Publications – Nektar++

If you use our software for your research, we would be grateful if you could cite one or more of the following papers.

C. D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakovlev, J-E. Lombard, D. Ekelschot, B. Jordi, H. Xu, Y. Mohamied, C. Eskilsson, B. Nelson, P. Vos, C. Biotto, R. M. Kirby, and S. J. Sherwin, “Nektar++: An open-source spectral/hp element framework,” Computer physics communications, vol. 192, pp. 205-219, 2015.

D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, J. Marcon, G. Mengaldo, D. Serson, M. Turner, H. Xu, J. Peiró, R. M. Kirby, S. J. Sherwin, “Nektar++: enhancing the capability and application of high-fidelity spectral/hp element methods”, Computer physics communications, vol. 249, 107110, 2020

This helps demonstrate impact to funding agencies and supports further development of the code.

Below is a list of publications which describe the developments in, or application of, Nektar++.

Journal Articles · Book Chapters · Conference Papers · Dissertations

2024

M. D. Green, K. S. Kirilov, M. Turner, J. Marcon, J. Eichstadt, E. Laughton, C. D. Cantwell, S. J. Sherwin, J. Peiró and D. Moxey

NekMesh: An Open-Source High-Order Mesh Generation Framework

Computer Physics Communications, 2024. doi 10.2139/ssrn.4632754

BiBTeX

@article{Green-2024,
  title = {NekMesh: An Open-Source High-Order Mesh Generation Framework},
  journal = {Computer Physics Communications},
  author = {Green, M. D. and Kirilov, K. S. and Turner, M. and Marcon, J. and Eichstadt, J. and Laughton, E. and Cantwell, C. D. and Sherwin, S. J. and Peir\'o, J. and Moxey, D.},
  doi = {10.2139/ssrn.4632754},
  keywords = {nekmesh},
  note = {Preprint. Accepted for publication},
  year = {2024}
}

2023

D. Lindblad, J. Isler, M. Moragues, S. J. Sherwin and C. D. Cantwell

Nektar++: Development of the Compressible Flow Solver for Large Scale Aeroacoustic Applications

2023.

BiBTeX

@article{lindblad-2023,
  title = {{Nektar++}: {Development} of the Compressible Flow Solver for Large Scale Aeroacoustic Applications},
  author = {Lindblad, D and Isler, J and Moragues, M and Sherwin, SJ and Cantwell, C. D.},
  year = {2023},
  groups = {app}
}

M. Lahooti, Y. Bao, D. Scott, R. Palacios and S. J. Sherwin

LES/DNS fluid-structure interaction simulation of non-linear slender structures in Nektar++ framework

Computer Physics Communications, 282, p. 108528, 2023.

BiBTeX

@article{lahooti-2023,
  title = {{LES/DNS} fluid-structure interaction simulation of non-linear slender structures in {Nektar++} framework},
  author = {Lahooti, Mohsen and Bao, Yan and Scott, David and Palacios, Rafael and Sherwin, Spencer J},
  journal = {Computer Physics Communications},
  volume = {282},
  pages = {108528},
  year = {2023},
  publisher = {Elsevier},
  groups = {app}
}

Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields
Computer Methods in Biomechanics and Biomedical Engineering, 26 (1), pp. 113–125, 2023. doi 10.1080/10255842.2022.2048374
BiBTeX Abstract
```
@article{lampropoulos-2023,
  author = {},
  title = {Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields},
  journal = {Computer Methods in Biomechanics and Biomedical Engineering},
  volume = {26},
  number = {1},
  pages = {113--125},
  year = {2023},
  publisher = {Taylor \& Francis},
  doi = {10.1080/10255842.2022.2048374},
  note = {PMID: 35297711},
  url = {https://doi.org/10.1080/10255842.2022.2048374},
  eprint = {https://doi.org/10.1080/10255842.2022.2048374},
  groups = {app}
}
```
Recent advances in diagnostic neuroradiological imaging, allowed the detection of unruptured intracranial aneurysms (IAs). The shape – irregular or multilobular – of the aneurysmal dome, is considered as a possible rupture risk factor, independently of the size, the location and patient medical background. Disturbed blood flow fields in particular is thought to play a key role in IAs progression. However, there is an absence of widely-used hemodynamic indices to quantify the extent of a multi-directional disturbed flow. We simulated blood flow in twelve patient-specific anterior circulation unruptured intracranial aneurysms with daughter blebs utilizing the spectral/hp element framework Nektar++. We simulated three cardiac cycles using a volumetric flow rate waveform while we considered blood as a Newtonian fluid. To investigate the multidirectionality of the blood flow fields, besides the time-averaged wall shear stress (TAWSS), we calculated the oscillatory shear index (OSI), the relative residence time (RRT) and the time-averaged cross flow index (TACFI). Our CFD simulations suggest that in the majority of our vascular models there is a formation of complex intrasaccular flow patterns, resulting to low and highly oscillating WSS, especially in the area of the daughter blebs. The existence of disturbed multi-directional blood flow fields is also evident by the distributions of the RRT and the TACFI. These findings further support the theory that IAs with daughter blebs are linked to a potentially increased rupture risk.

