371 results found
Chun S, Marcon J, Peiro J, et al., 2022, Reducing errors caused by geometrical inaccuracy to solve partial differential equations with moving frames on curvilinear domain, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 398, ISSN: 0045-7825
Weinberg P, Kandangwa P, Torii R, et al., 2022, Influence of right coronary artery motion, flow pulsatility and non-Newtonian rheology on wall shear stress metrics, Fontiers in Bioengineering and Biotechnology, ISSN: 2296-4185
The patchy distribution of atherosclerosis within the arterial system is consistent with a controlling influence of hemodynamic wall shear stress (WSS). Patterns of low, oscillatory and transverse WSS have been invoked to explain the distribution of disease in the aorta. Disease of coronary arteries has greater clinical importance but blood flow in these vessels may be complicated by their movement during the cardiac cycle. Previous studies have shown that time average WSS is little affected by the dynamic geometry, and that oscillatory shear is influenced more. Here we additionally investigate effects on transverse WSS. We also investigate the influence of non-Newtonian blood rheologyas it can influence vortical structure, on which transverse WSS depends; Carreau-Yasuda models were used. WSS metrics were derived from numerical simulations of blood flow in a model of a moving right coronary artery which, together with a subject-specific inflow waveform, was obtained by MR imaging of a healthy human subject in a previous study. The results confirmed that time average WSS was little affected by dynamic motion, and that oscillatory WSS was more affected. They additionally showed that transverse WSS and its non-dimensional analogue, the Cross Flow Index, were affected still further. This appeared to reflect time-varying vortical structures caused by the changes in curvature. The influence of non-Newtonian rheology was significant with some physiologically realistic parameter values, and hence may be important in certain subjects. Dynamic geometry and non-Newtonian rheology should be incorporated into models designed to produce maps of transverse WSS in coronary arteries.
Lyu G, Chen C, Du X, et al., 2022, Open-source Framework for Transonic Boundary Layer Natural Transition Analysis over Complex Geometries in Nektar++, AIAA Aviation 2022 Forum
Xu H, Tu G, Sherwin SJ, 2022, Theoretical advances and applications of high-fidelity computation and modelling in fluid dynamics, COMPUTERS & FLUIDS, Vol: 241, ISSN: 0045-7930
Lindblad D, Sherwin S, Cantwell C, et al., 2022, Aeroacoustic analysis of a subsonic jet using the discontinuous Galerkin method, 28th AIAA/CEAS Aeroacoustics 2022 Conference, Publisher: American Institute of Aeronautics and Astronautics, Pages: 1-21
In this work, the open-source spectral/hp element framework Nektar++ is coupled with the Antares library to predict noise from a subsonic jet. Nektar++ uses the high-order discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured grids. Unresolved turbulent scales are modeled using an implicit Large Eddy Simulation approach. In this approach, the favourable dissipation properties of the discontinuous Galerkin method are used to remove the highest resolved wavenumbers from the solution. For time-integration, an implicit, matrix-free, Newton-Krylov method is used. To compute the far-field noise, Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The simulation results are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton.
Son O, Gao A, Gursul I, et al., 2022, Leading-edge vortex dynamics on plunging airfoils and wings, Journal of Fluid Mechanics, Vol: 940, Pages: 1-30, ISSN: 0022-1120
The vortex dynamics of leading-edge vortices on plunging high-aspect-ratio (AR = 10) wings and airfoils were investigated by means of volumetric velocity measurements, numerical simulations, and stability analysis in order to understand the deformation of the leading-edge vortex filament and spanwise instabilities. The vortex filaments on both the wing and airfoilexhibit spanwise waves, but with different origins. The presence of a wing tip causes the leg of the vortex to remain attached to the wing upper surface, while the initial deformation of the filament near the wing-tip resembles a helical vortex. The essential features can be modelled as the deformation of initially L-shaped semi-infinite vortex column. In contrast, the instabilityof the vortices is well captured by the instability of counter-rotating vortex pairs, which are formed either by the trailing-edge vortices or the secondary vortices rolled-up from the wing surface. The wavelengths observed in the experiments and simulations are in agreement with the stability analysis of counter-rotating vortex pairs of unequal strength.
