Imperial College London

Professor Peter Vincent

Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Dynamics



+44 (0)20 7594 1975p.vincent




211City and Guilds BuildingSouth Kensington Campus





Publication Type

65 results found

Koch MK, Kelly PHJ, Vincent P, 2022, Identification and classification of off-vertex critical points for contour tree construction on unstructured meshes of hexahedra, IEEE Transactions on Visualization and Computer Graphics, Vol: 28, Pages: 5178-5180, ISSN: 1077-2626

The topology of isosurfaces changes at isovalues of critical points, making such points an important feature when building contour trees or Morse-Smale complexes. Hexahedral elements with linear interpolants can contain additional off-vertex critical points in element bodies and on element faces. Moreover, a point on the face of a hexahedron which is critical in the element-local context is not necessarily critical in the global context. In ‘`Exploring Scalar Fields Using Critical Isovalues’' Weber et al. introduce a method to determine whether critical points on faces are also critical in the global context, based on the gradient of the asymptotic decider in each element that shares the face. However, as defined, the method of Weber et al. contains an error, and can lead to incorrect results. In this work we correct the error.

Journal article

Caros Roca L, Buxton O, Shigeta T, Nagata T, Nonomura T, Asai K, Vincent Pet al., 2022, Direct numerical simulation of flow over a triangular airfoil under martian atmospheric conditions, AIAA Journal: devoted to aerospace research and development, Vol: 60, Pages: 3961-3972, ISSN: 0001-1452

Martian conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and low sound speed require Martian rotor blades to operate in a low Reynolds number (1,000 to 10,000) compressible regime, for which conventional airfoils are not designed. Here we utilize PyFR to undertake high-order Direct Numerical Simulations (DNS) of flow over a triangular airfoil at a Mach number of 0.15 and Reynolds number of 3,000. Initially, span-wise periodic DNS are undertaken. Extending the domain-span-to-chord ratio from 0.3 to 0.6 leads to better agreement with wind tunnel data at higher angles of attack, when the flow is separated. This is because smaller domain spans artificially suppress three-dimensional breakdown of coherent structures above the suction surface of the airfoil. Subsequently, full-span DNS in a virtual wind tunnel are undertaken, including all wind tunnel walls. These capture blockage and wall boundary layer effects, leading to better agreement with wind tunnel data for all angles of attack compared to span-wise periodic DNS. The results are important in terms of understanding discrepancies between previous span-wise periodic DNS and wind tunnel data. They also demonstrate the utility of high-order DNS as a tool for accurately resolving flow over triangular airfoils under Martian conditions.

Journal article

Giangaspero G, Witherden F, Vincent P, 2022, Synthetic turbulence generation for high-order scale-resolving simulations on unstructured grids, AIAA Journal: devoted to aerospace research and development, Vol: 60, Pages: 1032-1051, ISSN: 0001-1452

An extended version of the synthetic eddy method for generation of synthetic turbulence has been developed via asource term formulation and implemented in the open-source cross-platform solver PyFR. The method caters for thefull space-dependent anisotropy of the target turbulent length scales, and it is agnostic of the space and timediscretization of the underlying solver, which can be incompressible or compressible. Moreover, the method doesnot require each solution point to communicate with nearest neighbors; thus, it is well suited for modern, massivelyparallel, high-order unstructured codes which support mixed and possibly curved elements. The method has beenapplied to two test cases: incompressible plane channel flow at Reτ 180 and compressible flow over an SD7003aerofoil at Re 66;000, Ma 0.2, and α 4 deg. The channel flow case was run on three topologically differentmeshes composed of hexahedra, prisms, and a combination of prisms and tetrahedra, respectively. Almost identicalresults have been obtained on the three meshes. Results also show that taking into account the anisotropy of theturbulent length scales can reduce the development length. For the SD7003 aerofoil case, the injection of syntheticturbulence improves agreement between numerical and experimental results.