2022

M. W. Hess, A. Lario, G. Mengaldo and G. Rozza

Reduced order modeling for spectral element methods: current developments in Nektar++ and further perspectives

arXiv preprint arXiv:2201.05404, 2022.

BiBTeX

@article{hess-2022,
  title = {Reduced order modeling for spectral element methods: current developments in {Nektar++} and further perspectives},
  author = {Hess, Martin W and Lario, Andrea and Mengaldo, Gianmarco and Rozza, Gianluigi},
  journal = {arXiv preprint arXiv:2201.05404},
  year = {2022},
  groups = {core}
}

2021

M. Z. Hossain, C. D. Cantwell and S. J. Sherwin

A spectral/hp element method for thermal convection

International Journal for Numerical Methods in Fluids, 93 (7), pp. 2380–2395, 2021.

BiBTeX

@article{hossain-2021,
  title = {A spectral/$hp$ element method for thermal convection},
  author = {Hossain, Mohammad Z and Cantwell, Chris D and Sherwin, Spencer J},
  journal = {International Journal for Numerical Methods in Fluids},
  volume = {93},
  number = {7},
  pages = {2380--2395},
  year = {2021},
  publisher = {Wiley Online Library},
  groups = {app}
}

A. V. Proskurin and A. M. Sagalakov

A simple scenario of the laminar breakdown in liquid metal flows

Magnetohydrodynamics (0024-998X), 57 (2), 2021.

BiBTeX

@article{proskurin-2021,
  title = {A simple scenario of the laminar breakdown in liquid metal flows},
  author = {Proskurin, AV and Sagalakov, AM},
  journal = {Magnetohydrodynamics (0024-998X)},
  volume = {57},
  number = {2},
  year = {2021},
  groups = {app}
}

Z.-G. Yan, Y. Pan, G. Castiglioni, K. Hillewaert, J. Peiró, D. Moxey and S. J. Sherwin

Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach

Computers & Mathematics with Applications, 81, pp. 351–372, 2021.

BiBTeX

@article{yan-2021a,
  title = {Nektar++: Design and implementation of an implicit, spectral/hp element, compressible flow solver using a Jacobian-free Newton Krylov approach},
  author = {Yan, Zhen-Guo and Pan, Yu and Castiglioni, Giacomo and Hillewaert, Koen and Peir{\'o}, Joaquim and Moxey, David and Sherwin, Spencer J},
  journal = {Computers \& Mathematics with Applications},
  volume = {81},
  pages = {351--372},
  year = {2021},
  publisher = {Elsevier},
  groups = {core}
}

2020

G. Guo, J. Gong and M. Zhang

Numerical investigation on flow characteristics of low-speed flow over a cavity with small aspect ratio

International Journal of Mechanical Sciences, 178, p. 105632, 2020.

BiBTeX

@article{guo-2020,
  title = {Numerical investigation on flow characteristics of low-speed flow over a cavity with small aspect ratio},
  author = {Guo, Guangming and Gong, Junjie and Zhang, Mengqi},
  journal = {International Journal of Mechanical Sciences},
  volume = {178},
  pages = {105632},
  year = {2020},
  publisher = {Elsevier},
  groups = {app}
}

F. F. Buscariolo, W. Hambli, J. Slaughter and S. Sherwin

Using a spectral/hp element method for high-order implicit-LES of bluff automotive geometries

2020.

BiBTeX

@article{buscariolo-2020,
  title = {Using a spectral/$hp$ element method for high-order implicit-{LES} of bluff automotive geometries},
  author = {Buscariolo, Filipe Fabian and Hambli, Walid and Slaughter, James and Sherwin, Spencer},
  publisher = {Loughborough University},
  year = {2020},
  groups = {app}
}