Pan Y, Yan Z-G, Peiro J, et al., 2022, Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver, Communications on Applied Mathematics and Computation, Vol: 4, Pages: 728-757, ISSN: 2661-8893
A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded Runge-Kutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously influencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state flow past a flat plate, Taylor-Green vortex and turbulent flow over a circular cylinder at Re=3900. The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efficiency is obtained for unsteady and steady, well-resolved and under-resolved simulations.
Hambli W, Slaughter J, Buscariolo FF, et al., 2022, Extension of Spectral/hp Element Methods towards Robust Large-Eddy Simulation of Industrial Automotive Geometries, FLUIDS, Vol: 7
Cassinelli A, Mateo Gabín A, Montomoli F, et al., 2022, Reynolds sensitivity of the wake passing effect on a LPT cascade using spectral/hp element methods, International Journal of Turbomachinery, Propulsion and Power, Vol: 7, Pages: 8-8, ISSN: 2504-186X
Reynolds-Averaged Navier–Stokes (RANS) methods continue to be the backbone of CFD-based design; however, the recent development of high-order unstructured solvers and meshing algorithms, combined with the lowering cost of HPC infrastructures, has the potential to allow for the introduction of high-fidelity simulations in the design loop, taking the role of a virtual wind tunnel. Extensive validation and verification is required over a broad design space. This is challenging for a number of reasons, including the range of operating conditions, the complexity of industrial geometries and their relative motion. A representative industrial low pressure turbine (LPT) cascade subject to wake passing interactions is analysed, adopting the incompressible Navier–Stokes solver implemented in the spectral/hp element framework Nektar++. The bar passing effect is modelled by leveraging a spectral-element/Fourier Smoothed Profile Method. The Reynolds sensitivity is analysed, focusing in detail on the dynamics of the separation bubble on the suction surface as well as the mean flow properties, wake profiles and loss estimations. The main findings are compared with experimental data, showing agreement in the prediction of wake traverses and losses across the entire range of flow regimes, the latter within 5% of the experimental measurements.
Sherwin S, Schmid P, Wu X, 2022, Preface
Reavette RM, Sherwin SJ, Tang M-X, et al., 2021, Wave intensity analysis combined with machine learning can detect impaired stroke volume in simulations of heart failure, Frontiers in Bioengineering and Biotechnology, Vol: 9, Pages: 1-13, ISSN: 2296-4185
Heart failure is treatable, but in the United Kingdom, the 1-, 5- and 10-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques; the disease is often advanced by the time a diagnosis is made. Previous studies have demonstrated that certain metrics derived from pressure-velocity-based wave intensity analysis are significantly altered in the presence of impaired heart performance when averaged over groups, but to date, no study has examined the diagnostic potential of wave intensity on an individual basis, and, additionally, the pressure waveform can only be obtained accurately using invasive methods, which has inhibited clinical adoption. Here, we investigate whether a new form of wave intensity based on noninvasive measurements of arterial diameter and velocity can detect impaired heart performance in an individual. To do so, we have generated a virtual population of two-thousand elderly subjects, modelling half as healthy controls and half with an impaired stroke volume. All metrics derived from the diameter-velocity-based wave intensity waveforms in the carotid, brachial and radial arteries showed significant crossover between groups-no one metric in any artery could reliably indicate whether a subject's stroke volume was normal or impaired. However, after applying machine learning to the metrics, we found that a support vector classifier could simultaneously achieve up to 99% recall and 95% precision. We conclude that noninvasive wave intensity analysis has significant potential to improve heart failure screening and diagnosis.
Basso R, Hwang Y, Assi G, et al., 2021, Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate, Journal of Fluid Mechanics, Vol: 928, Pages: 1-32, ISSN: 0022-1120
This paper investigates the origin of flow-induced instabilities and their sensitivities ina flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linearstability and sensitivity problem is formulated in the Eulerian frame by considering thegeometric nonlinearity arising from the rotational motion of the cylinder which is notpresent in the stationary or purely translating stability methodology. This nonlinearityneeds careful and consistent treatment in the linearised problem particularly whenconsidering the Eulerian frame or reference adopted in this study and not so widelyconsidered. Two types of instabilities arising from the fluid-structure interaction arefound. The first type of the instabilities is the stationary symmetry-breaking mode, whichwas well reported in previous studies. This instability exhibits a strong correlation withthe length of the recirculation zone. A detailed analysis of the instability mode andits sensitivity reveals the importance of the flow near the tip region of the plate for thegeneration and control of this instability mode. The second type is an oscillatory torsionalflapping mode, which has not been well reported. This instability typically emerges whenthe length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode,it is not so closely correlated with the length of the recirculation zone. The sensitivityanalysis however also reveals the crucial role played by the flow near the tip region inthis instability. Finally, it is found that many physical features of this instability arereminiscent of those of the flapping (or flutter instability) observed in a flow over aflexible plate or a flag, suggesting that these instabilities share the same physical origin.