Journal article

Akkurt S, Witherden F, Vincent P, 2022, Cache blocking strategies applied to flux reconstruction, Computer Physics Communications, Vol: 271, Pages: 1-9, ISSN: 0010-4655

On modern hardware architectures, the performance of Flux Reconstruction (FR) methods can be limitedby memory bandwidth. In a typical implementation, these methods are implemented as a chain ofdistinct kernels. Often, a dataset which has just been written in the main memory by a kernel isread back immediately by the next kernel. One way to avoid such a redundant expenditure of memorybandwidth is kernel fusion. However, on a practical level kernel fusion requires that the source for allkernels be available, thus preventing calls to certain third-party library functions. Moreover, it can addsubstantial complexity to a codebase. An alternative to full kernel fusion is cache blocking. But for thisto be effective, CPU cache has to be meaningfully big. Historically, size of L1 and L2 caches preventedcache blocking for high-order CFD applications. However in recent years, size of L2 cache has grownfrom around 0.25 MiB to 1.25 MiB, and made it possible to apply cache blocking for high-order CFDcodes. In this approach, kernels remain distinct, and are executed one after another on small chunks ofdata that can fit in the cache, as opposed to on full datasets. These chunks of data stay in the cache andwhenever a kernel requests access to data that is already in the cache, memory bandwidth is conserved.In this study, a data structure that facilitates cache blocking is considered, and a range of kernel groupingconfigurations for an FR based Euler solver are examined. A theoretical study is conducted for hexahedralelements with no anti-aliasing at p = 3 and p = 4 in order to determine the predicted performance ofa few kernel grouping configurations. Then, these candidates are implemented in the PyFR solver andthe performance gains in practice are compared with the theoretical estimates that range between 2.05xand 2.50x. An inviscid Taylor-Green Vortex test case is used as a benchmark, and the most performantconfiguration leads to a speedup of approximately 2.81x in practice.

Journal article

Iyer AS, Abe Y, Vermeire BC, Bechlars P, Baier RD, Jameson A, Witherden FD, Vincent Pet al., 2021, High-order accurate direct numerical simulation of flow over a MTU-T161 low pressure turbine blade, Computers and Fluids, Vol: 226, ISSN: 0045-7930

Reynolds Averaged Navier-Stokes (RANS) simulations and wind tunnel testing have becomethe go-to tools for industrial design of Low-Pressure Turbine (LPT) blades. However, thereis also an emerging interest in use of scale-resolving simulations, including Direct NumericalSimulations (DNS). These could generate insight and data to underpin development of improvedRANS models for LPT design. Additionally, they could underpin a virtual LPT wind tunnelcapability, that is cheaper, quicker, and more data-rich than experiments. The current studyapplies PyFR, a Python based Computational Fluid Dynamics (CFD) solver, to fifth-orderaccurate petascale DNS of compressible flow over a three-dimensional MTU-T161 LPT bladewith diverging end walls at a Reynolds number of 200, 000 on an unstructured mesh with over 11billion degrees-of-freedom per equation. Various flow metrics, including isentropic Mach numberdistribution at mid-span, surface shear, and wake pressure losses are compared with availableexperimental data and found to be in agreement. Subsequently, a more detailed analysis ofvarious flow features is presented. These include the separation/transition processes on boththe suction and pressure sides of the blade, end-wall vortices, and wake evolution at variousspan-wise locations. The results, which constitute one of the largest and highest-fidelity CFDsimulations ever conducted, demonstrate the potential of high-order accurate GPU-acceleratedCFD as a tool for delivering industrial DNS of LPT blades.

Journal article

Kerrigan E, Nie Y, Faqir O, Kennedy CH, Niederer SA, Solis-Lemus JA, Vincent P, Williams SEet al., 2021, Direct transcription for dynamic optimization: a tutorial with a case study on dual-patient ventilation during the COVID-19 pandemic, 59th IEEE Conference on Decision and Control 2020, Publisher: IEEE, Pages: 2597-2614

A variety of optimal control, estimation, system identification and design problems can be formulated as functional optimization problems with differential equality and inequality constraints. Since these problems are infinite-dimensional and often do not have a known analytical solution, one has to resort to numerical methods to compute an approximate solution. This paper uses a unifying notation to outline some of the techniques used in the transcription step of simultaneous direct methods (which discretize-then-optimize) for solving continuous-time dynamic optimization problems. We focus on collocation, integrated residual and Runge-Kutta schemes. These transcription methods are then applied to a simulation case study to answer a question that arose during the COVID-19 pandemic, namely: If there are not enough ventilators, is it possible to ventilate more than one patient on a single ventilator? The results suggest that it is possible, in principle, to estimate individual patient parameters sufficiently accurately, using a relatively small number of flow rate measurements, without needing to disconnect a patient from the system or needing more than one flow rate sensor. We also show that it is possible to ensure that two different patients can indeed receive their desired tidal volume, by modifying the resistance experienced by the air flow to each patient and controlling the ventilator pressure.