J. Eichstädt, M. Vymazal, D. Moxey and J. Peiró
A comparison of the shared-memory parallel programming models OpenMP, OpenACC and Kokkos in the context of implicit solvers for high-order FEM
Computer Physics Communications, 255, p. 107245, 2020. doi 10.1016/j.cpc.2020.107245
BiBTeX Abstract
```
@article{eichstadt-2020,
  title = {A comparison of the shared-memory parallel programming models OpenMP, OpenACC and Kokkos in the context of implicit solvers for high-order FEM},
  author = {Eichst\"adt, J. and Vymazal, M. and Moxey, D. and Peir\'o, J.},
  journal = {Computer Physics Communications},
  volume = {255},
  pages = {107245},
  year = {2020},
  keywords = {nektar++},
  doi = {10.1016/j.cpc.2020.107245},
  url = {https://davidmoxey.uk/assets/pubs/2020-cpc-comparison.pdf}
}
```
We consider the application of three performance-portable programming models in the context of a high-order spectral element, implicit time-stepping solver for the Navier-Stokes equations. We aim to evaluate whether the use of these models allows code developers to deliver high-performance solvers for computational fluid dynamics simulations that are capable of effectively utilising both many-core CPU and GPU architectures. Using the core elliptic solver for the Navier-Stokes equations as a benchmarking guide, we evaluate the performance of these models on a range of unstructured meshes and give guidelines for the translation of existing codebases and their data structures to these models.
D. Moxey, R. Amici and R. M. Kirby
Efficient matrix-free high-order finite element evaluation for simplicial elements
SIAM Journal on Scientific Computing, 42 (3), pp. C97–C123, 2020. doi 10.1137/19M1246523
BiBTeX Abstract
```
@article{moxey-2020-matfree,
  title = {Efficient matrix-free high-order finite element evaluation for simplicial elements},
  author = {Moxey, D. and Amici, R. and Kirby, R. M.},
  journal = {SIAM Journal on Scientific Computing},
  year = {2020},
  volume = {42},
  number = {3},
  pages = {C97-C123},
  keywords = {nektar++},
  url = {https://davidmoxey.uk/assets/pubs/2020-vectorisation.pdf},
  doi = {10.1137/19M1246523}
}
```
With the gap between processor clock speeds and memory bandwidth speeds continuing to increase, the use of arithmetically intense schemes, such as high-order finite element methods, continues to be of considerable interest. In particular, the use of matrix-free formulations of finite element operators for tensor-product elements of quadrilaterals in two dimensions and hexahedra in three dimensions, in combination with single-instruction multiple-data (SIMD) instruction sets, is a well-studied topic at present for the efficient implicit solution of elliptic equations. However, a considerable limiting factor for this approach is the use of meshes comprising of only quadrilaterals or hexahedra, the creation of which is still an open problem within the mesh generation community. In this article, we study the efficiency of high-order finite element operators for the Helmholtz equation with a focus on extending this approach to unstructured meshes of triangles, tetrahedra and prismatic elements using the spectral/hp element method and corresponding tensor-product bases for these element types. We show that although performance is naturally degraded when going from hexahedra to these simplicial elements, efficient implementations can still be obtained that are capable of attaining 50–70% of the peak FLOPS of processors with both AVX2 and AVX512 instruction sets.
D. Moxey, C. D. Cantwell, Y. Bao, A. Cassinelli, G. Castiglioni, S. Chun, E. Juda, E. Kazemi, K. Lackhove, J. Marcon, G. Mengaldo, D. Serson, M. Turner, H. Xu, J. Peiró, R. M. Kirby and S. J. Sherwin
Nektar++: enhancing the capability and application of high-fidelity spectral/hp element methods
Computer Physics Communications, 249, p. 107110, 2020. doi 10.1016/j.cpc.2019.107110
BiBTeX Abstract
```
@article{moxey-2020-nektar,
  title = {\emph{Nektar++}: enhancing the capability and application of high-fidelity spectral/$hp$ element methods},
  author = {Moxey, D. and Cantwell, C. D. and Bao, Y. and Cassinelli, A. and Castiglioni, G. and Chun, S. and Juda, E. and Kazemi, E. and Lackhove, K. and Marcon, J. and Mengaldo, G. and Serson, D. and Turner, M. and Xu, H. and Peir\'o, J. and Kirby, R. M. and Sherwin, S. J.},
  journal = {Computer Physics Communications},
  year = {2020},
  volume = {249},
  pages = {107110},
  url = {https://www.sciencedirect.com/science/article/pii/S0010465519304175},
  doi = {10.1016/j.cpc.2019.107110},
  keywords = {nektar++}
}
```
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, \emphNektar++ 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 \emphNektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on \emphin situ processing, the use of collective operations for exploiting current and emerging 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 \emphNektar++. This release also incorporates a number of numerical method developments – in particular: the method of moving frames (MMF), 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 (which combine a 2D spectral element and 1D Fourier spectral method) 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 \emphNekMesh; a novel new \emphAcousticSolver for aeroacoustic problems; our development of a ‘thick’ strip model for the modelling of fluid-structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions for future code development and expansion.

2019

J. Marcon, D. A. Kopriva, S. J. Sherwin and J. Peiró

A high resolution PDE approach to quadrilateral mesh generation

Journal of Computational Physics, 399, p. 108918, 2019.

BiBTeX

@article{marcon-2019,
  title = {A high resolution {PDE} approach to quadrilateral mesh generation},
  author = {Marcon, Julian and Kopriva, David A and Sherwin, Spencer J and Peir{\'o}, Joaquim},
  journal = {Journal of Computational Physics},
  volume = {399},
  pages = {108918},
  year = {2019},
  publisher = {Elsevier},
  groups = {core}
}

C. D. Cantwell and A. S. Nielsen

A minimally intrusive low-memory approach to resilience for existing transient solvers

Journal of Scientific Computing, 78, pp. 565–581, 2019.

