Publications
401 results found
Burovskiy P, Grigoras P, Sherwin S, et al., 2017, Efficient Assembly for High-Order Unstructured FEM Meshes (FPL 2015), ACM TRANSACTIONS ON RECONFIGURABLE TECHNOLOGY AND SYSTEMS, Vol: 10, ISSN: 1936-7406
Serson D, Meneghini JR, Sherwin SJ, 2017, Direct numerical simulations of the flow around wings with spanwise waviness at a very low Reynolds number, Computers and Fluids, Vol: 146, Pages: 117-124, ISSN: 0045-7930
Inspired by the pectoral flippers of the humpback whale, the use of spanwise waviness in the leading edge has been considered in the literature as a possible way of improving the aerodynamic performance of wings. In this paper, we present an investigation based on direct numerical simulations of the flow around infinite wavy wings with a NACA0012 profile, at a Reynolds number Re=1000Re=1000. The simulations were carried out using the Spectral/hp Element Method, with a coordinate system transformation employed to treat the waviness of the wing. Several combinations of wavelength and amplitude were considered, showing that for this value of Re the waviness leads to a reduction in the lift-to-drag ratio (L/D), associated with a suppression of the fluctuating lift coefficient. These changes are associated with a regime where the flow remains attached behind the peaks of the leading edge while there are distinct regions of flow separation behind the troughs, and a physical mechanism explaining this behaviour is proposed.
Xu H, Lombard J, Sherwin S, 2017, Influence of localised smooth steps on the instability of a boundary layer, Journal of Fluid Mechanics, Vol: 817, Pages: 138-170, ISSN: 1469-7645
We consider a smooth, spanwise-uniform forward facing step de ned by the Gauss error function of height 4-30% and four times the width of the local boundary layer thickness δ_99. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien-Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward facing smooth steps is conducted by linear analysis. The results indicate thatfor a TS wave with a frequency F 2 [140; 160] (F=! =U21 106 where ! and U1 denote the perturbation angle frequency and freestream velocity magnitude, respectively), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a at plate boundary layer. Furthermore, it is observed thattwo smooth forward facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20% of the local boundary layer thickness for a xed width parameter, the TS wave is amplified and thereby a destabilisation e ect is introduced. Therefore, stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward facingsmooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favorably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other externalperturbations, two forward facing smooth steps of height 5% and 12% of the boundary lay
Cantwell C, Sherwin S, 2017, Nektar++
Nektar++ is a tensor product based finite element package designed to allow one to construct efficient classical low polynomial order h-type solvers (where h is the size of the finite element) as well as higher p-order piecewise polynomial order solvers.
Ekelschot D, Moxey D, Sherwin SJ, et al., 2017, A p-adaptation method for compressible flow problems using a goal-based error indicator, Computers and Structures, Vol: 181, Pages: 55-69, ISSN: 0045-7949
An accurate calculation of aerodynamic force coefficients for a given geometry is of fundamental importance for aircraft design. High-order spectral/hp element methods, which use a discontinuous Galerkin discretisation of the compressible Navier–Stokes equations, are now increasingly being used to improve the accuracy of flow simulations and thus the force coefficients. To reduce error in the calculated force coefficients whilst keeping computational cost minimal, we propose a p-adaptation method where the degree of the approximating polynomial is locally increased in the regions of the flow where low resolution is identified using a goal-based error estimator as follows.Given an objective functional such as the aerodynamic force coefficients, we use control theory to derive an adjoint problem which provides the sensitivity of the functional with respect to changes in the flow variables, and assume that these changes are represented by the local truncation error. In its final form, the goal-based error indicator represents the effect of truncation error on the objective functional, suitably weighted by the adjoint solution. Both flow governing and adjoint equations are solved by the same high-order method, where we allow the degree of the polynomial within an element to vary across the mesh.We initially calculate a steady-state solution to the governing equations using a low polynomial order and use the goal-based error indicator to identify parts of the computational domain that require improved solution accuracy which is achieved by increasing the approximation order. We demonstrate the cost-effectiveness of our method across a range of polynomial orders by considering a number of examples in two- and three-dimensions and in subsonic and transonic flow regimes. Reductions in both the number of degrees of freedom required to resolve the force coefficients to a given error, as well as the computational cost, are both observed in using the p-adaptive technique.