Conference paper

Bassi F, Botti L, Verzeroli L, Hartmann R, Jägersküpper J, Martin E, Lorteau M, Vincent PE, Witherden FD, Vermeire BC, Park JS, Iyer A, Puri K, Gutzwiller D, Hirsch C, Chalot Fet al., 2021, Parallelisation to Several Tens-of-Thousands of Cores, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Pages: 259-319

In this Section a detailed and quantitative understanding is provided of how algorithms should be designed and implemented to effectively target a range of existing and emerging ‘massively parallel’ hardware platforms. The goal set up in the TILDA project was to demonstrate the capability and efficiency of the high-order methods developed by the partners on up to 50,000 cores.

Book chapter

Witherden F, Vincent P, 2021, On nodal point sets for Flux Reconstruction, Journal of Computational and Applied Mathematics, Vol: 381, Pages: 1-14, ISSN: 0377-0427

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal point sets that aim to minimise the L ∞ error of an associated interpolating polynomial. The present work combines a comprehensive review of known approximation theory results, with new results, and numerical experiments, to motivate that in fact point sets for FR should aim to minimise the L² error of an associated interpolating polynomial. New results include identification of a nodal point set that minimises the L² norm of an interpolating polynomial, and a proof of the equivalence between such an interpolating polynomial and an L² approximating polynomial with coefficients obtained using a Gauss–Legendre quadrature rule. Numerical experiments confirm that FR errors can be reduced by an order-ofmagnitude by switching from popular point sets such as Chebyshev, Chebyshev–Lobatto and Legendre–Lobatto to Legendre point sets.

Journal article

Rasquin M, Hillewaert K, Colombo A, Bassi F, Massa F, Puri K, Iyer AS, Abe Y, Witherden FD, Vermeire BC, Vincent PEet al., 2021, Computational Campaign on the MTU T161 Cascade, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Pages: 479-518

Preliminary high-fidelity simulations of the MTU T161 low pressure turbine cascade with diverging end walls have been performed on massively parallel computational resources with four different high-order methods at outlet isentropic Mach number M2s= 0.601 and two outlet isentropic Reynolds numbers, namely Re2s=90K and Re2s=200K. First the flow regime and the boundary conditions are thoroughly described. The implementation of each method is then briefly introduced before the main results are presented. The main flow features of this test case have been qualitatively highlighted by these simulations. However, discrepancies have been observed quantitatively in terms of separation point on the suction side of the blade, especially at the lowest Reynolds. These simulations relied mainly on a laminar boundary layer at the inlet of the domain, which is likely the root cause of the observed discrepancies. Additional simulations with turbulent boundary layer imposed at the inlet are required to characterize the flow separation based on the turbulence intensity at the inlet.

Book chapter

Solis-Lemus JA, Costar E, Doorly D, Kerrigan EC, Kennedy CH, Tait F, Niederer S, Vincent PE, Williams SEet al., 2020, A simulated single ventilator/dual patient ventilation strategy for acute respiratory distress syndrome during the COVID-19 pandemic, Royal Society Open Science, Vol: 7, Pages: 1-12, ISSN: 2054-5703

The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs, we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard set-up where we simulate the introduction of T-splitters to supply air to two patients and a modified set-up where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard set-up, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified set-up, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.

Journal article

Vermeire BC, Loppi NA, Vincent PE, 2020, Optimal embedded pair Runge-Kutta schemes for pseudo-time stepping, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 415, ISSN: 0021-9991

Journal article

Sherwin SJ, Moxey D, Peiró J, Vincent PE, Schwab Cet al., 2020, Preface, ISBN: 9783030396466


Loppi NA, Witherden FD, Jameson A, Vincent PEet al., 2019, Locally adaptive pseudo-time stepping for high-order Flux Reconstruction, Journal of Computational Physics, Vol: 399, ISSN: 0021-9991

This paper proposes a novel locally adaptive pseudo-time stepping convergence acceleration technique for dual time stepping which is a common integration method for solving unsteady low-Mach preconditioned/incompressibleNavier-Stokes formulations. In contrast to standard local pseudo-time stepping techniques that are based on computing the local pseudo-time stepsdirectly from estimates of the local Courant-Friedrichs-Lewy limit, the proposed technique controls the local pseudo-time steps using local truncationerrors which are computed with embedded pair RK schemes. The approachhas three advantages. First, it does not require an expression for the characteristic element size, which are difficult to obtain reliably for curved mixedelement meshes. Second, it allows a finer level of locality for high-ordernodal discretisations, such as FR, since the local time-steps can vary between solution points and field variables. Third, it is well-suited to beingcombined with P-multigrid convergence acceleration. Results are presentedfor a laminar 2D cylinder test case at Re = 100. A speed-up factor of 4.16is achieved compared to global pseudo-time stepping with an RK4 scheme,while maintaining accuracy. When combined with P-multigrid convergenceacceleration a speed-up factor of over 15 is achieved. Detailed analysis ofthe results reveals that pseudo-time steps adapt to element size/shape, solution state, and solution point location within each element. Finally, resultsare presented for a turbulent 3D SD7003 airfoil test case at Re = 60, 000.Speed-ups of similar magnitude are observed, and the flow physics is foundto be in good agreement with previous studies.