BiBTeX

@article{Cantwell-2019,
  title = {A minimally intrusive low-memory approach to resilience for existing transient solvers},
  author = {Cantwell, Chris D and Nielsen, Allan S},
  journal = {Journal of Scientific Computing},
  volume = {78},
  pages = {565--581},
  year = {2019},
  publisher = {Springer},
  groups = {core}
}

M. Vymazal, D. Moxey, S. Sherwin, C. D. Cantwell and R. M. Kirby
On weak Dirichlet boundary conditions for elliptic problems in the continuous Galerkin method
Journal of Computational Physics, 394, pp. 732–744, 2019. doi 10.1016/j.jcp.2019.05.021
BiBTeX Abstract
```
@article{vymazal-2019-weakhdg,
  title = {On weak {Dirichlet} boundary conditions for elliptic problems in the continuous {Galerkin} method},
  author = {Vymazal, M. and Moxey, D. and Sherwin, S. and Cantwell, C. D. and Kirby, R. M.},
  year = {2019},
  journal = {Journal of Computational Physics},
  volume = {394},
  pages = {732-744},
  doi = {10.1016/j.jcp.2019.05.021},
  url = {https://davidmoxey.uk/assets/pubs/2019-weak-bcs.pdf},
  keywords = {nektar++}
}
```
We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain - groups of elements that support a piecewise-polynomial continuous expansion. This step allows us to identify a new weak formulation of Dirichlet boundary condition in the continuous framework. We show that the boundary condition leads to a stable discretization with a single parameter insensitive to mesh size and polynomial order of the expansion. The robustness of the approach is demonstrated on several numerical examples.

2018

M. Bareford, N. Johnson and M. Weiland

Improving Nektar++ IO performance for cray XC architecture

Cray User Group Proceedings, Stockholm, Sweden, 2018.

BiBTeX

@article{ba.jo.we:18,
  title = {Improving Nektar++ IO performance for cray XC architecture},
  author = {Bareford, Michael and Johnson, Nick and Weiland, Michele},
  journal = {Cray User Group Proceedings, Stockholm, Sweden},
  year = {2018},
  keywords = {nektar++},
  groups = {core}
}

D. de Grazia, D. Moxey, S. J. Sherwin, M. A. Kravtsova and A. I. Ruban
DNS of a compressible boundary layer flow past an isolated three-dimensional hump in a high-speed subsonic regime
Physical Review Fluids, 3, p. 024101, 2018. doi 10.1103/PhysRevFluids.3.024101
BiBTeX Abstract
```
@article{degrazia-2016,
  title = {DNS of a compressible boundary layer flow past an isolated three-dimensional hump in a high-speed subsonic regime},
  author = {de Grazia, D. and Moxey, D. and Sherwin, S. J. and Kravtsova, M. A. and Ruban, A. I.},
  journal = {Physical Review Fluids},
  volume = {3},
  pages = {024101},
  year = {2018},
  doi = {10.1103/PhysRevFluids.3.024101},
  url = {https://davidmoxey.uk/assets/pubs/2018-prf.pdf},
  keywords = {nektar++}
}
```
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.
M. Turner, J. Peiró and D. Moxey
Curvilinear mesh generation using a variational framework
Computer-Aided Design, 103, pp. 73–91, 2018. doi 10.1016/j.cad.2017.10.004
BiBTeX Abstract
```
@article{turner-2018-variational,
  title = {Curvilinear mesh generation using a variational framework},
  author = {Turner, M. and Peir\'o, J. and Moxey, D.},
  journal = {Computer-Aided Design},
  volume = {103},
  pages = {73-91},
  year = {2018},
  doi = {10.1016/j.cad.2017.10.004},
  keywords = {nekmesh},
  url = {http://www.sciencedirect.com/science/article/pii/S0010448517301744}
}
```
We aim to tackle the challenge of generating unstructured high-order meshes of complex three-dimensional bodies, which remains a significant bottleneck in the wider adoption of high-order methods. In particular we show that by adopting a variational approach to the generation process, many of the current popular high-order generation methods can be encompassed under a single unifying framework. This allows us to compare the effectiveness of these methods and to assess the quality of the meshes they produce in a systematic fashion. We present a detailed overview of the theory and numerical implementation of the framework, and in particular we highlight how this can be effectively exploited to yield a highly-efficient parallel implementation. The effectiveness of this approach is examined by considering a number of two- and three-dimensional examples, where we show how it can be used for both mesh quality optimisation and untangling of invalid meshes.