Moura RC, Mengaldo G, Peiro J, et al., 2017, On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence, Journal of Computational Physics, Vol: 330, Pages: 615-623, ISSN: 0021-9991
We present estimates of spectral resolution power for under-resolved turbulent Euler flows obtained with high-order discontinuous Galerkin (DG) methods. The ‘1% rule’ based on linear dispersion–diffusion analysis introduced by Moura et al. (2015) [10] is here adapted for 3D energy spectra and validated through the inviscid Taylor–Green vortex problem. The 1% rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra. As the original rule relies on standard upwinding, different Riemann solvers are tested. Very good agreement is found for solvers which treat the different physical waves in a consistent manner. Relatively good agreement is still found for simpler solvers. The latter however displayed spurious features attributed to the inconsistent treatment of different physical waves. It is argued that, in the limit of vanishing viscosity, such features might have a significant impact on robustness and solution quality. The estimates proposed are regarded as useful guidelines for no-model DG-based simulations of free turbulence at very high Reynolds numbers.
Chooi KY, Comerford A, Sherwin SJ, et al., 2017, Noradrenaline has opposing effects on the hydraulic conductance of arterial intima and media., Journal of Biomechanics, Vol: 54, Pages: 4-10, ISSN: 1873-2380
The uptake of circulating macromolecules by the arterial intima is thought to be a key step in atherogenesis. Such transport is dominantly advective, so elucidating the mechanisms of water transport is important. The relation between vasoactive agents and water transport in the arterial wall is incompletely understood. Here we applied our recently-developed combination of computational and experimental methods to investigate the effects of noradrenaline (NA) on hydraulic conductance of the wall (Lp), medial extracellular matrix volume fraction (ϕ(ECM)) and medial permeability (K1(1)) in the rat abdominal aorta. Experimentally, we found that physiological NA concentrations were sufficient to induce SMC contraction and produced significant decreases in Lp and increases in ϕ(ECM). Simulation results based on 3D confocal images of the extracellular volume showed a corresponding increase in K1(1), attributed to the opening of the ECM. Conversion of permeabilities to layer-specific resistances revealed that although the total wall resistance increased, medial resistance decreased, suggesting an increase in intimal resistance upon application of NA.
Moura RC, Peiro J, Sherwin SJ, 2017, On the accuracy and robustness of implicit LES/under-resolved DNS approaches based on spectral element methods
We present a study on the suitability of under-resolved DNS (uDNS)-also called implicit LES (iLES)-approaches based on spectral element methods (SEM), with emphasis on high-order continuous and discontinuous Galerkin (i.e. CG and DG) schemes. Broadly speaking, these are model-free eddy-resolving approaches to turbulence which solve the governing equations in unfiltered form and rely on numerical stabilization techniques for small-scale regularization. Model problems in 1D, 2D and 3D are used in the assessment of solution quality and numerical stability. A rationale for the excellent potential of these methods for transitional and turbulent flows is offered on the basis of linear dispersion-diffusion analysis.
Serson D, Meneghini JR, Sherwin SJ, 2017, Extension of the Velocity-Correction Scheme to General Coordinate Systems, Pages: 331-342, ISSN: 1439-7358
The velocity-correction scheme is a time-integration method for the incompressible Navier-Stokes equations, and is a common choice in the context of spectral/hp methods. Although the spectral/hp discretization allows the representation of complex geometries, in some cases the use of a coordinate transformation is desirable, since it may lead to symmetries which allow a more efficient solution of the equations. One example of this occurs when the transformed geometry has a homogeneous direction, in which case a Fourier expansion can be applied in this direction, reducing the computational cost. In this paper, we revisit two recently proposed forms of extending the velocity-correction scheme to general coordinate systems, the first treating the mapping terms explicitly and the second treating them semi-implicitly. We then present some numerical examples illustrating the properties and applicability of these methods, including new tests focusing on the time-accuracy of these schemes.