Journal article

Zhou X, Vincent P, Zhou X, Leow CH, Tang M-Xet al., 2019, Optimization of 3-D Divergence-Free Flow Field Reconstruction Using 2-D Ultrasound Vector Flow Imaging, Ultrasound in Medicine and Biology, Vol: 45, Pages: 3042-3055, ISSN: 0301-5629

Abstract- 3D blood Vector Flow Imaging (VFI) is of great value for understanding and detecting cardiovascular diseases. Currently 3D Ultrasound (US) VFI requires 2D matrix probes which are expensive and suffer from sub-optimal image quality. Our recent study proposed an interpolation algorithm to obtain a divergence free reconstruction of the 3D flow field from 2D velocities obtained by High Frame Rate US Particle Imaging Velocimetry (HFR echo-PIV, also known as HFR UIV), using a 1D array transducer. This work aims to significantly improve the accuracy and reduce the time-to-solution of our previous approach thereby paving the way for clinical translation. More specifically, accuracy was improved by optimising the divergence free basis to reduce Runge-phenomena near domain boundaries, and time-to-solution was reduced by demonstrating that under certain conditions the resulting system could be solved using widely available and highly optimized Generalized Minimum Residual (GMRES) algorithms. To initially demonstrate the utility of the approach, coarse 2D sub-samplings of an analytical unsteady Womersely flow solution and a steady helical flow solution obtained using Computational Fluid Dynamics (CFD) were used to successfully reconstruct full flow solutions, with 0.82% and 4.8% average relative errors in the velocity field respectively. Subsequently, multi-plane 2D velocity fields were obtained through HFR UIV for a straight tube phantom and a carotid bifurcation phantom, from which full 3D flow fields were reconstructed. These were then compared with flow fields obtained via CFD in each of the two configurations, and average relative errors of 6.01% and 12.8% in the velocity field were obtained. These results reflect 15%-75% improvements in accuracy and 53~874 fold acceleration of reconstruction speeds for the four cases, when compared with the previous divergence free flow reconstruction method. In conclusion the proposed method provides an effective and fast metho

Journal article

Iyer A, Witherden F, Chernyshenko S, Vincent Pet al., 2019, Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, Vol: 875, Pages: 758-780, ISSN: 0022-1120

Eigenmodes of averaged small-amplitude perturbations to a turbulent channel flow — which is one of the most fundamental canonical flows — are identified for the first time via an extensive set of high-fidelity GPU-accelerated direct numerical simulations. While the system governing averaged small-amplitude perturbations to turbulent channel flow remains unknown, the fact such eigenmodes can be identified constitutes direct evidence that it is linear. Moreover, while the eigenvalue associated with the slowest-decaying anti-symmetric eigenmode mode is found to be real, the eigenvalue associated with the slowest-decaying symmetric eigenmode mode is found to be complex. This indicates that the unknown linear system governing the evolution of averaged small-amplitude perturbations cannot be self-adjoint, even for the case of a uni-directional flow. In addition to elucidating aspects of the flow physics, the findings provide guidance for development of new unsteady Reynolds-averaged Navier-Stokes turbulence models, and constitute a new and accessible benchmark problem for assessing the performance of existing models,which are used widely throughout industry.

Journal article

Koch MK, Kelly PHJ, Vincent PE, 2019, Towards in-situ vortex identification for peta-scale CFD using contour trees, 8th IEEE Symposium on Large-Scale Data Analysis and Visualization (LDAV), Publisher: Institute of Electrical and Electronics Engineers, Pages: 104-105

Turbulent flows exist in many fields of science and occur in a wide range of engineering applications. While in the past broad knowledge has been established regarding the statistical properties of turbulence at a range of Reynolds numbers, there is a lack of under-standing of the detailed structure of these flows. Since the physical processes involve a vast number of structures, extremely large data sets are required to fully resolve a flow field in both space and time. To make the analysis of such data sets possible, we propose a frame-work that uses state-of-the-art contour tree construction algorithms to identify, classify and track vortices in turbulent flow fields produced by large-scale high-fidelity massively-parallel computational fluid dynamics solvers such as PyFR. Since disk capacity and I/O have become a bottleneck for such large-scale simulations, the proposed framework will be applied in-situ, while relevant data is still in device memory.

