Parallel Two-Dimensional Unstructured Anisotropic Delaunay Mesh Generation for Aerospace Applications

A bottom-up approach to parallel anisotropic mesh generation is presented by building a mesh generator from the principles of point-insertion, triangulation, and Delaunay refinement. Applications focusing on high-lift design or dynamic stall, or numerical methods and modeling test cases focus on two-dimensional domains. This push-button parallel mesh generation approach can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field

Anisotropic Delaunay Meshes of Surfaces

Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown to be well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface repre- sentation. Given a surface S endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields.Les maillages anisotropes simpliciaux sont des triangulations dont les éléments sont étirés suivant certaines directions imposées. Les maillages anisotropes sont connus pour être bien adaptés à l'interpolation de fonctions ou à la résolution d'équations aux dérivées partiellles. Ces maillages peuvent aussi améliorer notablement la précision de l'approximation d'une surface. Etant donnée une surface S, munie d'un champs de tenseurs qui définit la métrique en tout point de la surface, nous proposons un nouvel algorithme pour générer un maillage anisotrope qui approxime S par des triangles dont les formes s'adaptent à la métrique locale. L'algorithme repose sur les concepts bien établis de triangulation de Delaunay restreinte et de raffinement de Delaunay et offre des garanties théoriques. L'étoile de chaque sommet dans le maillage est formée par des triangles de Delaunay pour la métrique du sommet central. Chaque triangle a un bon rapport d'aspect dans la métrique attachée à chacun de ces sommets. L'algorithme est facile à programmer. Il permet de mailler diff'rents types de surfaces, comme des surfaces implicites, des polyèdres ou encores des isosurfaces dans des images 3D. L'algorithme peut traiter des surfaces de géométrie ou topologie complexe, il peut aussi prendre en compte des anisotropies très prononcées

Surface modeling and rendering with line segments

Master'sMASTER OF SCIENC

Biting Ellipses to Generate Anisotropic Mesh

. In numerical simulation where the underlying function is strongly directional, it is desirable to use a mesh that is adaptive both in size and in shape. In such simulation, a metric tensor is used to quantify the ideal size and direction locally at each point in the domain, which in turn defines the local stretching and size of the triangles or quadrilaterals of the mesh. Given a metric tensor, the anisotropic meshing problem is to construct a good quality mesh satisfying the metric tensor. We present a new anisotropic meshing method which is called the ellipse biting method. Our algorithm uses the framework of advancing front to generate a close to optimal packing of ellipses. We then use the ae-Delaunay triangulation of the vertex set to generate the final mesh. Because it generates an ellipse packing that respects the underlying control spacing, this new method produce a high quality mesh whose element size and directionality conform well locally to the given input. As part of thi..