Moxey D, Cantwell CD, Mengaldo G, et al., 2017, Towards p-adaptive spectral/hp element methods for modelling industrial flows, ICOSAHOM-2016 - International Conference on Spectral and High-order Methods, Publisher: Springer International Publishing AG, Pages: 63-79, ISSN: 1439-7358
There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical methods and corresponding software frameworks which can deliver the next-generation of complex and detailed fluid simulations to scientists and engineers in an efficient way. In this article we discuss recent and upcoming advances in the use of the spectral/hp element method for addressing these modelling challenges. To use these methods efficiently for such applications, is critical that computational resolution is placed in the regions of the flow where it is needed most, which is often not known a priori. We propose the use of spatially and temporally varying polynomial order, coupled with appropriate error estimators, as key requirements in permitting these methods to achieve computationally efficient high-fidelity solutions to complex flow problems in the fluid dynamics community.
Moura RC, Mengaldo G, Peiró J, et al., 2017, An LES Setting for DG-Based Implicit LES with Insights on Dissipation and Robustness, Pages: 161-173, ISSN: 1439-7358
We suggest a new interpretation of implicit large eddy simulation (iLES) approaches based on discontinuous Galerkin (DG) methods by analogy with the LES-PLB framework (Pope, Fluid mechanics and the environment: dynamical approaches. Springer, Berlin, 2001), where PLB stands for ‘projection onto local basis functions’. Within this framework, the DG discretization of the unfiltered compressible Navier-Stokes equations can be recognized as a Galerkin solution of a PLB-based (and hence filtered) version of the equations with extra terms originating from DG’s implicit subgrid-scale modelling. It is shown that for under-resolved simulations of isotropic turbulence at very high Reynolds numbers, energy dissipation is primarily determined by the property-jump term of the Riemann flux employed. Additionally, in order to assess how this dissipation is distributed in Fourier space, we compare energy spectra obtained from inviscid simulations of the Taylor-Green vortex with different Riemann solvers and polynomial orders. An explanation is proposed for the spectral ‘energy bump’ observed when the Lax-Friedrichs flux is employed.
Mohamied Y, Sherwin SJ, Weinberg PD, 2016, Understanding the fluid mechanics behind transverse wall shear stress, Journal of Biomechanics, Vol: 50, Pages: 102-109, ISSN: 1873-2380
The patchy distribution of atherosclerosis within arteries is widely attributed to local variation in haemodynamic wall shear stress (WSS). A recently-introduced metric, the transverse wall shear stress (transWSS), which is the average over the cardiac cycle of WSS components perpendicular to the temporal mean WSS vector, correlates particularly well with the pattern of lesions around aortic branch ostia. Here we use numerical methods to investigate the nature of the arterial flows captured by transWSS and the sensitivity of transWSS to inflow waveform and aortic geometry. TransWSS developed chiefly in the acceleration, peak systolic and deceleration phases of the cardiac cycle; the reverse flow phase was too short, and WSS in diastole was too low, for these periods to have a significant influence. Most of the spatial variation in transWSS arose from variation in the angle by which instantaneous WSS vectors deviated from the mean WSS vector rather than from variation in the magnitude of the vectors. The pattern of transWSS was insensitive to inflow waveform; only unphysiologically high Womersley numbers produced substantial changes. However, transWSS was sensitive to changes in geometry. The curvature of the arch and proximal descending aorta were responsible for the principal features, the non-planar nature of the aorta produced asymmetries in the location and position of streaks of high transWSS, and taper determined the persistence of the streaks down the aorta. These results reflect the importance of the fluctuating strength of Dean vortices in generating transWSS.