Conference paper

Vermeire B, Loppi N, Vincent P, 2019, Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods, Journal of Computational Physics, Vol: 383, Pages: 55-71, ISSN: 0021-9991

In this study we generate optimal Runge-Kutta (RK) schemes forconverging the Artificial Compressibility Method (ACM) using dualtime-stepping with high-order unstructured spatial discretizations. Wepresent optimal RK schemes with between s = 2 and s = 7 stages forSpectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach withsolution polynomial degrees of k = 1 to k = 8. These schemes are optimal in the context of linear advection with predicted speedup factors inexcess of 1.80× relative to a classical RK4,4 scheme. Speedup factors ofbetween 1.89× and 2.11× are then observed for incompressible ImplicitLarge Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil.Finally, we demonstrate the utility of the schemes for incompressibleILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemesare suitable for simulating turbulent flows and can achieve significantspeedup factors when converging the ACM using dual time-steppingwith high-order unstructured spatial discretizations.

Journal article

Zhou X, Papadopoulou V, Leow CH, Vincent P, Tang M-Xet al., 2019, 3-D flow reconstruction using divergence-free interpolation of multiple 2-D contrast-enhanced ultrasound particle imaging velocimetry measurements, Ultrasound in Medicine and Biology, Vol: 45, Pages: 795-810, ISSN: 0301-5629

Quantification of 3-D intravascular flow is valuable for studying arterial wall diseases but currently there is a lack of effective clinical tools for this purpose. Divergence-free interpolation (DFI) using radial basis function (RBF) is an emerging approach for full-field flow reconstruction using experimental sparse flow field samples. Previous DFI reconstructs full-field flow from scattered 3-D velocity input obtained using phase-contrast magnetic resonance imaging with low temporal resolution. In this study, a new DFI algorithm is proposed to reconstruct full-field flow from scattered 2-D in-plane velocity vectors obtained using ultrafast contrast-enhanced ultrasound (>1000 fps) and particle imaging velocimetry. The full 3-D flow field is represented by a sum of weighted divergence-free RBFs in space. Because the acquired velocity vectors are only in 2-D and hence the problem is ill-conditioned, a regularized solution of the RBF weighting is achieved through singular value decomposition (SVD) and the L-curve method. The effectiveness of the algorithm is determined via numerical experiments for Poiseuille flow and helical flow with added noise, and it is found that an accuracy as high as 95.6% can be achieved for Poiseuille flow (with 5% input noise). Experimental feasibility is also determined by reconstructing full-field 3-D flow from experimental 2-D ultrasound image velocimetry measurements in a carotid bifurcation phantom. The method is typically faster for a range of problems compared with computational fluid dynamics, and has been found to be effective for the three flow cases.

Journal article

Zhou X, Zhou X, Leow CH, Vincent P, Tang Met al., 2018, 3D Flow Reconstruction and Wall Shear Stress Evaluation with 2D Ultrafast Ultrasound Particle Imaging Velocimetry, IEEE International Ultrasonics Symposium (IUS), Publisher: IEEE, ISSN: 1948-5719

Conference paper

Loppi N, Witherden F, Jameson A, Vincent PEet al., 2018, A high-order cross-platform incompressible Navier-Stokes solver via artificial compressibility with application to a turbulent jet, Computer Physics Communications, Vol: 233, Pages: 193-205, ISSN: 0010-4655

Modern hardware architectures such as GPUs and manycore processors are characterised by an abundance of compute capability relative to memory bandwidth. This makes them well-suited to solving temporally explicit and spatially compact discretisations of hyperbolic conservation laws. However, classical pressure-projection-based incompressible Navier–Stokes formulations do not fall into this category. One attractive formulation for solving incompressible problems on modern hardware is the method of artificial compressibility. When combined with explicit dual time stepping and a high-order Flux Reconstruction discretisation, the majority of operations can be cast as compute bound matrix–matrix multiplications that are well-suited for GPU acceleration and manycore processing. In this work, we develop a high-order cross-platform incompressible Navier–Stokes solver, via artificial compressibility and dual time stepping, in the PyFR framework. The solver runs on a range of computer architectures, from laptops to the largest supercomputers, via a platform-unified templating approach that can generate/compile CUDA, OpenCL and C/OpenMP code at runtime. The extensibility of the cross-platform templating framework defined within PyFR is clearly demonstrated, as is the utility of -multigrid for convergence acceleration. The platform independence of the solver is verified on Nvidia Tesla P100 GPUs and Intel Xeon Phi 7210 KNL manycore processors with a 3D Taylor–Green vortex test case. Additionally, the solver is applied to a 3D turbulent jet test case at , and strong scaling is reported up to 144 GPUs. The new software constitutes the first high-order accurate cross-platform implementation of an incompressible Navier–Stokes solver via artificial compressibility and -multigrid accelerated dual time stepping to be published in the literature. The technology has applications in a range of sectors, including the maritime and automotive industries. Moreove

