Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Mechanics



+44 (0)20 7594 5052s.sherwin Website




313BCity and Guilds BuildingSouth Kensington Campus





Publication Type

339 results found

Xu H, Cantwell C, Monteserin C, Eskilsson C, Engsig-Karup AP, Sherwin SJet al., 2018, Spectral/hp element methods: Recent developments, applications, and perspectives, Journal of Hydrodynamics, Vol: 30, Pages: 1-22, ISSN: 1001-6058

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.

Journal article

Mengaldo G, De Grazia D, Moura RC, Sherwin Set al., 2018, Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness, Journal of Computational Physics, Vol: 358, Pages: 1-20, ISSN: 0021-9991

This study focusses on the dispersion and diffusion characteristics of high-order energy-stable flux recon-struction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis isperformed for five ESFR schemes, where the parameter ‘c’ dictating the properties of the specific schemerecovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes,proposed in [2]. In particular, we used five values of ‘c’, two that correspond to its lower and upper boundsand the others that identify three schemes that are linked to common high-order methods, namely theESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral differencescheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g.different levels of upwinding), ranging from “under-” to “over-upwinding”. In contrast to the more commontemporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucialinsights into the diffusion and dispersion properties of FR schemes for problems involving non-periodicboundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamicsand aeroacoustics.

Journal article

Bao Y, Palacios R, Graham M, Sherwin Set al., 2018, A strip modelling of flow past a freely vibrating cable, ERCOFTAC Series, Vol: 24, Pages: 221-227, ISSN: 1382-4309

© 2018, Springer International Publishing AG. Vortex-induced vibration of long flexible structures with cylindrical cross-section are widely encountered in various engineering fields.

Journal article

Marcon J, Turner M, Moxey D, Sherwin SJ, Peiro Jet al., A variational approach to high-order r-adaptation, 26th International Meshing Roundtable

A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the initial mesh are manipulated using metric tensors to obtain target elements. The nonlinear optimisation in turns adapts the final high-order mesh to best fit the description of the target elements by minimising the element distortion. Encouraging preliminary results prove that the method behaves well and can be used in the future for more extensive work which shall include the use of error indicators from CFD simulations.

Conference paper

Serson D, Meneghini JR, Sherwin SJ, 2017, Direct numerical simulations of the flow around wings with spanwise waviness, Journal of Fluid Mechanics, Vol: 826, Pages: 714-731, ISSN: 0022-1120

The use of spanwise waviness in wings has been proposed in the literature as a possible mechanism for obtaining improved aerodynamic characteristics, motivated by the tubercles that cover the leading edge of the pectoral flippers of the humpback whale. We investigate the effect of this type of waviness on the incompressible flow around infinite wings with a NACA0012 profile, using direct numerical simulations employing the spectral/hp method. Simulations were performed for Reynolds numbers of and , considering different angles of attack in both the pre-stall and post-stall regimes. The results show that the waviness can either increase or decrease the lift coefficient, depending on the particular and flow regime. We observe that the flow around the wavy wing exhibits a tendency to remain attached behind the waviness peak, with separation restricted to the troughs, which is consistent with results from the literature. Then, we identify three important physical mechanisms in this flow. The first mechanism is the weakening of the suction peak on the sections corresponding to the waviness peaks. This characteristic had been observed in a previous investigation for a very low Reynolds number of , and we show that this is still important even at . As a second mechanism, the waviness has a significant effect on the stability of the separated shear layers, with transition occurring earlier for the wavy wing. In the pre-stall regime, for , the flow around the baseline wing is completely laminar, and the earlier transition leads to a large increase in the lift coefficient, while for , the earlier transition leads to a shortening of the separation bubble which does not lead to an increased lift coefficient. The last mechanism corresponds to a sub-harmonic behaviour, with the flow being notably different between subsequent wavelengths. This allows the wing to maintain higher lift coefficients in some portions of the span.

Journal article

Ghim M, Alpresa P, Yang S, Braakman ST, Gray SG, Sherwin SJ, van Reeuwijk M, Weinberg PDet al., 2017, Visualization of three pathways for macromolecule transport across cultured endothelium and their modification by flow., AJP - Heart and Circulatory Physiology, Vol: 313, Pages: H959-H973, ISSN: 1522-1539

