335 results found
Moxey D, Cantwell CD, Bao Y, et al., 2020, Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods, Computer Physics Communications, ISSN: 0010-4655
Nektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in-situ processing, the use of collective operations for exploiting current andemerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enable more rapid on-boarding of new users unfamiliar with spectral/$hp$ element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments - in particular: the method of moving frames, which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a 'thick' strip model for the modelling of fluid-structure interaction problems in the context of vortex-induced vibrations. We conclude by commenting some directions for future code development and expansion.
Marcon J, Kopriva DA, Sherwin SJ, et al., 2019, A high resolution PDE approach to quadrilateral mesh generation, Journal of Computational Physics, Vol: 399, Pages: 1-17, ISSN: 0021-9991
We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of pi/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.
Moura RC, Aman M, Peiró J, et al., 2019, Spatial eigenanalysis of spectral/hp continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows, Journal of Computational Physics, Pages: 109112-109112, ISSN: 0021-9991
Vymazal M, Moxey D, Cantwell CD, et al., 2019, On weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin method, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 394, Pages: 732-744, ISSN: 0021-9991
Marcon J, Castiglioni G, Moxey D, et al., 2019, rp-adaptation for compressible flows, Publisher: arXiv
We present an rp-adaptation strategy for the high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to r-adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature-based sensors or error estimators. We demonstrate this proof-of-concept using two geometries at transonic and supersonic flow regimes. The method was implemented in the open-source spectral/hp element framework Nektar++, and its dedicated high-order mesh generation tool NekMesh. The results show that the proposed rp-adaptation methodology is a reasonably cost-effective way of improving accuracy.
Buscariolo FF, Hoessler J, Moxey D, et al., 2019, Spectral/hp element simulation of flow past a Formula One front wing: validation against experiments, Publisher: arXiv
Emerging commercial and academic tools are regularly being applied to thedesign of road and race cars, but there currently are no well-establishedbenchmark cases to study the aerodynamics of race car wings in ground effect.In this paper we propose a new test case, with a relatively complex geometry,supported by the availability of CAD model and experimental results. We referto the test case as the Imperial Front Wing, originally based on the front wingand endplate design of the McLaren 17D race car. A comparison of differentresolutions of a high fidelity spectral/hp element simulation usingunder-resolved DNS/implicit LES approach with fourth and fifth polynomial orderis presented. The results demonstrate good correlation to both the wall-boundedstreaklines obtained by oil flow visualization and experimental PIV results,correctly predicting key characteristics of the time-averaged flow structures,namely intensity, contours and locations. This study highlights the resolutionrequirements in capturing salient flow features arising from this type ofchallenging geometry, providing an interesting test case for both traditionaland emerging high-fidelity simulations.
Chun S, Marcon J, Peiro J, et al., 2019, High-order curvilinear mesh in the numerical solution of PDEs with moving frames on the sphere, Publisher: arXiv
When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. This paper aims to investigate the effect of geometric approximation error by using a high-order mesh with negligible geometric approximation error, even for high order polynomial of order p. To achieve this goal, the high-order mesh generator from CAD geometry called NekMesh is adapted for surface mesh generation in comparison to traditional meshes with non-negligible geometric approximation error. Two types of numerical tests are considered. Firstly, the accuracy of differential operators, such as the gradient, divergence, curl, and Laplacian, is compared for various p on a curved element of the sphere. Secondly, by applying the method of moving frames, four different time-dependent PDEs on the sphere, such as conservation laws, diffusion equations, shallow water equations, and Maxwell's equations are numerically solved to investigate the impact of geometric approximation error on the accuracy and conservation properties of high-order numerical schemes for PDEs on the sphere.
Marcon J, Kopriva DA, Sherwin SJ, et al., 2019, Naturally curved quadrilateral mesh generation using an adaptive spectral element solver, 28th International Meshing Roundtable and User Forum, Publisher: arXiv
We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two dimensional domains. The a priori curved quadrilateral blocks can be further split into a finer high-order mesh as needed. The guiding field is computed by a Laplace equation solver using a continuous Galerkin or discontinuous Galerkin spectral element formulation. This operation is aided by using p-adaptation to achieve faster convergence of the solution with respect to the computational cost. From the guiding field, irregular nodes and separatrices can be accurately located. A first version of the code is implemented in the open source spectral element framework Nektar++ and its dedicated high order mesh generation platform NekMesh.
