277 results found
Xu H, Hall P, sherwin S, Effect of curvature modulation on Gortler vortices in boundary layers, 67th Annual Meeting of the APS Division of Fluid Dynamics
Xu H, Mughal MS, Gowree ER, et al., 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, Sherwin S, 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.
Xu H, Sherwin S, Hall P, Transmission coefficient of Tollmien-Schlichting waves undergoing small indentation/hump distortion, The 29th Congress of the International Council of the Aeronautical Sciences
Xu H, lombard J, sherwin S, Delaying natural transition of a boundary layer using smooth steps, Sixth International Symposium on Bifurcations and Instabilities in Fluid Dynamics
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: 0021-9290
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.
Ekelschot D, Moxey D, Sherwin SJ, et al., 2017, A p-adaptation method for compressible flow problems using a goal-based error indicator, COMPUTERS & STRUCTURES, Vol: 181, Pages: 55-69, ISSN: 0045-7949
© 2016 Elsevier Ltd 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 usin
Ghim M, Alpresa P, Yang S, et al., 2017, Visualisation of three pathways for macromolecule transport across cultured endothelium and their modification by flow., Am J Physiol Heart Circ Physiol, ISSN: 0363-6135
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.
Mao X, Zaki TA, Sherwin SJ, et 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
© 2017 Cambridge University Press. 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.
Mohamied Y, Sherwin SJ, Weinberg PD, et al., 2017, Understanding the fluid mechanics behind transverse wall shear stress, JOURNAL OF BIOMECHANICS, Vol: 50, Pages: 102-109, ISSN: 0021-9290
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.
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
© 2016 The Authors 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)  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.
Serson D, Meneghini JR, Sherwin SJ, et al., 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
© 2017 The Authors 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=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-EW, Sherwin SJ, et al., 2017, Influence of localised smooth steps on the instability of a boundary layer, JOURNAL OF FLUID MECHANICS, Vol: 817, Pages: 138-170, ISSN: 0022-1120
© 2017 Cambridge University Press. We consider a smooth, spanwise-uniform forward-facing step defined by a 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 that for a TS wave with a frequency F ∈ [140, 160] (F = ων/U ∝ 2 × 10 6 where ω and U ∝ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unst able regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two 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 fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the 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-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably 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 pa
Xu H, Mughal SM, Gowree ER, et al., 2017, Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation, Journal of Fluid Mechanics, Vol: 819, Pages: 592-620, ISSN: 0022-1120
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
Xu H, Mughal SM, Gowree ER, et al., 2017, Destabilisation and modification of Tollmien-Schlichting disturbances by a three-dimensional surface indentation, JOURNAL OF FLUID MECHANICS, Vol: 819, Pages: 592-620, ISSN: 0022-1120
© 2017 Cambridge University Press. 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 δ 99 and δ 99 width at depths of 45%, 52% and 60% of δ 99 where δ 99 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 , results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using -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 values are attained. However -factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdow
Bao Y, Palacios R, Graham M, 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: 0021-9991
© 2016 The Authors. 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.
Bolls 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: 0010-4655
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.
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: 13, Pages: 20160234-20160234, 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, these transport 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 (SMCs) and extracellular matrix (ECM). Numerical methods were used to compute water flux through the media. Intimal values were obtained by subtraction. A mechanism was identified that modulates pressure-induced changes in medial transport properties: compaction of the ECM leading to spatial reorganization of SMCs. This is summarized in an empirical constitutive law for permeability and volumetric strain. It 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 approximately 93 mmHg in this vessel.
Lombard J-EW, Moxey D, Sherwin SJ, et al., 2016, Implicit Large-Eddy Simulation of a Wingtip Vortex, AIAA JOURNAL, Vol: 54, Pages: 506-518, ISSN: 0001-1452
© Copyright 2015 by the authors. 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 R ec = 1.2 × 10 6 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.
Mengaldo G, De Grazia D, Vincent PE, et al., 2016, On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes, JOURNAL OF SCIENTIFIC COMPUTING, Vol: 67, Pages: 1272-1292, ISSN: 0885-7474
© 2015, The Author(s). 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.
Moura RC, Sherwin SJ, Peiro J, et al., 2016, 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: 0021-9991
© 2015 The Authors. This study addresses linear dispersion-diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection-diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves' behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Péclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Péclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms.
Moxey D, Cantwell CD, Kirby RM, et al., 2016, Optimising 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
© 2016 The Author(s) As computing hardware evolves, increasing core counts mean that memory bandwidth is becoming the deciding factor in attaining peak performance of numerical methods. High-order finite element methods, such as those implemented in the spectral/hp framework Nektar++, are particularly well-suited to this environment. Unlike low-order methods that typically utilise sparse storage, matrices representing high-order operators have greater density and richer structure. In this paper, we show how these qualities can be exploited to increase runtime performance on nodes that comprise a typical high-performance computing system, by amalgamating the action of key operators on multiple elements into a single, memory-efficient block. We investigate different strategies for achieving optimal performance across a range of polynomial orders and element types. As these strategies all depend on external factors such as BLAS implementation and the geometry of interest, we present a technique for automatically selecting the most efficient strategy at runtime.
Moxey D, Ekelschot D, Keskin U, et al., 2016, High-order curvilinear meshing using a thermo-elastic analogy, COMPUTER-AIDED DESIGN, Vol: 72, Pages: 130-139, ISSN: 0010-4485
With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect. Over the last few years, several curvilinear mesh generation techniques have been designed to tackle this issue, utilizing mesh deformation to move the interior nodes of the mesh in order to accommodate curvature at the boundary. Many of these are based on elastic models, where the mesh is treated as a solid body and deformed according to a linear or non-linear stress tensor. However, such methods typically have no explicit control over the validity of the elements in the resulting mesh. In this article, we present an extension of this elastic formulation, whereby a thermal stress term is introduced to 'heat' or 'cool' elements as they deform. We outline a proof-of-concept implementation and show that the adoption of a thermo-elastic analogy leads to an additional degree of robustness, by considering examples in both two and three dimensions.