Transport of macromolecules across vascular endothelium and its modification by fluid mechanical forces are important for normal tissue function and in the development of atherosclerosis. However, the routes by which macromolecules cross endothelium, the hemodynamic stresses that maintain endothelial physiology or trigger arterial disease, and the dependence of transendothelial transport on hemodynamic stresses are controversial. Here we visualised pathways for macromolecule transport and determined the effect on these pathways of different types of flow. Endothelial monolayers were cultured under static conditions or on an orbital shaker producing different flow profiles in different parts of the wells. Fluorescent tracers that bound to the substrate after crossing the endothelium were used to identify transport pathways. Maps of tracer distribution were compared with numerical simulations of flow to determine effects of different shear stress metrics on permeability. Albumin-sized tracers dominantly crossed the cultured endothelium via junctions between neighbouring cells, high-density-lipoprotein-sized tracers crossed at tricelluar junctions whilst low-density-lipoprotein-sized tracers crossed through cells. Cells aligned close to the angle that minimised shear stresses across their long axis. The rate of paracellular transport under flow correlated with the magnitude of these minimised transverse stresses, whereas transport across cells was uniformly reduced by all types of flow. These results contradict the long-standing two-pore theory of solute transport across microvessel walls and the consensus view that endothelial cells align with the mean shear vector. They suggest that endothelial cells minimise transverse shear, supporting its postulated pro-atherogenic role. Preliminary data show that similar tracer techniques are practicable in vivo.

Journal article

Mao X, Zaki TA, Sherwin SJ, Blackburn HMet al., 2017, Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade, Journal of Fluid Mechanics, Vol: 820, Pages: 604-632, ISSN: 0022-1120

Flow past a NACA 65 blade at chord-based Reynolds number 138 500 is studied using stability analysis, generalized (spatially weighted) transient growth analysis and direct numerical simulations (DNS). The mechanisms of transition on various sections of the blade observed in previous work by Zaki et al. (J. Fluid Mech., vol. 665, 2010, pp. 57-98) are examined, with a focus on the pressure side around the leading edge. In this region, the linearly most energetic perturbation has spanwise wavenumber 40π (five boundary-layer thicknesses) and is tilted against the mean shear to take advantage of the Orr mechanism. In a DNS, the nonlinear development of this optimal perturbation induces Λ structures, which are further stretched to hairpin vortices before breaking down to turbulence. At higher spanwise wavenumber, e.g. 120π, a free-stream optimal perturbation is obtained upstream of the leading edge, in the form of streamwise vortices. During its nonlinear evolution, this 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. This layout of streaks generates a mean shear with two inflectional points and activates secondary instabilities, namely inner and outer instabilities previously reported in the literature.

Journal article

Xu H, Mughal SM, Gowree E, Atkin CJ, Sherwin Set al., 2017, Destabilisation and modification of Tollmien-Schlichting disturbances by athree dimensional surface indentation, Journal of Fluid Mechanics, Vol: 819, Pages: 592-620, ISSN: 1469-7645

We consider the influence of a smooth three-dimensional (3-D) indentation on the instability of an incompressible boundary layer by linear and nonlinear analyses. The numerical work was complemented by an experimental study to investigate indentations of approximately 11δ99 and 22δ99 width at depths of 45 %, 52 % and 60 % of δ99 , where δ99 indicates 99% boundary layer thickness. For these indentations a separation bubble confined within the indentation arises. Upstream of the indentation, spanwise-uniform Tollmien–Schlichting (TS) waves are assumed to exist, with the objective to investigate how the 3-D surface indentation modifies the 2-D TS disturbance. Numerical corroboration against experimental data reveals good quantitative agreement. Comparing the structure of the 3-D separation bubble to that created by a purely 2-D indentation, there are a number of topological changes particularly in the case of the widest indentation; more rapid amplification and modification of the upstream TS waves along the symmetry plane of the indentation is observed. For the shortest indentations, beyond a certain depth there are then no distinct topological changes of the separation bubbles and hence on flow instability. The destabilising mechanism is found to be due to the confined separation bubble and is attributed to the inflectional instability of the separated shear layer. Finally for the widest width indentation investigated ( 22δ99 ), results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using N -factors to assess instability of properly 3-D disturbances reveals that a general indication of flow destabilisation and development of strongly nonlinear behaviour is indicated as N=6 values are attained. However N -factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdown to turbu

Journal article

Burovskiy P, Grigoras P, Sherwin S, Luk Wet al., 2017, Efficient Assembly for High-Order Unstructured FEM Meshes (FPL 2015), ACM TRANSACTIONS ON RECONFIGURABLE TECHNOLOGY AND SYSTEMS, Vol: 10, ISSN: 1936-7406

Journal article

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

Journal article

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.


Chooi KY, Comerford A, Sherwin SJ, Weinberg PDet 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.

Journal article

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 & 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.

