Publications

Journal Articles

2018

• 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{2018:turner.peiro.ea:curvilinear,
    author = {Turner, M. and Peir\'o, J. and Moxey, D.},
    title = {Curvilinear mesh generation using a variational framework},
    journal = {Computer-Aided Design},
    year = {2018},
    volume = {103},
    pages = {73--91},
    doi = {10.1016/j.cad.2017.10.004},
    groups = {core, meshing}
  }
  

  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.

Book Chapters

Conference Papers

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{2019:marcon.peiro.ea:semi-structured,
    author = {Marcon, J. and Peir\'o, J. and Moxey, D. and Bergemann, N. and Bucklow, H. and Gammon, M. R.},
    title = {A semi-structured approach to curvilinear mesh generation around streamlined bodies},
    booktitle = {2019 AIAA Aerospace Sciences Meeting},
    year = {2019},
    doi = {10.2514/6.2019-1725},
    groups = {core, meshing}
  }
  

  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.

Dissertations

2020

• J. Marcon

  Mesh adaptation for high-order flow simulations

  PhD thesis, Imperial College London, 2020. doi 10.25560/79407 BiBTeX Abstract

  @phdthesis{2020:marcon:mesh,
    author = {Marcon, Julien},
    title = {Mesh adaptation for high-order flow simulations},
    school = {Imperial College London},
    year = {2020},
    groups = {thesis,meshing},
    url = {http://hdl.handle.net/10044/1/79407},
    doi = {10.25560/79407}
  }
  

  Mesh adaptation has only been considered for high-order flow simulations in recent years and many techniques are still to be made more robust and efficient with curvilinear meshes required by these high-order methods. This thesis covers the developments made to improve the mesh generation and adaptation capabilities of the open-source spectral/hp element framework Nektar++ and its dedicated mesh utility NekMesh. This thesis first covers the generation of quality initial meshes typically required before an iterative adaptation procedure can be used. For optimal performance of the spectral/hp element method, quadrilateral and hexahedral meshes are preferred and two methods are presented to achieve this, either entirely or partially. The first method, inspired from cross field methods, solves a Laplace problem to obtain a guiding field from which a valid two-dimensional quadrilateral block decomposition can be automatically obtained. In turn, naturally curved meshes are generated. The second method takes advantage of the medial axis to generate structured partitions in the boundary layer region of three-dimensional domains. The method proves to be robust in generating hybrid high-order meshes with boundary layer aligned prismatic elements near boundaries and tetrahedral elements elsewhere. The thesis goes on to explore the adaptation of high-order meshes for the simulation of flows using a spectral/hp element formulation. First a new approach to moving meshes, referred to here as r-adaptation, based on a variational framework, is described. This new r-adaptation module is then enhanced by p-adaptation for the simulation of compressible inviscid flows with shocks. Where the flow is smooth, p-adaptation is used to benefit from the spectral convergence of the spectral/hp element methods. Where the flow is discontinuous, e.g. at shock waves, r-adaptation clusters nodes together to better capture these field discontinuities. The benefits of this dual, rp-adaptation approach are demonstrated through two-dimensional benchmark test cases.

2017

• M. Turner

  High-order mesh generation for CFD solvers

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

  @phdthesis{2017:turner:high-order,
    author = {Turner, Michael},
    title = {High-order mesh generation for {CFD} solvers},
    school = {Imperial College London},
    year = {2017},
    groups = {thesis, meshing},
    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.