Serson D, Meneghini JR, Sherwin SJ, et al., 2016, Velocity-correction schemes for the incompressible Navier-Stokes equations in general coordinate systems, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 316, Pages: 243-254, ISSN: 0021-9991
© 2016 The Authors. 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.
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.
Xu H, Mughal S, Gowree ER, et al., 2016, Effect of a 3D indentation on boundary layer instability, 24th International Congress of Theoretical and Applied Mechanics ICTAM 2016, Publisher: ICAS
We are concerned about effect of a 3D surface indentation on instability and laminar-turbulent transition in a boundary layer. For natural transition in a boundary layer, the transition onset is dominated by growth of the Tollmien-Schlichting (TS) wave and its subsequent secondary instability. In the paper, both linear analysis and nonlinear calculations are carried out to address the 3D surface indentation effect on amplifying TS waves' amplitudes and prompting transition onset. By the linear analysis, we address sudden amplification of the TS modes by a separation bubble in a surface indentation region. The nonlinear calculations are implemented to validate the traditional transition criteria predicted by the linear theory when a 3D indentation is present. Finally, applicability of the traditional transition criteria is assessed.
Xu H, Sherwin SJ, Halle 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: 0022-1120
© 2016 Cambridge University Press. This paper is concerned with the behaviour of Tollmien-Schlichting (TS) waves experiencing small localised distortions within an incompressible boundary layer developing over a flat plate. In particular, the distortion is produced by an isolated roughness element located at Re xc = 440 000. We considered the amplification of an incoming TS wave governed by the two-dimensional linearised Navier-Stokes equations, where the base flow is obtained from the two-dimensional nonlinear Navier-Stokes equations. We compare these solutions with asymptotic analyses which assume a linearised triple-deck theory for the base flow and determine the validity of this theory in terms of the height of the small-scale humps/indentations taken into account. The height of the humps/indentations is denoted by h, which is considered to be less than or equal to x c Re xc -5/8 (corresponding to h/δ 99 < 6 % for our choice of Re xc ). The rescaled width d(≡ d/x c Re xc -3/8 of the distortion is of order and the width is shorter than the TS wavelength (λ; TS = 11.3δ 99 ). We observe that, for distortions which are smaller than 0.1 of the inner deck height (h/δ 99 < 0.4%), the numerical simulations confirm the asymptotic theory in the vicinity of the distortion. For larger distortions which are still within the inner deck (0.4% < h/δ 99 < 5.5%) and where the flow is still attached, the numerical solutions show that both humps and indentations are destabilising and deviate from the linear theory even in the vicinity of the distortion. We numerically determine the transmission coefficient which provides the relative amplification of the TS wave over the distortion as compared to the flat plate. We observe that for small distortions, h/δ 99 < 5.5%, where the width of the distortion is of the order of the boundary layer, a maximum amplification of only 2 % is achieved. This amplificatio
© 2015, Springer Science+Business Media New York. Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method—the hybridizable discontinuous Galerkin (HDG) method—it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this work, we extend upon an earlier 2D comparative study, providing numerical results and discussion of the CG and HDG method performance in three dimensions. The comparison categories covered include steady-state elliptic and time-dependent parabolic problems, various element types and serial and parallel performance. The postprocessing technique, which allows for superconvergence in the HDG case, is also discussed. Depending on the direct linear system solver used and the type of the problem (steady-state vs. time-dependent) in question the HDG method either outperforms or demonstrates a comparable performance when compared with the CG method. The HDG method however falls behind performance-wise when the iterative solver is used, which indicates the need for an effective preconditioning strategy for the method.
Ali RL, Cantwell CD, Qureshi NA, et al., 2015, Automated fiducial point selection for reducing registration error in the co-localisation of left atrium electroanatomic and imaging data, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Publisher: IEEE, Pages: 1989-1992, ISSN: 1557-170X
Registration of electroanatomic surfaces and segmented images for the co-localisation of structural and functional data typically requires the manual selection of fiducial points, which are used to initialise automated surface registration. The identification of equivalent points on geometric features by the human eye is heavily subjective, and error in their selection may lead to distortion of the transformed surface and subsequently limit the accuracy of data co-localisation. We propose that the manual trimming of the pulmonary veins through the region of greatest geometrical curvature, coupled with an automated angle-based fiducial-point selection algorithm, significantly reduces target registration error compared with direct manual selection of fiducial points.
Burovskiy P, Grigoras P, Sherwin S, et al., 2015, Efficient assembly for high order unstructured FEM meshes, Publisher: IEEE, Pages: 1-6
© 2015 Imperial College. The Finite Element Method (FEM) is a common numerical technique used for solving Partial Differential Equations (PDEs) on complex domain geometries. Large and unstructured FEM meshes are used to represent the computation domains which makes an efficient mapping of the Finite Element Method onto FPGAS particularly challenging. The focus of this paper is on assembly mapping, a key kernel of FEM, which induces the sparse and unstructured nature of the problem. We translate FEM vector assembly mapping into data access scheduling to perform vector assembly directly on the FPGA, as part of the hardware pipeline. We show how to efficiently partition the problem into dense and sparse sub-problems which map well onto FPGAS. The proposed approach, implemented on a single FPGA could outperform highly optimised FEM software running on two Xeon E5-2640 processors.
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