies in the Reynolds stress eigenvectors in machine learning due to the requirements of spatial smoothness, frame-independence, and realizability. This challenge also exists in the data-driven computational mechanics in general where quantifying the perturbation of stress tensors is needed. In this work, we propose three schemes for representing perturbations to the eigenvectors of RANS modeled Reynolds stresses: (1) discrepancy-based Euler angles, (2) direct-rotation-based Euler angles, and (3) unit quaternions. We compare these metrics by performing a priori and a posteriori tests on two canonical flows: fully developed turbulent flows in a square duct and massively separated flows over periodic hills. The results demonstrate that the direct-rotation-based Euler angles representation lacks spatial smoothness while the discrepancy-based Euler angles representation lacks frame-independence, making them unsuitable for being used in machine-learning-assisted turbulence modeling. In contrast, the representation based on unit quaternion satisfies all the requirements stated above, and thus it is an ideal choice in representing the perturbations associated with the eigenvectors of Reynolds stress tensors. This finding has clear importance for uncertainty quantification and machine learning in turbulence modeling and for data-driven computational mechanics in general.

Deskos G, Laizet S, Piggott M, 2019, Turbulence-resolving simulations of wind turbine wakes, *Renewable Energy*, Vol: 134, Pages: 989-1002, ISSN: 1879-0682

Turbulence-resolving simulations of wind turbine wakes are presented using a high-order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include mean velocity and turbulent intensity profiles, as well as integral rotor quantities such as power and thrust coefficients. For the standard (also termed static) case the magnitude of the spectral vanishing viscosity is selected via a heuristic analysis of the wake statistics, while in the case of the dynamic model the magnitude is adjusted both in space and time at each time step. The study focuses on examining the ability of the two approaches, standard (static) and dynamic, to accurately capture the wake features, both qualitatively and quantitatively. The results suggest that the static method can become over-dissipative when the magnitude of the spectral viscosity is increased, while the dynamic approach which adjusts the magnitude of dissipation locally is shown to be more appropriate for a non-homogeneous flow such that of a wind turbine wake.

Lamballais E, Dairay T, Laizet S, et al., 2019, Implicit/explicit spectral viscosity and large-scale SGS effects, ERCOFTAC Series, Pages: 107-113

In order to investigate the scale-selective influence of SGS on the large scale dynamics, DNS and LES are performed for the Taylor-Green vortex problem. An a priori analysis confirms the interest of the hyperviscous feature at small scale as used in implicit LES, SVV and VMS. However, the assumption of zero SGS dissipation at very large scales is found unrealistic for the high Reynolds number and coarse LES mesh considered. A posteriori analysis shows that SGS modelling based on the assumption of an inviscid cascade leads to a bottleneck effect on the kinetic energy spectrum with a significant underprediction of the total SGS dissipation. The simple addition of a constant eddy viscosity, even targeted to be optimal in terms of SGS dissipation, is unable to give realistic results. To allow accurate predictions by LES, a specific closure that incorporates both the hyperviscous feature (i.e. regularisation) and the expected SGS dissipation at large scales has to be developed.

Deskos G, Piggott MD, Laizet S, 2019, Development and validation of the higher-order finite-difference wind farm simulator, winc3d, Pages: 721-728

High-fidelity wind farm models typically employ Large–Eddy Simulation (LES) formulations and turbine parametrisations (e.g. actuator disc models) to resolve the turbine wakes at spatial and temporal scales so that all flow features of engineering importance are well–captured. Such features include the low frequency dynamic wake meandering, which plays a key role in the fatigue loading expe-rienced by downstream turbines clustered in arrays. By the term ‘Wind Farm Simulator’ (WFS) we refer to an integrated framework which offers these capabilities and can be used as a research tool to study wake–to–wake and turbine–to–wake interactions. In this work, we present a validation study for WInc3D, a WFS based on the powerful, sixth-order finite-difference flow solver, incompact3d. For our validation study, we use operational scenarios from the Horns Rev offshore wind farm. The comparison of the present model with existing Supervisory Control and Data Acquisition (SCADA) measurements and previous LES studies shows an overall good agreement.

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