Mengaldo G, Moxey D, Turner M, et al., 2021, Industry-Relevant Implicit Large-Eddy Simulation of a High-Performance Road Car via Spectral/hp Element Methods, SIAM REVIEW, Vol: 63, Pages: 723-755, ISSN: 0036-1445
Moura R, Cassinelli A, da Silva AFC, et al., 2021, Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations, Computer Methods in Applied Mechanics and Engineering, Vol: 388, Pages: 1-29, ISSN: 0045-7825
One of the strengths of the discontinuous Galerkin (DG) method has been its balance between accuracy and robustness, which stems from DG’s intrinsic (upwind) dissipation being biased towards high frequencies/wave numbers. This is particularly useful in high Reynolds-number flow simulations wherelimitations on mesh resolution typically lead to potentially unstable under-resolved scales. In continuous Galerkin (CG) discretisations, similar properties are achievable through the addition of artificial difusion, such as spectral vanishing viscosity (SVV). The latter, although recognised as very useful in CG-based high-fidelity turbulence simulations, has been observed to be sub-optimal when compared toDG at intermediate polynomials orders (P⇡≈3). In this paper we explore an alternative stabilisation approach by the introduction of a continuous interior penalty on the gradient discontinuity at elemental boundaries, which we refer to as a gradient jump penalisation (GJP). Analogous to DG methods, this introduces a penalisation at the elemental interfaces as opposed to the interior element stabilisation of SVV. Detailed eigen analysis of the GJP approach shows its potential as equivalent (sometimes superior) to DG dissipation and hence superior to previous SVV approaches. Through eigenanalysis, a judicious choice of GJP’sP-dependent scaling parameter is made and found to be consistent with previous a-priori error analysis. The favourable properties of the GJP stabilisation approach are also supported by turbulent flow simulations of the incompressible Navier-Stokes equation, as we achieve high-quality flow solutions atP= 3 using GJP, whereas SVV performs marginally worse atP= 5 with twice as many degrees of freedom in total.
Arshad M, Rowland EM, Riemer K, et al., 2021, Improvement and validation of a computational model of flow in the swirling well cell culture model, Biotechnology and Bioengineering, ISSN: 0006-3592
Effects of fluid dynamics on cells are often studied by growing the cells on the base of cylindrical wells or dishes that are swirled on the horizontal platform of an orbital shaker. The swirling culture medium applies a shear stress to the cells that varies in magnitude and directionality from the centre to the edge of the vessel. Computational fluid dynamics methods are used to simulate the flow and hence calculate shear stresses at the base of the well. The shear characteristics at each radial location are then compared with cell behaviour at the same position. Previous simulations have generally ignored effects of surface tension and wetting, and results have only occasionally been experimentally validated. We investigated whether such idealized simulations are sufficiently accurate, examining a commonly-used swirling well configuration. The breaking wave predicted by earlier simulations was not seen, and the edge-to-centre difference in shear magnitude (but not directionality) almost disappeared, when surface tension and wetting were included. Optical measurements of fluid height and velocity agreed well only with the computational model that incorporated surface tension and wetting. These results demonstrate the importance of including accurate fluid properties in computational models of the swirling well method.