Serbanovic-Canic J, de Luca A, Warboys C, et al., 2016, Zebrafish model for functional screening of flow-responsive genes, Arteriosclerosis Thrombosis and Vascular Biology, Vol: 36, ISSN: 1524-4636
OBJECTIVE: Atherosclerosis is initiated at branches and bends of arteries exposed to disturbed blood flow that generates low shear stress. This mechanical environment promotes lesions by inducing endothelial cell (EC) apoptosis and dysfunction via mechanisms that are incompletely understood. Although transcriptome-based studies have identified multiple shear-responsive genes, most of them have an unknown function. To address this, we investigated whether zebrafish embryos can be used for functional screening of mechanosensitive genes that regulate EC apoptosis in mammalian arteries. APPROACH AND RESULTS: First, we demonstrated that flow regulates EC apoptosis in developing zebrafish vasculature. Specifically, suppression of blood flow in zebrafish embryos (by targeting cardiac troponin) enhanced that rate of EC apoptosis (≈10%) compared with controls exposed to flow (≈1%). A panel of candidate regulators of apoptosis were identified by transcriptome profiling of ECs from high and low shear stress regions of the porcine aorta. Genes that displayed the greatest differential expression and possessed 1 to 2 zebrafish orthologues were screened for the regulation of apoptosis in zebrafish vasculature exposed to flow or no-flow conditions using a knockdown approach. A phenotypic change was observed in 4 genes; p53-related protein (PERP) and programmed cell death 2-like protein functioned as positive regulators of apoptosis, whereas angiopoietin-like 4 and cadherin 13 were negative regulators. The regulation of perp, cdh13, angptl4, and pdcd2l by shear stress and the effects of perp and cdh13 on EC apoptosis were confirmed by studies of cultured EC exposed to flow. CONCLUSIONS: We conclude that a zebrafish model of flow manipulation coupled to gene knockdown can be used for functional screening of mechanosensitive genes in vascular ECs, thus providing potential therapeutic targets to prevent or treat endothelial injury at atheroprone sites.
Grigoras P, Burovskiy P, Luk W, et al., 2016, Optimising Sparse Matrix Vector multiplication for large scale FEM problems on FPGA, 2016 26th International Conference on Field Programmable Logic and Applications (FPL), ISSN: 1946-1488
Sparse Matrix Vector multiplication (SpMV) is an important kernel in many scientific applications. In this work we propose an architecture and an automated customisation method to detect and optimise the architecture for block diagonal sparse matrices. We evaluate the proposed approach in the context of the spectral/hp Finite Element Method, using the local matrix assembly approach. This problem leads to a large sparse system of linear equations with block diagonal matrix which is typically solved using an iterative method such as the Preconditioned Conjugate Gradient. The efficiency of the proposed architecture combined with the effectiveness of the proposed customisation method reduces BRAM resource utilisation by as much as 10 times, while achieving identical throughput with existing state of the art designs and requiring minimal development effort from the end user. In the context of the Finite Element Method, our approach enables the solution of larger problems than previously possible, enabling the applicability of FPGAs to more interesting HPC problems.
Xu H, Mughal MS, Gowree ER, et al., 2016, Effect of a 3d indentation on boundary layer instability, ICAS 2016, 30th Congress of the International Council of the Aeronautical Sciences, Publisher: ICAS
Xu H, Mughal MS, Gowree ER, et al., 2016, Effect of a 3d surface indentation on boundary layer stability, 24th International Congress of Theoretical and Applied Mechanics ICTAM 2016, Publisher: ICAS
We are concerned about effect of a 3D surfaceindentation on instability and laminar-turbulenttransition in a boundary layer. For naturaltransition in a boundary layer, the transitiononset is dominated by growth of the Tollmien-Schlichting (TS) wave and its subsequentsecondary instability. In the paper, both linearanalysis and nonlinear calculations are carriedout to address the 3D surface indentation effecton amplifying TS waves’ amplitudes andprompting transition onset. By the linearanalysis, we address sudden amplification of theTS modes by a separation bubble in a surfaceindentation region. The nonlinear calculationsare implemented to validate the traditionaltransition criteria predicted by the linear theorywhen a 3D indentation is present. Finally,applicability of the traditional transitioncriteria is assessed.