Cooke EE, Mughal MS, Sherwin S, et al., 2019, Destabilisation of Stationary and Travelling Crossflow Disturbances Due to Steps over a Swept Wing, AIAA Aviation 2019 Forum, Publisher: American Institute of Aeronautics and Astronautics
Destabilization effects of forward facing steps, backward facing steps and bumps on stationary and travelling crossflow disturbances are investigated computationally for a 40° infinite swept wing. Step and bump heights range from 24% to 53% of the boundary layer thickness and are located at 10% chord. The spectral/hp element solver, Nektar++, is used to compute base flow profiles with an embedded swept wing geometry. Parabolized Stability Equations (PSE) and Linearized Harmonic Navier-Stokes (LHNS) models are used to evaluate growth of convecting instabilities. The paper describes derivations of the PSE and LHNS models which accurately solve for the perturbed field over the very localized and rapid variations imposed by the surface step-features. Unlike the PSE, which suffer from a stream-wise numerical step size restriction, the LHNS are a fully elliptic set of equations which may use arbitrarily fine grid resolution. Unsurprisingly, the PSE codes fail to capture the effect of abrupt changes in surface geometry introduced by the steps features. Results for the LHNS and roughness incorporating LHNS are given for the varying step types. Comparisons are made between the LHNS model and direct numerical simulations involving the time-stepping linearized Navier-Stokes solver in the Nektar++ software suite. Most previous work in the topic area has focused on Tollmien-Schlichting perturbations over two-dimensional flat plate flows or airfoils, the novelty of this work lies with analyzing crossflow instability over a swept wing boundary-layer flow with step features.
Cookson AN, Doorly DJ, Sherwin SJ, 2019, Efficiently Generating Mixing by Combining Differing Small Amplitude Helical Geometries, FLUIDS, Vol: 4, ISSN: 2311-5521
Zhu H, Wang R, Bao Y, et al., 2019, Flow over a symmetrically curved circular cylinder with the free stream parallel to the plane of curvature at low Reynolds number, JOURNAL OF FLUIDS AND STRUCTURES, Vol: 87, Pages: 23-38, ISSN: 0889-9746
Bao Y, Zhu HB, Huan P, et al., Numerical prediction of vortex-induced vibration of flexible riser with thick strip method, Journal of Fluids and Structures, ISSN: 0889-9746
We present numerical prediction results of vortex-induced vibration (VIV) of a long flexible tensioned riser subject to uniform currents. The VIV model of long length-to-diameter ratio is considered and ‘thick’ strip technique based on high-order spectral/hp element method is employed for computational simulation. The model parameter of the riser for the simulation is chosen according to the dimensional counterparts used in the experimental tests in Lehn (2003). The numerical results are displayed in terms of motion responses, hydrodynamic forces and wake patterns as well and compared and discussed with the available data in the literature.
Yakhot A, Feldman Y, Moxey D, et al., 2019, Near-wall turbulence in a localized puff in a pipe, Pages: 15-20, ISSN: 0930-8989
© Springer Nature Switzerland AG 2019. We have performed direct numerical simulations of a transitional flow in a pipe for Rem=2250 when turbulence manifests in the form of fleshes (puffs). From experiments and simulations, Rem ≈ 2250 has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Song et al. in J Fluid Mech 813:283–304, 2017, ). The flow regime upstream of its trailing edge and downstream of its leading edge is almost laminar. To collect the velocity data, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at the location of the maximum energy of the transverse (turbulent) motion. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities and Reynolds shear stress becomes similar to a fully-developed turbulent pipe flow.
Buscariolo FF, Meneghini JR, da Silva Assi GR, et al., 2019, Diffuser study on a squared-back ahmed body considering ILES-SVV
© 2019 International Symposium on Turbulence and Shear Flow Phenomena, TSFP. All rights reserved. The Ahmed Body is one of the most studied 3D bluff bodies used for automotive research and was first proposed by Ahmed et al. (1984). Due to the variation of the slant angle of the read upper surface, it can generate different flow behaviours, similar to a standard road vehicles. In this study we also use the Ahmed body to evaluate the performance of the introduction of a rear underbody diffuser which are commonly applied in high performance and race cars to improve downforce. As a default body we consider the Ahmed Body with Squared-Back or 0° slant angle to perform a parametric study of the rear diffuser angle. We employing a high-fidelity CFD based on Spectral/hp element discretisation that combines classical mesh refinement with polynomial expansions in order to achieve both better accuracy. The diffuser length was fixed at the same length that the top slant angle has previously been studies of 222mm and the angle was changed from 0° to 50° in increments of 10°. An additional case considering the diffuser angle of 5° was also evaluated. It was observed that peak values for drag and negative lift (downforce) coefficient were achieved at 30° diffuser angle, in which the topology indicates flow fully attached with two streamwise vortical structures, similar to results obtained from Ahmed et al. (1984), but in this case with the the body flipped upside down.