Cooke EE, Mughal MS, Sherwin S, et al., 2021, Destabilisation of stationary and travelling crossflow disturbances due to forward and backward facing steps over a swept wing, IUTAM Laminar-Turbulent Transition, Vol: 38, Pages: 713-723
The destabilisation effects of forward and backward facing steps on cross-flow (CF) disturbances on an infinite swept wing is investigated. Stationary and travelling CF-wave instability modulations, as they convect over the abrupt surface features, are investigated computationally with step heights ranging from 18% to 53% of the boundary layer thickness at chordwise locations of 10% and 20%. An embedded mesh approach is used to compute boundary layer base flow profiles over the swept wing with the high order spectral / hp element solver, Nektar++. Linear Stability Theory (LST), Parabolised Stability Equations (PSE) and Linearised Harmonic Navier-Stokes (LHNS) models are used to investigate the development of the convecting CF disturbances. LST is used to understand the instability parameter space and map out neutral curves. PSE equations fail to correctly capture the effects of the steps due to the strong short scale variations introduced whereas, the LHNS provide a rapid and more physics correct technique to ascertain flow destabilisation effects.
Hossain MZ, Cantwell CD, Sherwin SJ, 2021, A spectral/hp element method for thermal convection, International Journal for Numerical Methods in Fluids, Vol: 93, Pages: 2380-2395, ISSN: 0271-2091
We report on a high‐fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. We consider the incompressible Navier–Stokes (NS) and advection–diffusion equations coupled through a thermal body‐forcing term. The flow is driven by a prescribed flowrate forcing with explicit treatment of the nonlinear advection terms. The explicit treatment of the body‐force term also decouples both the NS and the advection–diffusion equations. The problem is then temporally discretized using an implicit–explicit scheme in conjunction with a velocity‐correction splitting scheme to decouple the velocity and pressure fields in the momentum equation. Although not unique, this type of discretization has not been widely applied to thermal convection problems and we therefore provide a comprehensive overview of the algorithm and implementation which is available through the open‐source package Nektar++. After verifying the algorithm on a number of illustrative problems we then apply the code to investigate flow in a channel with uniform or streamwise sinusoidal lower wall, in addition to a patterned sinusoidal heating. We verify the solver against previously published two‐dimensional results. Finally, for the first time we consider a three‐dimensional problem with a streamwise sinusoidal lower wall and sinusoidal heating which, for the chosen parameter, leads to the unusual dynamics of an initially unsteady two‐dimensional instability leading to a steady three‐dimensional nonlinear saturated state.
Wang R, Wu F, Xu H, et al., 2021, Implicit large-eddy simulations of turbulent flow in a channel via spectral/hp element methods, PHYSICS OF FLUIDS, Vol: 33, ISSN: 1070-6631
Mariscal-Harana J, Charlton PH, Vennin S, et al., 2021, Estimating central blood pressure from aortic flow: development and assessment of algorithms, AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY, Vol: 320, Pages: H494-H510, ISSN: 0363-6135
Weinberg P, Arshad M, Ghim M, et al., 2021, Endothelial cells do not align with the mean wall shear stress vector, Journal of the Royal Society Interface, Vol: 18, Pages: 1-10, ISSN: 1742-5662
Alignment of arterial endothelial cells with the mean wall shear stress (WSS) vector is the prototypical example of their responsiveness to flow. However, evidence for this behaviour rests on experiments where many WSS metrics had the same orientation or where they were incompletely characterised. In the present study, we tested the phenomenon more rigorously. Aortic endothelial cells were cultured in cylindrical wells on the platform of an orbital shaker. In this system, orientation would differ depending on the WSS metric to which the cells aligned. Variation in flow features and hence in possible orientations was further enhanced by altering the viscosity of the medium. Orientation of endothelial nuclei was compared to WSS characteristics obtained by computational fluid dynamics. At low mean WSS magnitudes, endothelial cells aligned with the modal WSS vector whilst at high mean WSS magnitudes they aligned so as to minimise the shear acting across their long axis (“transverse WSS”). Their failure to align with the mean WSS vector implies that other aspects of endothelial behaviour attributed to this metric require re-examination. The evolution of a mechanism for minimising transverse WSS is consistent with it having detrimental effects on the cells and with its putative role in atherogenesis.