Moxey D, Cantwell C, Kirby RM, et al., 2016, Optimizing the performance of the spectral/hp element method with collective linear algebra operations, Computer Methods in Applied Mechanics and Engineering, Vol: 310, Pages: 628-645, ISSN: 0045-7825
As computing hardware evolves, increasing core counts mean that memory bandwidth is becomingthe deciding factor in attaining peak performance of numerical methods. High-orderfinite element methods, such as those implemented in the spectral/hp framework Nektar++,are particularly well-suited to this environment. Unlike low-order methods that typicallyutilize sparse storage, matrices representing high-order operators have greater density andricher structure. In this paper, we show how these qualities can be exploited to increaseruntime performance on nodes that comprise a typical high-performance computing system,by amalgamating the action of key operators on multiple elements into a single, memorye!cientblock. We investigate di↵erent strategies for achieving optimal performance acrossa range of polynomial orders and element types. As these strategies all depend on externalfactors such as BLAS implementation and the geometry of interest, we present a techniquefor automatically selecting the most e!cient strategy at runtime.
Serson D, Meneghini JR, Sherwin SJ, 2016, Velocity-correction schemes for the incompressible Navier-Stokes equations in general coordinate systems, Journal of Computational Physics, Vol: 316, Pages: 243-254, ISSN: 1090-2716
This paper presents methods of including coordinate transformations into the solution of the incompressible Navier–Stokes equations using the velocity-correction scheme, which is commonly used in the numerical solution of unsteady incompressible flows. This is important when the transformation leads to symmetries that allow the use of more efficient numerical techniques, like employing a Fourier expansion to discretize a homogeneous direction. Two different approaches are presented: in the first approach all the influence of the mapping is treated explicitly, while in the second the mapping terms related to convection are treated explicitly, with the pressure and viscous terms treated implicitly. Through numerical results, we demonstrate how these methods maintain the accuracy of the underlying high-order method, and further apply the discretisation strategy to problems where mixed Fourier-spectral/hp element discretisations can be applied, thereby extending the usefulness of this discretisation technique.
Chooi KY, Comerford A, Sherwin SJ, et al., 2016, Intimal and medial contributions to the hydraulic resistance of the arterial wall at different pressures: a combined computational and experimental study, Journal of the Royal Society Interface, Vol: 11, ISSN: 1742-5689
The hydraulic resistances of the intima and media determine water flux and the advection of macromolecules into and across the arterial wall. Despite several experimental and computational studies, however, these trans- port processes and their dependence on transmural pressure remain incompletely understood. Here we use a combination of experimental and computational methods to ascertain how the hydraulic permeability of the rat abdominal aorta depends on these two layers and how it is affected by structural rearrangement of the media under pressure. Ex vivo experiments determined the conductance of the whole wall, the thickness of the media, and the geometry of medial smooth muscle cells and extracellular matrix. Numerical methods were used to compute water flux through the media. Intimal values were obtained by subtraction. A mechanism was iden- tified that modulates pressure-induced changes in medial transport properties: compaction of the extracellular matrix leading to spatial reorganisation of smooth muscle cells. This is summarised in an empirical constitutive law for permeability and volumetric strain. This led to the physiologically interesting observation that, as a consequence of the changes in medial microstructure, the relative contributions of the intima and media to the hydraulic resistance of the wall depend on the applied pressure; medial resistance dominated at pressures above ∼93mmHg in this vessel.