2017

W. He, R. S. Gioria, J. M. Pérez and V. Theofilis

Linear instability of low Reynolds number massively separated flow around three NACA airfoils

Journal of Fluid Mechanics, 811, pp. 701–741, 2017. doi 10.1017/jfm.2016.778

BiBTeX

@article{he-2017,
  title = {Linear instability of low {Reynolds} number massively separated flow around three {NACA} airfoils},
  author = {He, W. and Gioria, R. S. and Pérez, J. M. and Theofilis, V.},
  volume = {811},
  doi = {10.1017/jfm.2016.778},
  journal = {Journal of Fluid Mechanics},
  publisher = {Cambridge University Press},
  keywords = {nektar++},
  year = {2017},
  pages = {701–741}
}

R. C. Moura, G. Mengaldo, J. Peiró and S. J. Sherwin

On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES/under-resolved DNS of Euler turbulence

Journal of Computational Physics, 330, pp. 615–623, 2017.

BiBTeX

@article{moura-2017,
  title = {On the eddy-resolving capability of high-order discontinuous {Galerkin} approaches to implicit {LES}/under-resolved {DNS} of {Euler} turbulence},
  author = {Moura, R.C. and Mengaldo, G. and Peir{\'o}, J. and Sherwin, S.J.},
  journal = {Journal of Computational Physics},
  volume = {330},
  pages = {615--623},
  year = {2017},
  keywords = {nektar++},
  publisher = {Elsevier},
  groups = {core}
}

G. Mengaldo, R. C. Moura, B. Giralda, J. Peiró and S. J. Sherwin

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

Computers & Fluids, 2017.

BiBTeX

@article{mengaldo-2017,
  title = {Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit {LES}},
  author = {Mengaldo, G. and Moura, R.C. and Giralda, B. and Peir{\'o}, J. and Sherwin, S.J.},
  journal = {Computers \& Fluids},
  year = {2017},
  keywords = {nektar++},
  publisher = {Elsevier},
  groups = {core}
}

S. Ma, C.-W. Kang, T.-B. A. Lim, C.-H. Wu and O. Tutty

Wake of two side-by-side square cylinders at low Reynolds numbers

Physics of Fluids, 29 (3), p. 033604, 2017.

BiBTeX

@article{ma-2017,
  title = {Wake of two side-by-side square cylinders at low {Reynolds} numbers},
  author = {Ma, Shengwei and Kang, Chang-Wei and Lim, Teck-Bin Arthur and Wu, Chih-Hua and Tutty, Owen},
  journal = {Physics of Fluids},
  volume = {29},
  number = {3},
  pages = {033604},
  year = {2017},
  publisher = {AIP Publishing},
  keywords = {nektar++},
  groups = {app}
}

S. Chun and C. Eskilsson

Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces

Journal of Computational Physics, 333, pp. 1–23, 2017.

BiBTeX

@article{chun+eskilsson-2017,
  title = {Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces},
  author = {Chun, S and Eskilsson, Claes},
  journal = {Journal of Computational Physics},
  volume = {333},
  pages = {1--23},
  year = {2017},
  keywords = {moving frames},
  publisher = {Elsevier},
  groups = {app}
}

S. Chun

Method of moving frames to solve time-dependent Maxwell’s equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

Journal of Computational Physics, 340, pp. 85–104, 2017.

BiBTeX

@article{chun-2017,
  title = {Method of moving frames to solve time-dependent {Maxwell}'s equations on anisotropic curved surfaces: {Applications} to invisible cloak and {ELF} propagation},
  author = {Chun, Sehun},
  journal = {Journal of Computational Physics},
  volume = {340},
  pages = {85--104},
  year = {2017},
  keywords = {moving frames},
  publisher = {Elsevier},
  groups = {app}
}

2023

D. Lindblad, S. J. Sherwin, C. Cantwell, J. Lawrence, A. Proenca and M. Moragues Ginard

Large Eddy Simulations of Isolated and Installed Jet Noise using the High-Order Discontinuous Galerkin Method

in AIAA SciTech 2023 Forum, 2023, p. 1546.

BiBTeX

@inproceedings{li.sh.ca.la:23,
  title = {Large Eddy Simulations of Isolated and Installed Jet Noise using the High-Order Discontinuous Galerkin Method},
  author = {Lindblad, Daniel and Sherwin, Spencer J and Cantwell, Chris and Lawrence, Jack and Proenca, Anderson and Moragues Ginard, Margarida},
  booktitle = {AIAA SciTech 2023 Forum},
  pages = {1546},
  year = {2023},
  groups = {app}
}

2022

G. Vivarelli, J. A. Isler, F. Montomoli, S. J. Sherwin and P. Adami

High-Order Spectral/hp Compressible and Incompressible Comparison of Transitional Boundary-Layers Subject to a Realistic Pressure Gradient and High Reynolds Number

in Turbo Expo: Power for Land, Sea, and Air, 2022, 86113, p. V10CT32A024.