Buscariolo FF, Assi GRS, Sherwin SJ, 2021, Computational study on an Ahmed Body equipped with simplified underbody diffuser, JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS, Vol: 209, ISSN: 0167-6105
Lahooti M, Palacios R, Sherwin SJ, 2021, Thick strip method for efficient large-eddy simulations of flexible wings in stall, AIAA Scitech 2021 Forum, Publisher: American Institute of Aeronautics and Astronautics
An efficient computational method is presented based on the thick strip method for Large-Eddy simulation of flexible wings in stall. Fluid domain is break down into series of smaller 3D strips which one independently solved using implicit LES method. Force and moments are obtained from each strips and used to evolved the nonlinear dynamics of the structure. High deformation response of high-altitude long-endurance wing under several angle of attacks leading to the stall regions are presented to show the capability of proposed FSI method
Sherwin S, Lahooti M, Bao Y, et al., 2021, The thick strip method for slender body fluid structure interaction
For slender body fluid structure interaction which arise in problems such as the vortex induced vibration of oil riser pipes, flexible wings  or parked wind turbine blades, there is a natural separation of spatial scales between the fluid and structural problem. Nevertheless the large scale dynamics of the structure can have a notable impact on the fluid flow, for example leading to large scale separation which then modify the fluid forces applied to the structure. To resolve the full scale fluid structure interaction problem at realistic flow conditions/Reynolds number is typically prohibitive even on the largest HPC systems currently available. A reasonable modelling approach to address these challenging problems is to leverage the scale separation between the fluid and structural problem and only model the fluid on a strip at a series of locations along the slender body. Earlier approaches to this type of modelling used potential flow, two-dimensional U-RANS or even empirical data, in "thin" strip approximations. However these approaches were unable to capture the near body anisotropic or transitional flow features which are often responsible for energising the slender body dynamics. In  we proposed a generalized "thick" strip method where we adopt a finite thickness strip, which is still thin compared to the slender body, within which we apply an under-resolved Direct Numerical Simulation uDNS or implicit Large Eddy Simulation iLES modelling to capture the anisotropic flow behaviour and if sufficiently resolved the transitional nature of the flow. Within each strip we apply a high fidelity spectral/hp element-Fourier approximation using the Nektar++ package . In this presentation we will outline the development and application of the thick strip modelling method for vortex induced problem of riser pipes and wind turbine blades. We will also discuss the challenges of the high fidelity modelling using spectral/hp element approximati
Yan Z-G, Pan Y, Castiglioni G, et al., 2021, Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach, Computers & Mathematics with Applications, Vol: 81, Pages: 351-372, ISSN: 0898-1221
At high Reynolds numbers the use of explicit in time compressible flow simulations with spectral/ element discretization can become significantly limited by time step. To alleviate this limitation we extend the capability of the spectral/ element open-source software framework, Nektar++, to include an implicit discontinuous Galerkin compressible flow solver. The integration in time is carried out by a singly diagonally implicit Runge–Kutta method. The non-linear system arising from the implicit time integration is iteratively solved by the Jacobian-free Newton Krylov (JFNK) method. A favorable feature of the JFNK approach is its extensive use of the explicit operators available from the previous explicit in time implementation. The functionalities of different building blocks of the implicit solver are analyzed from the point of view of software design and placed in appropriate hierarchical levels in the C++ libraries. In the detailed implementation, the contributions of different parts of the solver to computational cost, memory consumption and programming complexity are also analyzed. A combination of analytical and numerical methods is adopted to simplify the programming complexity in forming the preconditioning matrix. The solver is verified and tested using cases such as manufactured compressible Poiseuille flow, Taylor–Green vortex, turbulent flow over a circular cylinder at and shock wave boundary-layer interaction. The results show that the implicit solver can speed-up the simulations while maintaining good simulation accuracy.
Cassinelli A, Mateo A, Montomoli F, et al., 2021, REYNOLDS SENSITIVITY OF THE WAKE PASSING EFFECT ON A LPT CASCADE USING SPECTRAL/HP ELEMENT METHODS
RANS methods will continue to be the backbone of CFD-based design, but the recent development of high-order unstructured solvers and meshing algorithms, combined with the lowering cost of HPC infrastructures, has the potential to allow for the introduction of high-fidelity simulations in the design loop, taking the role role of a virtual wind tunnel. A representative industrial low pressure turbine (LPT) cascade subject to wake passing interactions is analysed, adopting the incompressible Navier-Stokes solver implemented in the spectral/hp element framework Nektar++. The bar passing effect is modelled by leveraging a spectral-element/Fourier Smoothed Profile Method. The Reynolds sensitivity is analysed, focusing in detail on the dynamics of the separation bubble on the suction surface as well as mean flow properties, wake profiles and loss estimations. The main findings are compared with experimental data, showing remarkable agreement in the prediction of wake traverses and losses across the entire range of flow regimes.