Bao Y, Palacios R, Graham JMR, et al., 2016, Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders, Journal of Computational Physics, Vol: 321, Pages: 1079-1097, ISSN: 1090-2716
We propose a generalized strip modelling method that is computationally efficient for the VIV prediction of long flexible cylinders in three-dimensional incompressible flow. In order to overcome the shortcomings of conventional strip-theory-based 2D models, the fluid domain is divided into “thick” strips, which are sufficiently thick to locally resolve the small scale turbulence effects and three dimensionality of the flow around the cylinder. An attractive feature of the model is that we independently construct a three-dimensional scale resolving model for individual strips, which have local spanwise scale along the cylinder's axial direction and are only coupled through the structural model of the cylinder. Therefore, this approach is able to cover the full spectrum for fully resolved 3D modelling to 2D strip theory. The connection between these strips is achieved through the calculation of a tensioned beam equation, which is used to represent the dynamics of the flexible body. In the limit, however, a single “thick” strip would fill the full 3D domain. A parallel Fourier spectral/hp element method is employed to solve the 3D flow dynamics in the strip-domain, and then the VIV response prediction is achieved through the strip-structure interactions. Numerical tests on both laminar and turbulent flows as well as the comparison against the fully resolved DNS are presented to demonstrate the applicability of this approach.
Bolis A, Cantwell CD, Moxey D, et al., 2016, An adaptable parallel algorithm for the direct numerical simulation of incompressible turbulent flows using a Fourier spectral/hp element method and MPI virtual topologies, Computer Physics Communications, Vol: 206, Pages: 17-25, ISSN: 1879-2944
A hybrid parallelisation technique for distributed memory systems is investigated for a coupled Fourier-spectral/hp element discretisation of domains characterised by geometric homogeneity in one or more directions. The performance of the approach is mathematically modelled in terms of operation count and communication costs for identifying the most efficient parameter choices. The model is calibrated to target a specific hardware platform after which it is shown to accurately predict the performance in the hybrid regime. The method is applied to modelling turbulent flow using the incompressible Navier-Stokes equations in an axisymmetric pipe and square channel. The hybrid method extends the practical limitations of the discretisation, allowing greater parallelism and reduced wall times. Performance is shown to continue to scale when both parallelisation strategies are used.
Mao X, Zaki T, Sherwin S, et al., 2016, Bypass transition induced by free-stream noise in flow past a blade cascade, 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
© Open Archives of the 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC 2016. All rights reserved. Flow past a NACA 65 blade cascade at Reynolds number 138, 500 is studied through weighted transient growth and Direct Numerical Simulations (DNS). The mechanism of bypass transition on the pressure side around the leading edge observed in a previous work [1] is examined. The weighted optimal initial perturbations have spanwise wavenumber 40π and are amplified via the Orr mechanism. At higher spanwise wavenumber, e.g. 120π, a free-stream optimal initial perturbation, upstream of the leading edge in the form of streamwise vortices, is obtained. In nonlinear evolution, this high-wavenumber optimal perturbation tilts the mean shear and generates spanwise periodic high and low-speed streaks. Then through a nonlinear lift-up mechanism, the low-speed streaks are lifted above the high-speed ones and generate a mean shear with inflectional points. This layout of streaks activates secondary instabilities and both inner and outer instabilities addressed in literature are observed.
Cantwell C, Sherwin S, 2016, Nektar++
Nektar++ is a tensor product based finite element package designed to allow one to construct efficient classical low polynomial order h-type solvers (where h is the size of the finite element) as well as higher p-order piecewise polynomial order solvers.