BiBTeX

@inproceedings{vivarelli-2022,
  title = {High-Order Spectral/$hp$ Compressible and Incompressible Comparison of Transitional Boundary-Layers Subject to a Realistic Pressure Gradient and High $Reynolds$ Number},
  author = {Vivarelli, Guglielmo and Isler, Jo{\~a}o Anderson and Montomoli, Francesco and Sherwin, Spencer J and Adami, Paolo},
  booktitle = {Turbo Expo: Power for Land, Sea, and Air},
  volume = {86113},
  pages = {V10CT32A024},
  year = {2022},
  organization = {American Society of Mechanical Engineers},
  groups = {core}
}

B. Liu, C. D. Cantwell, D. Moxey, G. Mashy and S. J. Sherwin

Vectorised spectral/hp element matrix-free operator for anisotropic heat transport in tokamak edge plasma

in 8th European Congress on Computational Methods in Applied Sciences and Engineering, 2022.

BiBTeX

@inproceedings{liu-2022,
  title = {Vectorised spectral/$hp$ element matrix-free operator for anisotropic heat transport in tokamak edge plasma},
  author = {Liu, Bin and Cantwell, CD and Moxey, David and Mashy, G and Sherwin, SJ},
  booktitle = {8th European Congress on Computational Methods in Applied Sciences and Engineering},
  year = {2022},
  organization = {Newcastle University},
  groups = {app}
}

D. Lindblad, S. Sherwin, C. Cantwell, J. Lawrence, A. Proenca and M. Moragues Ginard

Aeroacoustic analysis of a subsonic jet using the discontinuous Galerkin method

in 28th AIAA/CEAS Aeroacoustics 2022 Conference, 2022, p. 2932.

BiBTeX

@inproceedings{liindblad-2022,
  title = {Aeroacoustic analysis of a subsonic jet using the discontinuous {Galerkin} method},
  author = {Lindblad, Daniel and Sherwin, Spencer and Cantwell, Chris and Lawrence, Jack and Proenca, Anderson and Moragues Ginard, Margarida},
  booktitle = {28th AIAA/CEAS Aeroacoustics 2022 Conference},
  pages = {2932},
  year = {2022},
  groups = {app}
}

G. Lyu, C. Chen, X. Du, M. S. Mughal and S. J. Sherwin

Open-source framework for transonic boundary layer natural transition analysis over complex geometries in Nektar++

in AIAA AVIATION 2022 Forum, 2022, p. 4032.

BiBTeX

@inproceedings{lyu-2022,
  title = {Open-source framework for transonic boundary layer natural transition analysis over complex geometries in {Nektar++}},
  author = {Lyu, Ganlin and Chen, Chao and Du, Xi and Mughal, Mohammed S and Sherwin, Spencer J},
  booktitle = {AIAA AVIATION 2022 Forum},
  pages = {4032},
  year = {2022},
  groups = {app}
}

2021

H. Jiang, X. Ju and Y. Lu

Large-Eddy Simulation of Flow Past a Circular Cylinder Using OpenFOAM and Nektar++

in International Conference on Offshore Mechanics and Arctic Engineering, 2021, 85185, p. V008T08A019.

BiBTeX

@inproceedings{jiang-2021,
  title = {Large-Eddy Simulation of Flow Past a Circular Cylinder Using {OpenFOAM} and {Nektar++}},
  author = {Jiang, Hongyi and Ju, Xiaoying and Lu, Yucen},
  booktitle = {International Conference on Offshore Mechanics and Arctic Engineering},
  volume = {85185},
  pages = {V008T08A019},
  year = {2021},
  organization = {American Society of Mechanical Engineers},
  groups = {app}
}

2020

Mejı́a Manuel F, D. Serson, R. C. Moura, B. S. Carmo, J. Escobar-Vargas and A. González-Mancera

Erosion Wear Evaluation Using Nektar++

in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018, 2020, pp. 419–428.

BiBTeX

@inproceedings{mejia-2020,
  title = {Erosion Wear Evaluation Using {Nektar++}},
  author = {Mej{\'\i}a, Manuel F and Serson, Douglas and Moura, Rodrigo C and Carmo, Bruno S and Escobar-Vargas, Jorge and Gonz{\'a}lez-Mancera, Andr{\'e}s},
  booktitle = {Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM 2018}: Selected Papers from the {ICOSAHOM} Conference, London, UK, July 9-13, 2018},
  pages = {419--428},
  year = {2020},
  organization = {Springer International Publishing},
  groups = {app}
}

Fürst Jiřı́, M. Lasota, J. Musil and J. Pech

Numerical Investigation of Aeroelastic Flutter in Two-Dimensional Cascade of Compressor Blades

in MATEC Web of Conferences, 2020, 328, p. 02020.