Journal article

Corbett RW, Grechy L, Iori F, Crane J, Herbert P, Di Cocco P, Gedroyc W, Vincent PE, Caro C, Duncan Net al., 2018, Heterogeneity in the non-planarity and arterial curvature of arteriovenous fistulae in vivo, Journal of Vascular Surgery, Vol: 68, Pages: 152s-163s, ISSN: 0741-5214

Objective: Native arteriovenous fistulae (AVF) for haemodialysis are susceptible to non-maturation. Adverse features of local blood flow have been implicated in the formation of peri-anastomotic neointimal hyperplasia which may underpin non-maturation. While computational fluid dynamic simulations of idealised models highlight the importance of geometry on fluid and vessel wall interactions, little is known in vivo about AVF geometry and its role in adverse clinical outcomes. This study set out to examine the three-dimensional geometry of native AVF and the geometric correlates of AVF failure.Methods: As part of an observational study between 2013 and 2016, patients underwent creation of an upper limb AVF according to current surgical best practice. Phase-contrast MRI was performed on the day of surgery to obtain luminal geometry along with ultrasound measurements of flow. MRI datasets were segmented and reconstructed for quantitative and qualitative analysis of local geometry. Clinical maturation was evaluated at six weeks. Results: 60 patients were successfully imaged on the day of surgery. Radiocephalic (n=17), brachiocephalic (n=40) and brachiobasilic (n=3) fistulae were all included in the study. Centrelines extracted from segmented vessel lumen exhibited significant heterogeneity in arterial non-planarity and curvature. Furthermore, these features are more marked in brachiocephalic as compared to radiocephalic fistulae. Across the cohort, the projected bifurcation angle was was 73° (±16°) mean (±sd). Geometry was preserved at two weeks in 20 patients who underwent repeat imaging. A greater degree of arterial non-planarity (log odds ratio (logOR) 0.95 per 0.1/vessel diameter (95% CI 0.22 to 1.90, P= .03)) along with a larger bifurcation angle (logOR 0.05 per degree (95% CI 0.01 to 0.09, P= .02)) are associated with a great rate of maturation, as is fistula location (upper vs lower arm) logOR -1.9 (95% CI -3.2 to 0.7, P = .002) . Con

Journal article

Grechy L, Iori F, Corbett R, Shurey S, Gedroyc W, Duncan N, Caro C, Vincent PEet al., 2017, Suppressing unsteady flow in arterio-venous fistulae, Physics of Fluids, Vol: 29, ISSN: 1070-6631

Arterio-Venous Fistulae (AVF) are regarded as the “gold standard” method of vascular access for patients with end-stage renal disease who require haemodialysis. However, a large proportion of AVF do not mature, and hence fail, as a result of various pathologies such as Intimal Hyperplasia (IH). Unphysiological flow patterns, including high-frequency flow unsteadiness, associated with the unnatural and often complex geometries of AVF are believed to be implicated in the development of IH. In the present study, we employ a Mesh Adaptive Direct Search optimisation framework, computational fluid dynamics simulations, and a new cost function to design a novel non-planar AVF configuration that can suppress high-frequency unsteady flow. A prototype device for holding an AVF in the optimal configuration is then fabricated, and proof-of-concept is demonstrated in a porcine model. Results constitute the first use of numerical optimisation to design a device for suppressing potentially pathological high-frequency flow unsteadiness in AVF.

