In this lecture, we provide a status on anisotropic mesh adaptation: its benifits and the future issues. The link between metric fields and discrete meshes is emphasized pointing out the necessity to consider metric for anisotropic mesh adaptation.
As an example, we focus on the contribution of mesh adaptation to high-order methods for stationary and time-dependent problems. We demonstrate that anisotropic mesh adaptation allows second-order flow solvers to achieve a global second-order mesh convergence for numerical solutions with discontinuities in Lp norm. This theoretical result is illustrated on 2D and 3D examples for stationary and time-dependent simulations.

A Delaunay triangulation restricted to a surface is obtained by filtering a 3D Delaunay triangulation. Filtering herein consists of selecting a subset of the 3D Delaunay facets whose dual edges intersect the surface. In this talk I will explain how the restricted Delaunay triangulation paradigm can be used to simultaneously mesh a surface together with its interior. I will then describe two mesh generation algorithms. The first algorithm is greedy and proceeds by Delaunay refinement. The second algorithm is variational and alternates updates of the vertex positions and of the mesh connectivity.

An extension of a previous work by Lohner for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds-Averaged Navier-Stokes computations (RANS). Multiple normals are introduced along convex ridges. The original technique generates a semi-structured boundary layer of prismatic elements growing along point normals. Therefore, extra faces of null area must be introduced to take into account the multiple growth curves at convex ridges and produce a valid topological surface triangulation. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Several complex geometries have been chosen to illustrate the proposed procedure and timings are given, showing that the new module does not place any extra burden in the previous semi-structured approach.

Founded in 1997, Sharc is the developer of harpoon, the Extreme Mesher and the UK/Ireland distributor for EnSight, the world's leading visualisation package (www.ensight.com). Sharc provides solutions to the most demanding engineering problems. This presentation provides an overview of Harpoon's capabilities including specific industrial examples.

Local grid refinement (LGR) becomes a major need in reservoir simulation of new generation. This increases the accuracy, hence the predictability of the reservoir simulation. This presentation provides a review of a hybrid LGR approach developed at the IFP in order to capture the radial aspect of the flow at well vicinities in the refined mesh. Hexahedral structured grid of the reservoir is refined by inserting inside, around the well, a local structured radial grid that follows the flow directions at the drainage area. The two structured grids are connected together by the mean of an unstructured polyhedral mesh.

New contributions to the adaptive strategy using adaptive remeshing and a posteriori error estimation in large elasto-plasticity with damage is developed in this work. We are interested in the problem of remeshing a mechanical structure subjected to large plastic deformations with damage. A general scheme, constituted by several steps necessary to an almost optimal representation of the evolving domain, is presented. These steps are divided into two main categories: the definition of the boundary of the deformed domain and the adaptive remeshing of the domain. The remeshing is governed by a mesh element size map representing the conformity with the underlying geometry of the deformed domain, the improvement of the accuracy of the desired mechanical fields (stress, plastic strain, damage), and the convergence of the mechanical process as well. This map results from an a posteriori estimation of the â˜interpolation error♠independently from the considered mechanical fields. This remeshing procedure must be applied at each iteration of small deformation increment which depends on the specified minimal size of mesh elements. In addition, the macroscopic cracks propagation are modelled by removing the fully damaged elements using the adaptive remeshing. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the proposed adaptive 3D mesher.

In this work the meshing engine is be based on a local optimisation principle. Mesh construction, mesh integrity or remeshing are achieved by using the minimal volume criterion since adaptation is obtained by the local optimisation of the element shape. The local mesh topology operator remains simple and global optimisation is performed by iterating an improvement process. One of the interests of our approach is the robustness. Anisotropic meshes are obtained by calculating the element shape factor with respect to a given metric field. Application presented here will focus on the construction of interface layers associated with a description of boundary, interfaces or free surfaces by a Level Set technique. In that case, the metric fields can be calculated everywhere from the distance function and the mesh refinement can be controlled in the normal direction of the interface. Applications will be shown in the field of material sciences, multi-domain applications and forming process simulations.

Many problems require a displacement or a deformation of the geometry with time. Most of them needed anisotropic meshes to be solved correctly. In this talk, we will present a method to rigid bodies movement through anisotropic tetrahedral meshes.
Given a displacement on a part of the domain boundary and an anisotropic metric defined on mesh vertices, our aim is to generate a new mesh adapted to the prescribed metric and in which the domain boundary has moved.
Our approach is the following: first, we solve a linear elasticity equation to impose a displacement vector on each mesh vertex. Then we move all the mesh vertices and possibly applied optimization operators (edge swap, point relocation) to improve the mesh quality. After having detaille this two points, we will illustrate this approach with several examples.