Xu H, Sherwin S, Hall P, et al., 2016, The behaviour of Tollmien-Schlichting waves undergoing small-scale localised distortions, Journal of Fluid Mechanics, Vol: 792, Pages: 499-525, ISSN: 1469-7645
This paper is concerned with the behaviour of Tollmien-Schlichting (T-S) waves experiencingsmall localised distortions within an incompressible boundary layer developingover a flat-plate. In particular, the distortion is produced by an isolated roughness elementlocated at Rexc = 440 000. We considered the amplification of an incoming T-S wavegoverned by the two-dimensional linearised Navier-Stokes equations, where the base flowis obtained from the two-dimensional non-linear Navier-Stokes equations. We comparethese solutions with asymptotic analyses which assume a linearised triple-deck theory forthe base flow and determine the validity of this theory in terms of the height of the smallscalehumps/indentations taken into account. The height of the humps/indentations isdenoted by h which is considered to be less than or equal to xcRe−5/8xc(correspondingto h/δ99 < 6% for our choice of Rexc). The rescaled width ˆd(≡ d/(xcRe−3/8xc)) ofthe distortion is of the order O(1) and the width d is shorter than the T-S wavelength(λT S = 11.3 δ99).We observe that for distortions which are smaller than 0.1 of the inner deck height(h/δ99 < 0.4%) the numerical simulations confirm the asymptotic theory in the vicinityof the distortion. For larger distortions which are still within the inner deck (0.4% <h/δ99 < 5.5%) and where the flow is still attached the numerical solutions show thatboth humps and indentations are destabilising and deviate from the linear theory evenin the vicinity of the distortion.We numerically determine the transmission coefficient which provides the relative amplificationof the T-S wave over the distortion as compared to the flat-plate. We observethat for small distortions, h/δ99 < 5.5%, where the width of the distortion is of orderof the boundary layer a maximum amplification of only 2% is achieved. This amplificationcan however be increased as the width of the distortion is increased or
Lombard J-EW, Moxey D, Sherwin SJ, et al., 2016, Implicit large-eddy simulation of a wingtip vortex, AIAA Journal: devoted to aerospace research and development, Vol: 54, Pages: 506-518, ISSN: 0001-1452
In this article, recent developments in numerical methods for performing a large-eddy simulation of the formation and evolution of a wingtip vortex are presented. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, makes these types of test cases particularly challenging to investigate numerically. First, an overview is given of the spectral vanishing viscosity/implicit large-eddy simulation solver that is used to perform the simulations, and techniques are highlighted that have been adopted to solve various numerical issues that arise when studying such cases. To demonstrate the method’s viability, results are presented from numerical simulations of flow over a NACA 0012 profile wingtip at Rec=1.2×106Rec=1.2×106 and they are compared against experimental data, which is to date the highest Reynolds number achieved for a large-eddy simulation that has been correlated with experiments for this test case. The model in this paper correlates favorably with experiment, both for the characteristic jetting in the primary vortex and pressure distribution on the wing surface. The proposed method is of general interest for the modeling of transitioning vortex-dominated flows over complex geometries.
Turner M, Moxey D, Sherwin SJ, et al., 2016, Automatic generation of 3D unstructured high-order curvilinear meshes, Pages: 428-443
The generation of suitable, good quality high-order meshes is a significant obstacle in the academic and industrial uptake of high-order CFD methods. These methods have a number of favourable characteristics such as low dispersion and dissipation and higher levels of numerical accuracy than their low-order counterparts, however the methods are highly susceptible to inaccuracies caused by low quality meshes. These meshes require significant curvature to accuratly describe the geometric surfaces, which presents a number of difficult challenges in their generation. As yet, research into the field has produced a number of interesting technologies that go some way towards achieving this goal, but are yet to provide a complete system that can systematically produce curved high-order meshes for arbitrary geometries for CFD analysis. This paper presents our efforts in that direction and introduces an open-source high-order mesh generator, NekMesh, which has been created to bring high-order meshing technologies into one coherent pipeline which aims to produce 3D high-order curvilinear meshes from CAD geometries in a robust and systematic way.