BiBTeX

@inproceedings{furst-2020,
  title = {Numerical Investigation of Aeroelastic Flutter in Two-Dimensional Cascade of Compressor Blades},
  author = {F{\"u}rst, Ji{\v{r}}{\'\i} and Lasota, Martin and Musil, Josef and Pech, Jan},
  booktitle = {MATEC Web of Conferences},
  volume = {328},
  pages = {02020},
  year = {2020},
  organization = {EDP Sciences},
  groups = {app}
}

2019

J. Marcon, J. Peiró, D. Moxey, N. Bergemann, H. Bucklow and M. R. Gammon
A semi-structured approach to curvilinear mesh generation around streamlined bodies
in 2019 AIAA Aerospace Sciences Meeting, 2019. doi 10.2514/6.2019-1725
BiBTeX Abstract
```
@inproceedings{marcon-2019-structured,
  title = {A semi-structured approach to curvilinear mesh generation around streamlined bodies},
  author = {Marcon, J. and Peir\'o, J. and Moxey, D. and Bergemann, N. and Bucklow, H. and Gammon, M. R.},
  booktitle = {2019 AIAA Aerospace Sciences Meeting},
  year = {2019},
  doi = {10.2514/6.2019-1725},
  url = {https://davidmoxey.uk/assets/pubs/2019-aiaa-scitech.pdf},
  keywords = {nekmesh}
}
```
We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-structured approach which combines the high quality of structured meshes in the near-field with the flexibility of unstructured meshes in the far-field. We utilise medial axis technology to robustly partition the near-field into blocks which can be meshed coarsely with a linear swept mesher. A high-order mesh of the near-field is then generated and split using an isoparametric approach which allows us to obtain highly stretched elements aligned with the flow field. Special treatment of the partition is performed on the wing root juntion and the trailing edge — into the wake — to obtain an H-type mesh configuration with anisotropic hexahedra ideal for the strong shear of high Reynolds number simulations. We then proceed to discretise the far-field using traditional robust tetrahedral meshing tools. This workflow is made possible by two sets of tools: CADfix, focused on CAD system, the block partitioning of the near-field and the generation of a linear mesh; and NekMesh, focused on the curving of the high-order mesh and the generation of highly-stretched boundary layer elements. We demonstrate this approach on a NACA0012 wing attached to a wall and show that a gap between the wake partition and the wall can be inserted to remove the dependency of the partitioning procedure on the local geometry.
J. Eichstädt, D. Moxey and J. Peiró
Towards a performance-portable high-order implicit flow solver
in 2019 AIAA Aerospace Sciences Meeting, 2019. doi 10.2514/6.2019-1404
BiBTeX Abstract
```
@inproceedings{eichstadt-2019-performance,
  title = {Towards a performance-portable high-order implicit flow solver},
  author = {Eichst\"adt, J. and Moxey, D. and Peir\'o, J.},
  booktitle = {2019 AIAA Aerospace Sciences Meeting},
  year = {2019},
  doi = {10.2514/6.2019-1404},
  url = {https://davidmoxey.uk/assets/pubs/2019-aiaa-scitech-2.pdf},
  keywords = {nektar++}
}
```
We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-structured approach which combines the high quality of structured meshes in the near-field with the flexibility of unstructured meshes in the far-field. We utilise medial axis technology to robustly partition the near-field into blocks which can be meshed coarsely with a linear swept mesher. A high-order mesh of the near-field is then generated and split using an isoparametric approach which allows us to obtain highly stretched elements aligned with the flow field. Special treatment of the partition is performed on the wing root juntion and the trailing edge — into the wake — to obtain an H-type mesh configuration with anisotropic hexahedra ideal for the strong shear of high Reynolds number simulations. We then proceed to discretise the far-field using traditional robust tetrahedral meshing tools. This workflow is made possible by two sets of tools: CADfix, focused on CAD system, the block partitioning of the near-field and the generation of a linear mesh; and NekMesh, focused on the curving of the high-order mesh and the generation of highly-stretched boundary layer elements. We demonstrate this approach on a NACA0012 wing attached to a wall and show that a gap between the wake partition and the wall can be inserted to remove the dependency of the partitioning procedure on the local geometry.

2018

J. Cohen, J. Marcon, M. Turner, C. Cantwell, S. J. Sherwin, J. Peiró and D. Moxey

Simplifying high-order mesh generation for computational scientists

2018.

BiBTeX

@inproceedings{co.ma.tu.ca:18,
  title = {Simplifying high-order mesh generation for computational scientists},
  author = {Cohen, Jeremy and Marcon, Julian and Turner, Michael and Cantwell, Chris and Sherwin, SJ and Peir{\'o}, Joaquim and Moxey, David},
  year = {2018},
  organization = {CEUR Workshop Proceedings},
  keywords = {nekmesh},
  groups = {core}
}