Journal article

Vincent P, Grechy L, Corbett R, 2017, A device for maintaining vascular connections

There is provided a device for maintaining a vascular connection comprising a vein- supporting section and an artery-supporting section. The centreline of the vein-supporting section and the centreline of the artery-supporting section meet at an intersection point which defines the origin of a right-handed Cartesian coordinate system. The centreline of the artery-supporting section is arcuate and lies in the region y<=0 and has a tangent parallel to the x axis at the origin and wherein the artery-supporting section is configured to carry blood flow in a direction from negative x towards positive x. A tangent of the centreline of the vein-supporting section at the origin has direction [cos (Θ) sin (Φ), sin (Θ) sin (Φ), ± cos (Φ)], where Φ is in the range 225 to 270 degrees and Θ is in the range 200 to 300 degrees.


grechy L, iori F, corbett R, gedroyc W, duncan N, caro C, Vincent PEet al., 2017, The Effect of Arterial Curvature on Blood Flow in Arterio-Venous Fistulae: Realistic Geometries and Pulsatile Flow, Cardiovascular Engineering and Technology, Vol: 8, Pages: 313-329, ISSN: 1869-4098

Arterio-Venous Fistulae (AVF) are regarded as the “gold standard” method of vascular access for patients with End-Stage Renal Disease (ESRD) who require haemodialysis. However, up to 60% of AVF do not mature, and hence fail, as a result of Intimal Hyperplasia (IH). Unphysiological flow and oxygen transport patterns, associated with the unnatural and often complex geometries of AVF, are believed to be implicated in the development of IH. Previous studies have investigated the effect of arterial curvature on blood flow in AVF using idealized planar AVF configurations and non-pulsatile inflow conditions. The present study takes an important step forwards by extending this work to more realistic non-planar brachiocephalic AVF configurations with pulsatile inflow conditions. Results show that forming an AVF by connecting a vein onto the outer curvature of an arterial bend does not, necessarily, suppress unsteady flow in the artery. This finding is converse to results from a previous more idealized study. However, results also show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can suppress exposure to regions of low wall shear stress and hypoxia in the artery. This finding is in agreement with results from a previous more idealized study. Finally, results show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can significantly reduce exposure to high WSS in the vein. The results are important, as they demonstrate that in realistic scenarios arterial curvature can be leveraged to reduce exposure to excessively low/high levels of WSS and regions of hypoxia in AVF. This may in turn reduce rates of IH and hence AVF failure.

Journal article

Park JS, Witherden FD, Vincent PE, 2017, High-order implicit large-Eddy simulations of flow over a NACA0021 aerofoil, AIAA Journal: devoted to aerospace research and development, Vol: 55, Pages: 2186-2197, ISSN: 0001-1452

In this study the graphical-processing-unit-accelerated solver PyFR is used to simulate flow over a NACA0021 aerofoil in deep stall at a Reynolds number of 270,000 using the high-order flux reconstruction approach.Wall-resolved implicit large-eddy simulations are undertaken on unstructured hexahedral meshes at fourth- and fifth-order accuracy in space. It was found that either modal filtering or antialiasing via an approximate L2 projection is required in order to stabilize simulations. Time-span-averaged pressure coefficient distributions on the aerofoil and associated lift and drag coefficients are seen to converge toward experimental data as the simulation setup is made more realistic by increasing the aerofoil span. Indeed, the lift and drag coefficients obtained by fifth-order implicit large-eddy simulation with antialiasing via an approximate L2 projection agree better with experimental data than a wide range of previous studies. Stabilization via modal filtering, however, is found to reduce solution accuracy. Finally, performance of various PyFR simulations is compared, and it is found that fifth-order simulations with antialiasing via an L2 projection are the most efficient. Results indicate that high-order flux reconstruction schemes with antialiasing via an L2 projection are a good candidate for underpinning accurate wall- resolved implicit large-eddy simulation of separated, turbulent flows over complex engineering geometries.

Journal article

Vincent PE, Witherden FD, Vermeire, Park JS, Iyeret al., 2017, Towards green aviation with Python at petascale, International Conference for High Performance Computing, Networking, Storage and Analysis, Publisher: IEEE

Accurate simulation of unsteady turbulentflow is critical for improved design of greener aircraftthat are quieter and more fuel-efficient. We demonstrateapplication of PyFR, a Python based computational fluiddynamics solver, to petascale simulation of such flowproblems. Rationale behind algorithmic choices, whichoffer increased levels of accuracy and enable sustainedcomputation at up to 58% of peak DP-FLOP/s on unstruc-tured grids, will be discussed in the context of modernhardware. A range of software innovations will also bedetailed, including use of runtime code generation, whichenables PyFR to efficiently target multiple platforms,including heterogeneous systems, via a single implemen-tation. Finally, results will be presented from a full-scale simulation of flow over a low-pressure turbine bladecascade, along with weak/strong scaling statistics from thePiz Daint and Titan supercomputers, and performancedata demonstrating sustained computation at up to 13.7DP-PFLOP/s.