Journal article

Moura RC, Mengaldo G, Peiró J, Sherwin SJet al., 2017, An LES Setting for DG-Based Implicit LES with Insights on Dissipation and Robustness, Pages: 161-173, ISSN: 1439-7358

© 2017, Springer International Publishing AG. 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.

Conference paper

Moxey D, Cantwell CD, Mengaldo G, Serson D, Ekelschot D, Peiró J, Sherwin SJ, Kirby RMet 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.

Conference paper

Serson D, Meneghini JR, Sherwin SJ, 2017, Extension of the Velocity-Correction Scheme to General Coordinate Systems, Pages: 331-342, ISSN: 1439-7358

© 2017, Springer International Publishing AG. 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.

Conference paper

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.

Conference paper

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.

Journal article

Serbanovic-Canic J, de Luca A, Warboys C, Ferreira PF, Luong LA, Hsiao S, Gauci I, Mahmoud M, Feng S, Souilhol C, Bowden N, Ashton JP, Walczak H, Firmin D, Krams R, Mason JC, Haskard DO, Sherwin S, Ridger V, Chico TJ, Evans PCet 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.

Journal article

Moura RC, Mengaldo G, Peiro J, Sherwin Set al., 2016, 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-orderdiscontinuous Galerkin (DG) methods. The ‘1% rule’ based on linear dispersion–diusion analysis introduced byMoura et al. [J. Comput. Phys.298 (2015) 695–710] is here adapted for 3D energy spectra and validated throughthe inviscid Taylor–Green vortex problem. The 1% rule estimates the wavenumber beyond which numerical diusioninduces an artificial dissipation range on turbulent spectra. As the original rule relies on standard upwinding, dierentRiemann solvers are tested. Very good agreement is found for solvers which treat the dierent physical waves in aconsistent manner. Relatively good agreement is still found for simpler solvers. The latter however displayed spuriousfeatures attributed to the inconsistent treatment of dierent physical waves. It is argued that, in the limit of vanishingviscosity, such features might have a significant impact on robustness and solution quality. The estimates proposed areregarded as useful guidelines for no-model DG-based simulations of free turbulence at very high Reynolds numbers.

Journal article

Grigoras P, Burovskiy P, Luk W, Sherwin Set 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.

Conference paper

Xu H, Mughal MS, Gowree ER, Sherwin Set al., Effect of a 3d indentation on boundary layer instability, ICAS 2016, 30th Congress of the International Council of the Aeronautical Sciences, Publisher: ICAS

Conference paper

Xu H, Mughal MS, Gowree ER, Sherwin Set 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.

Conference paper

Moxey D, Cantwell C, Kirby RM, Sherwin Set 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.

Journal article

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.

Journal article

Chooi KY, Comerford A, Sherwin SJ, Weinberg PDet 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.

Journal article

Bao Y, Palacios R, Graham JMR, Sherwin SJet 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.

Journal article

Bolis A, Cantwell CD, Moxey D, Serson D, Sherwin SJet 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.

Journal article

Ekelschot, Moxey D, Sherwin, Peiro Jet al., 2016, A p-adaptation method for compressible flow problems using a goal-based error indicator, Computers and Structures, Vol: 181, Pages: 55-69, ISSN: 1879-2243

An accurate calculation of aerodynamic force coefficients for a given geometry isof fundamental importance for aircraft design. High-order spectral/hp elementmethods, which use a discontinuous Galerkin discretisation of the compressibleNavier-Stokes equations, are now increasingly being used to improve the accuracyof flow simulations and thus the force coefficients. To reduce error in thecalculated force coefficients whilst keeping computational cost minimal, we proposea p-adaptation method where the degree of the approximating polynomialis locally increased in the regions of the flow where low resolution is identifiedusing a goal-based error estimator as follows.Given an objective functional such as the aerodynamic force coefficients, weuse control theory to derive an adjoint problem which provides the sensitivityof the functional with respect to changes in the flow variables, and assumethat these changes are represented by the local truncation error. In its finalform, the goal-based error indicator represents the effect of truncation error onthe objective functional, suitably weighted by the adjoint solution. Both flowgoverning and adjoint equations are solved by the same high-order method,where we allow the degree of the polynomial within an element to vary acrossthe 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 partsof the computational domain that require improved solution accuracy whichis achieved by increasing the approximation order. We demonstrate the costeffectivenessof our method across a range of polynomial orders by considering anumber of examples in two- and three-dimensions and in subsonic and transonicflow regimes. Reductions in both the number of degrees of freedom required toresolve the force coefficients to a given error, as well as the computational cost,are both observed in using the p-adaptive technique

Journal article

Mao X, Zaki T, Sherwin S, Blackburn Het 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.

Conference paper

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