Cassinelli A, Xu H, Montomoli F, et al., 2019, ON THE EFFECT OF INFLOW DISTURBANCES ON THE FLOW PAST A LINEAR LPT VANE USING SPECTRAL/HP ELEMENT METHODS, ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS
Moura RC, Peiró J, Sherwin SJ, 2019, Implicit LES approaches via discontinuous galerkin methods at very large reynolds, ERCOFTAC Series, Pages: 53-59
© Springer Nature Switzerland AG 2019. We consider the suitability of implicit large-eddy simulation (iLES) approaches via discontinuous Galerkin (DG) schemes. These are model-free eddy-resolving approaches which solve the governing equations in unfiltered form and rely on numerical stabilization techniques to account for the missing scales. In DG, upwind dissipation from the Riemann solver provides the baseline mechanism for regularization. DG-based iLES approaches are currently under rapid dissemination due to their success in predicting complex transitional and turbulent flows at moderate Reynolds numbers (Uranga et al, Int J Numer Meth Eng 87(1–5):232–261, 2011, , Gassner and Beck, Theor Comput Fluid Dyn 27(3–4):221–237, 2013, , Beck et al, Int J Numer Methods Fluids 76(8):522–548, 2014, , Wiart et al Int J Numer Methods Fluids 78:335–354, 2015, ). However, at higher Reynolds number, accuracy and stability issues can arise due the highly under-resolved character of the computations and the suppression of stabilizing viscous effects.
© 2019, Springer Nature B.V. We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about t
Cassinelli A, Adami P, Sherwin S, et al., 2018, High Fidelity Spectral/hp Element Methods for Turbomachinery, ASME IGTI 2018
Buscariolo FF, Sherwin SJ, Assi GRS, et al., 2018, Spectral/hp iLES-SVV simulation methodology study on an Ahmed Body squared back, 2018 SAE Brasil Congress & Exhibition
© 2018 SAE International. All Rights Reserved. The Ahmed Body is one of the most widely studied bluff bodies used for automotive conceptual studies and Computational Fluid Dynamics - CFD software validation. With the advances of the computational processing capacity and improvement in cluster costs, high-fidelity turbulence models, such as Detached Eddies Simulation - DES and Large Eddies Simulation - LES, are becoming a reality for industrial cases, as studied by BUSCARIOLO et al. (2016) , evaluating DES models to automotive applications. This work presents a correlation study between a computational and physical model of an Ahmed Body with slant angle of 0 degree, also known as a squared back. Physical results are from a wind tunnel test, performed by STRACHAN et al. (2007)  considering moving ground and Reynolds number of 1.7M, based on the length of the body. CFD simulations were performed by the code Nektar++, which is an open source spectral/hp element high-order solver, which methodology combine both mesh refinement (h), with higher polynomial order (p) for lower error propagation and better convergence. It employs a high-fidelity turbulence model known as Spectral Vanish Viscosity - iLES-SVV model, which works as a filter for high frequencies. Same physical test conditions and tunnel test section were considered, with a total time of 4 convective lengths. The 4 cases studies consider high-order mesh of 6 th order, divided in two polynomial orders: 5 th and 6 th for two different mesh setups: one base mesh setup with around 95,000 elements corresponding to 6.3Million of DOFs and a second mesh considering a refinement (h) with around 310,000 elements, corresponding to 19.8 Million of DOFs. Meshes were generated by NekMesh, which works with Nektar++ for high-order mesh generation. In order to improve the computational costs, only half of the model is simulated, considering symmetric condition. Considering the converged drag coefficient values for c
Mengaldo G, Moura RC, Giralda B, et al., 2018, Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES, Computers and Fluids, Vol: 169, Pages: 349-364, ISSN: 0045-7930
The study focusses on the dispersion and diffusion characteristics of discontinuous spectral element methods - specifically discontinuous Galerkin (DG) - via the spatial eigensolution analysis framework built around a one-dimensional linear problem, namely the linear advection equation. Dispersion and diffusion characteristics are of critical importance when dealing with under-resolved computations, as they affect both the numerical stability of the simulation and the solution accuracy. The spatial eigensolution analysis carried out in this paper complements previous analyses based on the temporal approach, which are more commonly found in the literature. While the latter assumes periodic boundary conditions, the spatial approach assumes inflow/outflow type boundary conditions and is therefore better suited for the investigation of open flows typical of aerodynamic problems, including transitional and fully turbulent flows and aeroacoustics. The influence of spurious/reflected eigenmodes is assessed with regard to the presence of upwind dissipation, naturally present in DG methods. This provides insights into the accuracy and robustness of these schemes for under-resolved computations, including under-resolved direct numerical simulation (uDNS) and implicit large-eddy simulation (iLES). The results estimated from the spatial eigensolution analysis are verified using the one-dimensional linear advection equation and successively by performing two-dimensional compressible Euler simulations that mimic (spatially developing) grid turbulence.