Conference paper

Vermeire BC, Witherden, Vincent PE, 2017, On the utility of GPU accelerated high-order methods for unsteady flow simulations: a comparison with industry-standard tools, Journal of Computational Physics, Vol: 334, Pages: 497-521, ISSN: 0021-9991

First- and second-order accurate numerical methods, implemented forCPUs, underpin the majority of industrial CFD solvers. Whilst this technologyhas proven very successful at solving steady-state problems via aReynolds Averaged Navier-Stokes approach, its utility for undertaking scaleresolvingsimulations of unsteady flows is less clear. High-order methods forunstructured grids and GPU accelerators have been proposed as an enablingtechnology for unsteady scale-resolving simulations of flow over complexgeometries. In this study we systematically compare accuracy and cost ofthe high-order Flux Reconstruction solver PyFR running on GPUs and theindustry-standard solver STAR-CCM+ running on CPUs when applied to arange of unsteady flow problems. Specifically, we perform comparisons ofaccuracy and cost for isentropic vortex advection (EV), decay of the Taylor-Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flowover an SD7003 aerofoil. We consider two configurations of STAR-CCM+: asecond-order configuration, and a third-order configuration, where the latterwas recommended by CD-Adapco for more effective computation of unsteadyflow problems. Results from both PyFR and Star-CCM+ demonstrate thatthird-order schemes can be more accurate than second-order schemes for agiven cost e.g. going from second- to third-order, the PyFR simulations of theEV and TGV achieve 75x and 3x error reduction respectively for the same orreduced cost, and STAR-CCM+ simulations of the cylinder recovered wakestatistics significantly more accurately for only twice the cost. Moreover,advancing to higher-order schemes on GPUs with PyFR was found to offereven further accuracy vs. cost benefits relative to industry-standard tools.

Journal article

Vermeire BC, Vincent PE, 2016, On the behaviour of fully-discrete flux reconstruction schemes, Computer Methods in Applied Mechanics and Engineering, Vol: 315, Pages: 1053-1079, ISSN: 0045-7825

In this study we employ von Neumann analyses to investigate the disper-sion, dissipation, group velocity, and error properties of several fully discreteflux reconstruction (FR) schemes. We consider three FR schemes pairedwith two explicit Runge-Kutta (ERK) schemes and two singly diagonallyimplicit RK (SDIRK) schemes. Key insights include the dependence ofhigh-wavenumber numerical dissipation, relied upon for implicit large eddysimulation (ILES), on the choice of temporal scheme and time-step size.Also, the wavespeed characteristics of fully-discrete schemes and the relativedominance of temporal and spatial errors as a function of wavenumber andtime-step size are investigated. Salient properties from the aforementionedtheoretical analysis are then demonstrated in practice using linear advectiontest cases. Finally, a Burgers turbulence test case is used to demonstrate theimportance of the temporal discretisation when using FR schemes for ILES.

Journal article

Vermeire BC, Vincent PE, 2016, On the Properties of Energy Stable Flux Reconstruction Schemes for Implicit Large Eddy Simulation, Journal of Computational Physics, Vol: 327, Pages: 368-388, ISSN: 0021-9991

We begin by investigating the stability, order of accuracy, and dispersionand dissipation characteristics of the extended range of energy stable fluxreconstruction (E-ESFR) schemes in the context of implicit large eddy simulation(ILES). We proceed to demonstrate that subsets of the E-ESFR schemesare more stable than collocation nodal discontinuous Galerkin methods recoveredwith the flux reconstruction approach (FRDG) for marginally-resolvedILES simulations of the Taylor-Green vortex. These schemes are shown tohave reduced dissipation and dispersion errors relative to FRDG schemes ofthe same polynomial degree and, simultaneously, have increased CourantFriedrichs-Lewy(CFL) limits. Finally, we simulate turbulent flow over anSD7003 aerofoil using two of the most stable E-ESFR schemes identifiedby the aforementioned Taylor-Green vortex experiments. Results demonstratethat subsets of E-ESFR schemes appear more stable than the commonlyused FRDG method, have increased CFL limits, and are suitable for ILES ofcomplex turbulent flows on unstructured grids.

Journal article

Witherden FD, Park JS, Vincent PE, 2016, An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements, Journal of Scientific Computing, Vol: 69, Pages: 905-920, ISSN: 0885-7474

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders ℘=3,4,5℘=3,4,5 . We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility.

Journal article

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