2017

D. Moxey, C. D. Cantwell, G. Mengaldo, D. Serson, D. Ekelschot, J. Peiró, S. J. Sherwin and R. M. Kirby
Towards p-adaptive spectral/hp element methods for modelling industrial flows
in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, 2017, pp. 63–79. doi 10.1007/978-3-319-65870-4_4
BiBTeX Abstract
```
@inproceedings{moxey-2017a,
  title = {Towards $p$-adaptive spectral/$hp$ element methods for modelling industrial flows},
  author = {Moxey, D. and Cantwell, C. D. and Mengaldo, G. and Serson, D. and Ekelschot, D. and Peir\'o, J. and Sherwin, S. J. and Kirby, R. M.},
  booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016},
  pages = {63-79},
  year = {2017},
  doi = {10.1007/978-3-319-65870-4_4},
  url = {https://davidmoxey.uk/assets/pubs/2017-icosahom16.pdf},
  keywords = {nektar++}
}
```
There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical methods and corresponding software frameworks which can deliver the next-generation of complex and detailed fluid simulations to scientists and engineers in an efficient way. In this article we discuss recent and upcoming advances in the use of the spectral/hp element method for addressing these modelling challenges. To use these methods efficiently for such applications, is critical that computational resolution is placed in the regions of the flow where it is needed most, which is often not known \empha priori. We propose the use of spatially and temporally varying polynomial order, coupled with appropriate error estimators, as key requirements in permitting these methods to achieve computationally efficient high-fidelity solutions to complex flow problems in the fluid dynamics community.

2022

A. J. Jurecki

Characterization of flow states in corrugated annuli

PhD thesis, Instytut Techniki Lotniczej i Mechaniki Stosowanej, 2022.

BiBTeX

@phdthesis{jurecki-2022,
  title = {Characterization of flow states in corrugated annuli},
  author = {Jurecki, Aleksander Jan},
  year = {2022},
  school = {Instytut Techniki Lotniczej i Mechaniki Stosowanej},
  groups = {thesis}
}

2021

M. Duran

The Stability of Two-Dimensional Cylinder Wakes in the Presence of a Wavy Ground

PhD thesis, University of Central Florida, 2021.

BiBTeX

@phdthesis{duran-2021,
  title = {The Stability of Two-Dimensional Cylinder Wakes in the Presence of a Wavy Ground},
  author = {Duran, Matt},
  year = {2021},
  school = {University of Central Florida},
  groups = {thesis}
}

Z. Yan

Efficient implicit spectral/hp element DG techniques for compressible flows

PhD thesis, Imperial College London, 2021.

BiBTeX

@phdthesis{yan-2021b,
  title = {Efficient implicit spectral/$hp$ element {DG} techniques for compressible flows},
  author = {Yan, Zhenguo},
  year = {2021},
  school = {Imperial College London},
  groups = {thesis}
}

A. Cassinelli

A spectral/hp element DNS study of flow past low-pressure turbine cascades and the effects of inflow conditions

PhD thesis, Imperial College London, 2021.

BiBTeX

@phdthesis{cassinelli-2021,
  title = {A spectral/$hp$ element {DNS} study of flow past low-pressure turbine cascades and the effects of inflow conditions},
  author = {Cassinelli, Andrea},
  year = {2021},
  school = {Imperial College London},
  groups = {thesis}
}

V. Saini

Performance and accuracy of high-order accurate large-eddy simulations for gas turbine combustor aerodynamics

PhD thesis, Loughborough University, 2021.

BiBTeX

@phdthesis{saini-2021,
  title = {Performance and accuracy of high-order accurate large-eddy simulations for gas turbine combustor aerodynamics},
  author = {Saini, Vishal},
  year = {2021},
  school = {Loughborough University},
  groups = {thesis}
}

2020

E. Cooke

Modelling the effect of step and roughness features on swept wing boundary layer instabilities

PhD thesis, Imperial College London, 2020.

BiBTeX

@phdthesis{cook-2020,
  title = {Modelling the effect of step and roughness features on swept wing boundary layer instabilities},
  author = {Cooke, Emma},
  year = {2020},
  school = {Imperial College London},
  groups = {thesis}
}

2019

N. Yadav

Hydrodynamic instability and mixing enhancement in grooved channels

PhD thesis, The Institute of Aeronautics and Applied Mechanics, 2019.

BiBTeX

@phdthesis{yadav-2019,
  title = {Hydrodynamic instability and mixing enhancement in grooved channels},
  author = {Yadav, Nikesh},
  year = {2019},
  school = {The Institute of Aeronautics and Applied Mechanics},
  groups = {thesis}
}

2017

M. Turner

High-order mesh generation for CFD solvers

PhD thesis, Imperial College London, 2017. doi 10.25560/57956

BiBTeX

@phdthesis{turner-2017-thesis,
  title = {High-order mesh generation for {CFD} solvers},
  author = {Turner, Michael},
  year = {2017},
  school = {Imperial College London},
  url = {https://spiral.imperial.ac.uk/bitstream/10044/1/57956/1/Turner-M-2018-PhD-Thesis.pdf},
  keywords = {nekmesh},
  doi = {10.25560/57956}
}