360 results found
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, 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.
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.
Pan Y, Yan Z-G, Peiro J, et al., 2021, Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver, Communications on Applied Mathematics and Computation, ISSN: 2096-6385
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.
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
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
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.
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.
Lahooti M, Palacios R, Sherwin SJ, 2021, Thick strip method for efficient large-eddy simulations of flexible wings in stall, Pages: 1-20
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 3k 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.
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
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.
Moura RC, Fernandez P, Mengaldo G, et al., 2020, Viscous diffusion effects in the eigenanalysis of (hybridisable) dg methods, Pages: 371-382, ISSN: 1439-7358
We present the first eigenanalysis of hybridisable discontinuous Galerkin (HDG) schemes for the advection-diffusion equation in one dimension. This study is also one of the first to include viscous diffusion effects in the eigenanalysis of discontinuous spectral element methods. The interplay between upwind dissipation and viscous diffusion is discussed and preliminary insights deemed relevant to (under-resolved) turbulence computation approaches are presented.
Sherwin SJ, Moxey D, Peiró J, et al., 2020, Preface, ISBN: 9783030396466
Buscariolo FF, Sherwin SJ, Assi GRS, et al., 2020, Spectral/hp methodology study for iles-svv on an ahmed body, Pages: 297-311, ISSN: 1439-7358
The Ahmed Body is one of the most widely studied bluff bodies used for automotive conceptual studies and Computational Fluid Dynamics (CFD) software validation. With the advances of the computational processing capacity and improvement in computing costs, high-fidelity turbulence models, such as Detached Eddies Simulation (DES) and Large Eddies Simulation (LES), are becoming a reality for industrial cases, as studied by Buscariolo et al. (Analysis of turbulence models applied to CFD drag simulations of a small hatchback vehicle. SAE Paper 2016-36-0201, Society of Automotive Engineers, 2016), evaluating DES models to automotive applications.
Marcon J, Kopriva DA, Sherwin SJ, et al., 2019, A high resolution PDE approach to quadrilateral mesh generation, Journal of Computational Physics, Vol: 399, Pages: 1-17, ISSN: 0021-9991
We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of pi/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.
Moura RC, Aman M, Peiró J, et al., 2019, Spatial eigenanalysis of spectral/hp continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows, Journal of Computational Physics, Pages: 109112-109112, ISSN: 0021-9991
Vymazal M, Moxey D, Cantwell CD, et al., 2019, On weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin method, Journal of Computational Physics, Vol: 394, Pages: 732-744, ISSN: 0021-9991
We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain – groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a new weak formulation of Dirichlet boundary condition in the continuous framework. We show that the boundary condition leads to a stable discretization with a single parameter insensitive to mesh size and polynomial order of the expansion. The robustness of the approach is demonstrated on several numerical examples.
Buscariolo FF, Hoessler J, Moxey D, et al., 2019, Spectral/hp element simulation of flow past a Formula One front wing: validation against experiments, Publisher: arXiv
Emerging commercial and academic tools are regularly being applied to thedesign of road and race cars, but there currently are no well-establishedbenchmark cases to study the aerodynamics of race car wings in ground effect.In this paper we propose a new test case, with a relatively complex geometry,supported by the availability of CAD model and experimental results. We referto the test case as the Imperial Front Wing, originally based on the front wingand endplate design of the McLaren 17D race car. A comparison of differentresolutions of a high fidelity spectral/hp element simulation usingunder-resolved DNS/implicit LES approach with fourth and fifth polynomial orderis presented. The results demonstrate good correlation to both the wall-boundedstreaklines obtained by oil flow visualization and experimental PIV results,correctly predicting key characteristics of the time-averaged flow structures,namely intensity, contours and locations. This study highlights the resolutionrequirements in capturing salient flow features arising from this type ofchallenging geometry, providing an interesting test case for both traditionaland emerging high-fidelity simulations.
Chun S, Marcon J, Peiro J, et al., 2019, Numerical study on the effect of geometric approximation error in the numerical solution of PDEs using a high-order curvilinear mesh, Publisher: arXiv
When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. This paper aims to investigate the effect of geometric approximation error by using a high-order mesh with negligible geometric approximation error, even for high order polynomial of order p. To achieve this goal, the high-order mesh generator from CAD geometry called NekMesh is adapted for surface mesh generation in comparison to traditional meshes with non-negligible geometric approximation error. Two types of numerical tests are considered. Firstly, the accuracy of differential operators is compared for various p on a curved element of the sphere. Secondly, by applying the method of moving frames, four different time-dependent PDEs on the sphere are numerically solved to investigate the impact of geometric approximation error on the accuracy and conservation properties of high-order numerical schemes for PDEs on the sphere.
Cooke EE, Mughal MS, Sherwin S, et al., 2019, Destabilisation of Stationary and Travelling Crossflow Disturbances Due to Steps over a Swept Wing, AIAA Aviation 2019 Forum, Publisher: American Institute of Aeronautics and Astronautics
Destabilization effects of forward facing steps, backward facing steps and bumps on stationary and travelling crossflow disturbances are investigated computationally for a 40° infinite swept wing. Step and bump heights range from 24% to 53% of the boundary layer thickness and are located at 10% chord. The spectral/hp element solver, Nektar++, is used to compute base flow profiles with an embedded swept wing geometry. Parabolized Stability Equations (PSE) and Linearized Harmonic Navier-Stokes (LHNS) models are used to evaluate growth of convecting instabilities. The paper describes derivations of the PSE and LHNS models which accurately solve for the perturbed field over the very localized and rapid variations imposed by the surface step-features. Unlike the PSE, which suffer from a stream-wise numerical step size restriction, the LHNS are a fully elliptic set of equations which may use arbitrarily fine grid resolution. Unsurprisingly, the PSE codes fail to capture the effect of abrupt changes in surface geometry introduced by the steps features. Results for the LHNS and roughness incorporating LHNS are given for the varying step types. Comparisons are made between the LHNS model and direct numerical simulations involving the time-stepping linearized Navier-Stokes solver in the Nektar++ software suite. Most previous work in the topic area has focused on Tollmien-Schlichting perturbations over two-dimensional flat plate flows or airfoils, the novelty of this work lies with analyzing crossflow instability over a swept wing boundary-layer flow with step features.
Cookson AN, Doorly DJ, Sherwin SJ, 2019, Efficiently Generating Mixing by Combining Differing Small Amplitude Helical Geometries, FLUIDS, Vol: 4, ISSN: 2311-5521
Zhu H, Wang R, Bao Y, et al., 2019, Flow over a symmetrically curved circular cylinder with the free stream parallel to the plane of curvature at low Reynolds number, JOURNAL OF FLUIDS AND STRUCTURES, Vol: 87, Pages: 23-38, ISSN: 0889-9746
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