Winters A, Moura RC, Mengaldo G, et al., A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations, Journal of Computational Physics, ISSN: 0021-9991
Calder M, Craig C, Culley D, et al., 2018, Computational modelling for decision-making: where, why, what, who and how, Royal Society Open Science, Vol: 5, ISSN: 2054-5703
In order to deal with an increasingly complex world, we need ever more sophisticated computational models that can help us make decisions wisely and understand the potential consequences of choices. But creating a model requires far more than just raw data and technical skills: it requires a close collaboration between model commissioners, developers, users and reviewers. Good modelling requires its users and commissioners to understand more about the whole process, including the different kinds of purpose a model can have and the different technical bases. This paper offers a guide to the process of commissioning, developing and deploying models across a wide range of domains from public policy to science and engineering. It provides two checklists to help potential modellers, commissioners and users ensure they have considered the most significant factors that will determine success. We conclude there is a need to reinforce modelling as a discipline, so that misconstruction is less likely; to increase understanding of modelling in all domains, so that the misuse of models is reduced; and to bring commissioners closer to modelling, so that the results are more useful.
Cohen J, Marcon J, Turner M, et al., 2019, Simplifying high-order mesh generation for computational scientists, 10th International Workshop on Science Gateways, Publisher: CEUR Workshop Proceedings, ISSN: 1613-0073
Computational modelling is now tightly integrated into many fields of research in science and industry. Computational fluid dynamics software, for example, gives engineers the ability to model fluid flow around complex geometries defined in Computer-Aided Design (CAD) packages, without the expense of constructing large wind tunnel experiments. However, such modelling requires translation from an initial CAD geometry to a mesh of many small elements that modelling software uses to represent the approximate solution in the numerical method. Generating sufficiently high-quality meshes for simulation is a time-consuming, iterative and error-prone process that is often complicated by the need to interact with multiple command-line tools to generate and visualise the mesh data. In this paper we describe our approach to overcoming this complexity through the addition of a meshing console to Nekkloud, a science gateway for simplifying access to the functionality of the Nektar++ spectral/hp element framework. The meshing console makes use of the NekMesh tool in Nektar++ to help reduce the complexity of the mesh generation process. It offers a web-based interface for specifying parameters, undertaking meshing and visualising results. The meshing console enables Nekkloud to offer support for a full, end-to-end simulation pipeline from initial CAD geometry to simulation results.
Alpresa P, Sherwin S, Weinberg P, et al., 2018, Orbitally shaken shallow fluid layers. II. An improved wall shear stress model, PHYSICS OF FLUIDS, Vol: 30, ISSN: 1070-6631
A new model for the analytical prediction of wall shear stress distributions at the base of orbitally shaken shallow fluid layers is developed. This model is a generalisation of the classical extended Stokes solution and will be referred to as the potential theory-Stokes model. The model is validated using a large set of numerical simulations covering a wide range of flow regimes representative of those used in laboratory experiments. It is demonstrated that the model is in much better agreement with the simulation data than the classical Stokes solution, improving the prediction in 63% of the studied cases. The central assumption of the model—which is to link the wall shear stress with the surface velocity—is shown to hold remarkably well over all regimes covered.
Alpresa P, Sherwin S, Weinberg P, et al., 2018, Orbitally shaken shallow fluid layers. I. Regime classification, PHYSICS OF FLUIDS, Vol: 30, ISSN: 1070-6631
Orbital shakers are simple devices that provide mixing, aeration, and shear stress at multiple scales and high throughput. For this reason, they are extensively used in a wide range of applications from protein production to bacterial biofilms and endothelial cell experiments. This study focuses on the behaviour of orbitally shaken shallow fluid layers in cylindrical containers. In order to investigate the behaviour over a wide range of different conditions, a significant number of numerical simulations are carried out under different configuration parameters. We demonstrate that potential theory—despite the relatively low Reynolds number of the system—describes the free-surface amplitude well and the velocity field reasonably well, except when the forcing frequency is close to a natural frequency and resonance occurs. By classifying the simulations into non-breaking, breaking, and breaking with part of the bottom uncovered, it is shown that the onset of wave breaking is well described by Δh/(2R) = 0.7Γ, where Δh is the free-surface amplitude, R is the container radius, and Γ is the container aspect ratio; Δh can be well approximated using the potential theory. This result is in agreement with standard wave breaking theories although the significant inertial forcing causes wave breaking at lower amplitudes.
De Grazia D, Moxey D, Sherwin SJ, et al., 2018, Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime, Physical Review Fluids, Vol: 3, ISSN: 2469-990X
In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.
Xu H, Cantwell C, Monteserin C, et 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.
Mengaldo G, De Grazia D, Moura RC, et 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 . 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 . 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.
Bao Y, Palacios R, Graham M, et 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.
Marcon J, Turner M, Moxey D, et 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.
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