nekmesh.info » Publications

Below is a complete list of publication that NekMesh is built upon. Wherever available, we give links to preprints or full versions of articles.

Journal Articles · Book Chapters · Conference Papers · Dissertations

2018

M. Turner, J. Peiró and D. Moxey
Curvilinear mesh generation using a variational framework
Computer-Aided Design, 103, pp. 73–91, 2018. 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}
}
```
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.

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 Abstract
```
@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}
}
```
Computational modelling is now tightly integrated into many fields of research in science and industry. Computa- tional 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.

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. 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},
  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.

2017

M. Turner
High-order mesh generation for CFD solvers
PhD thesis, Imperial College London, 2017. 10.25560/57956 BibTeX Abstract
```
@phdthesis{turner-2017-thesis,
  title = {High-order mesh generation for {CFD} solvers},
  author = {Turner, Michael},
  year = {2017},
  school = {Imperial College London},
  keywords = {nekmesh},
  doi = {10.25560/57956}
}
```
The generation of curvilinear, high-order meshes for CFD applications remains a significant bottleneck in the progress and application of high-order CFD methods. These methods have superior numerical accuracy over low-order methods due to their use of piecewise polynomial representations of domains and solutions. As such they are viewed as a potential source of higher fidelity simulations with a view of industrial application [81]. The current state of the art in high-order mesh generation does not provide a reliable and efficient approach which would be required in an industrial setting. This thesis investigates the generation of high-order curvilinear meshes for CFD applications. It focuses around the design and algorithms of an open-source high- order mesh generator, NekMesh, which has been created as part of this project and is part of the Nektar++ high-order CFD suite. The program aims to create high-order meshes directly from CAD as automatically and robustly as possible. This means that all parts of the high-order meshing problem must be addressed including CAD handling and linear mesh generation. A significant contribution of this thesis to high-order mesh generation is the work on a variational approach to the generation of curved meshes. This has been encompassed in a framework within NekMesh. It has been shown to be able to apply several high-order mesh generation methods found throughout the literature and unify them in one context. In addition to this the algorithms used within this framework mitigate a significant amount of the high computational cost associated with high-order mesh generation and attempts to address robustness issues. In addition to the work on NekMesh this thesis also explores using a semi- structured approach to linear mesh generation which can address several robustness issues. It also applies several the methods created to industrially relevant examples.