We present an rp-adaptation strategy for high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to r-adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature-based sensors or error estimators. We demonstrate this proof-of-concept using two geometries at transonic and supersonic flow regimes. The method has been implemented in the open-source spectral/hp element framework Nektar++, and its dedicated high-order mesh generation tool NekMesh. The results show that the proposed rp-adaptation methodology is a reasonably cost-effective way of improving accuracy.
Reavette RM, Sherwin SJ, Tang M, et al., 2020, Comparison of arterial wave intensity analysis by pressure-velocity and diameter-velocity methods in a virtual population of adult subjects., Proceedings of the Institution of Mechanical Engineers Part H: Journal of Engineering in Medicine, Vol: 234, Pages: 1260-1276, ISSN: 0954-4119
Pressure-velocity-based analysis of arterial wave intensity gives clinically relevant information about the performance of the heart and vessels, but its utility is limited because accurate pressure measurements can only be obtained invasively. Diameter-velocity-based wave intensity can be obtained noninvasively using ultrasound; however, due to the nonlinear relationship between blood pressure and arterial diameter, the two wave intensities might give disparate clinical indications. To test the magnitude of the disagreement, we have generated an age-stratified virtual population to investigate how the two dominant nonlinearities 'viscoelasticity and strain-stiffening' cause the two formulations to differ. We found strong agreement between the pressure-velocity and diameter-velocity methods, particularly for the systolic wave energy, the ratio between systolic and diastolic wave heights, and older subjects. The results are promising regarding the introduction of noninvasive wave intensities in the clinic.
Moxey D, Cantwell CD, Bao Y, et al., 2020, Nektar++: enhancing the capability and application of high-fidelity spectral/hp element methods, Computer Physics Communications, Vol: 249, Pages: 1-18, ISSN: 0010-4655
Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/ element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments – in particular: the method of moving frames (MMF), which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations (which combine a 2D spectral element and 1D Fourier spectral method) to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a ‘thick’ strip model for the modelling of fluid–structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions fo
Marcon J, Kopriva DA, Sherwin SJ, et al., 2020, Naturally curved quadrilateral mesh generation using an adaptive spectral element solver, 28th International Meshing Roundtable and User Forum, Publisher: arXiv, Pages: 254-266
We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two dimensional domains. The a priori curved quadrilateral blocks can be further split into a finer high-order mesh as needed. The guiding field is computed by a Laplace equation solver using a continuous Galerkin or discontinuous Galerkin spectral element formulation. This operation is aided by using p-adaptation to achieve faster convergence of the solution with respect to the computational cost. From the guiding field, irregular nodes and separatrices can be accurately located. A first version of the code is implemented in the open source spectral element framework Nektar++ and its dedicated high order mesh generation platform NekMesh.
Moura RC, Peiró J, Sherwin SJ, 2020, Under-Resolved DNS of Non-trivial Turbulent Boundary Layers via Spectral/hp CG Schemes, ERCOFTAC Series, Pages: 389-395
This study assesses the suitability of spectral/hp continuous Galerkin (CG) schemes  for model-free under-resolved simulations of a non-trivial turbulent boundary layer flow. We consider a model problem proposed by Spalart in  that features a rotating free-stream velocity and admits an asymptotic solution with significant crossflow effects. Note this test case is substantially more complex than typical turbulent boundary layer canonical problems owing to its unsteadiness and enhanced small-scale anisotropy. Reported LES-based solutions to this problem are known to require sophisticated modelling and relatively fine grids to achieve meaningful results, with traditional models exhibiting poor performance. The model-free CG-based approach advocated, on the other hand, yields surprisingly good results with considerably less degrees of freedom for higher order discretisations. Usefully accurate results for the mean flow quantities could even be obtained with half as many degrees of freedom per direction (in comparison to reference LES solutions). Usage of high-order spectral element methods (CG in particular) is therefore strongly motivated for wall-bounded turbulence simulations via under-resolved DNS (uDNS), sometimes called implicit LES (iLES), approaches.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.