Moura RC, Sherwin SJ, Peiro J, 2015, Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity, Journal of Computational Physics, Vol: 307, Pages: 401-422, ISSN: 1090-2716
This study addresses linear dispersion–diffusion analysis for the spectral/hp continuousGalerkin (CG) formulation in one dimension. First, numerical dispersion and diffusioncurves are obtained for the advection–diffusion problem and the role of multipleeigencurves peculiar to spectral/hp methods is discussed. From the eigencurves’ behaviour,we observe that CG might feature potentially undesirable non-smooth dispersion/diffusioncharacteristics for under-resolved simulations of problems strongly dominated by eitherconvection or diffusion. Subsequently, the linear advection equation augmented withspectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics ofCG with SVV-based stabilization are verified to display similar non-smooth features inflow regions where convection is much stronger than dissipation or vice-versa, owing toa dependency of the standard SVV operator on a local Péclet number. First a modificationis proposed to the traditional SVV scaling that enforces a globally constant Péclet numberso as to avoid the previous issues. In addition, a new SVV kernel function is suggestedand shown to provide a more regular behaviour for the eigencurves along with aconsistent increase in resolution power for higher-order discretizations, as measured bythe extent of the wavenumber range where numerical errors are negligible. The dissipationcharacteristics of CG with the SVV modifications suggested are then verified to be broadlyequivalent to those obtained through upwinding in the discontinuous Galerkin (DG)scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme isfound to have a slightly higher resolution power for the same dissipation levels. Theseresults show that improved CG-SVV characteristics can be pursued via different kernelfunctions with the aid of optimization algorithms.
Xu H, Mughal MS, Sherwin S, 2015, Effect of a 3D surface depression on boundary layer transition, 68th Annual Meeting of the APS Division of Fluid Dynamics
The influence of a three-dimensional surface depression on the transitional boundary layer is investigated numerically. In the boundary layer transition, the primary mode is a Tollmien-Schlichting (TS) wave which is a viscous instability. These modes are receptive to surface roughness interacting with free stream disturbances and/or surface vibrations. In this paper, numerical calculations are carried out to investigate the effect of the depression on instability of the boundary layer. In order to implement linear analysis, two/three (2D/3D)-dimensional nonlinear Navier-Stokes equations are solved by spectral element method to generate base flows in a sufficient large domain. The linear analyses are done by the parabolic stability equations (PSE). Finally, a DNS calculation is done to simulate the boundary layer transition.
Mao X, Blackburn H, Sherwin S, 2015, Optimal suppression of flow perturbations using boundary control, COMPUTERS & FLUIDS, Vol: 121, Pages: 133-144, ISSN: 0045-7930
Mengaldo G, De Grazia D, Vincent PE, et al., 2015, On the connections between discontinuous Galerkin and flux reconstruction schemes: extension to curvilinear meshes, Journal of Scientific Computing, Vol: 67, Pages: 1272-1292, ISSN: 1573-7691
This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these connections by analysing three nodal versions of tensor-product discontinuous Galerkin spectral element approximations and three types of flux reconstruction schemes for solving systems of conservation laws on irregular tensor-product meshes. We demonstrate that the existing connections established on regular grids are also valid on deformed and curved meshes for both linear and nonlinear problems, provided that the metric terms are accounted for appropriately. We also find that the aliasing issues arising from nonlinearities either due to a deformed/curved elements or due to the nonlinearity of the equations are equivalent and can be addressed using the same strategies both in the discontinuous Galerkin method and in the flux reconstruction approach. In particular, we show that the discontinuous Galerkin and the flux reconstruction approach are equivalent also when using higher-order quadrature rules that are commonly employed in the context of over- or consistent-integration-based dealiasing methods. The connections found in this work help to complete the picture regarding the relations between these two numerical approaches and show the possibility of using over- or consistent-integration in an equivalent manner for both the approaches.
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