A Cartesian shrink wrapping technique has been developed to construct triangular surface meshes for three-dimensional dirty faceted geometries. An initial Cartesian grid is overlaid onto the dirty geometries and its cells are adaptively refined until a first resolution is achieved while recording intersections with geometric facets in cells. During further local refinement of the grid, holes or "leaks" are identified and they can either be closed or left open.
An initial watertight shell called the wrapper surface is constructed by selectively extracting the cell side faces on the boundary between the intersected cells and a continuous group of non-intersecting cells, which topologically represents the domain of interest. The wrapper surface is improved by a subsequence of operations such as projecting nodes onto geometry, adjusting nodes on the geometry to capture features and editing triangular faces to achieve better quality for commercial CFD calculation.
The objective of the proposed technique is to provide high quality triangular surface meshes for upstream solutions in large scale design processes with minimal user interactions. The described procedure is being used commercially at several Automotive and Aerospace sites and results from some applications are presented.

Various parallel approaches to providing a capability for producing larger meshes will be presented. These approaches varies in complexity from standard h--refinements to geometric partitioning using an octree data structure. The advantages and disadvantages of each approach will be highlighted and the ability of each approach to produce very well balance sub--domains will be discussed. In addition, a method based on combining mesh deformation methods with a local remeshing approach for the solution of the unsteady Navier--Stokes equations in the presence of moving boundaries will be described and the extension of this approach to handle hybrid highly stretched boundary layer elements will be presented. The parallel implementation of such approach will also be presented and demonstrated for a flow of practical interest.

Open CASCADE Technology is software development platform freely available in open source. It includes components for 3D surface and solid modeling, visualization, data exchange and application development. Some considerations are given about relation with 2D mesh algorithms and with the modeling data that supplies data structures to represent 2D and 3D geometric and topological models.

Often, at the interfaces between different meshes information has to be transferred. In case of, e.g. contact problems, this corresponds to the non-penetration constraints at the interface as well as the displacements and boundary stresses.We present a mortar-based approach, which allows for the efficient, flexible, and stable coupling between the surfaces of non-matching meshes at curvilinear boundaries and discuss it's implementation. Particular emphasis is put on the computation of the interface mapping. Since our transfer operator has been implemented in the framework of a non-smooth multigrid methods, we discuss the quantitative properties of our coupling strategy along examples from contact mechanics and biomechanics.
We also show that our approach can easily be extended for the information transfer between unstructered meshes in 3D.

The numerical simulation of physical phenomena takes an increasing part in the design of an industrial product. Most of CAD (computer aided design) systems use modelization where the surface boundary of the object is represented by a juxtaposition of patches of arbitrary shapes. Each patch is itself defined by a mapping from a planar parametric domain to the tridimensional space. A simulation by the finite element method (FEM) requires the discretization of the surface, and the volume if necessary, of the considered object. The quality of the generated mesh is crucial for the convergence of the simulation and the validity of the solution. This talk presents a methodology in which, starting from a CAD surface model (for instance in IGES format), the topology of the surface is automatically deduced from geometrical considerations and quality meshes are generated.

Tet-meshing is by now rather mature, but incremental improvements are still ongoing. The talk will cover recent developments, including:

• Generation of optimal space-filling tets;
• Parallel unstructured grid generation;
• RANS meshing for complex geometries; and
• Post-generation mesh improvement.

An iterative domain partitioning scheme is presented for parallelizing mesh generation schemes that use an iterative point placement approach. The iterative partitioning approach starts with a decomposition of the initial unresolved tetrahedral grid. As the mesh is resolved the partitions are dynamically modified. Within a given iteration of iterative point placement, the interfaces between the dynamic partitions are temporarily frozen to minimize communication between processors. The partitions are then regrouped, separated into completed and unfinished groups, and then the unfinished portion is repartitioned to generate more points within the previously frozen areas. This process is repeated until the mesh for the entire domain is generated. The resulting mesh has minimal residual artifacts if any from the partitioning process.

The effectiveness of anisotropic grids is surely acknowledged in the numerical modeling of many real-life applications, essentially due to the computational saving involved. The expertise gained in this area over the last years has been primarily addressed to mesh adaption strategies driven by suitable error estimators, mainly of a posteriori type. The leading feature of our approach is the employment of a proper metric, stemming from the error estimator itself, to generate the adapted mesh. This procedure, on the one hand turns out to be conceptually bulky, on the other hand it allows ones to build optimal grids, either by maximizing the solution accuracy for a given number of elements or by minimizing the number of elements for an assigned accuracy. The model problems tackled so far comprise 2D elliptic problems (both pure diffusive and advective-dominated), as well as Stokes and Navier-Stokes equations, up to the heat equation. In this communication we review the salient steps of our anisotropic ``journey'', hopefully leading us soon out of our ``flatland''.

In recent years there has been increasing interest in the use of adaptive mesh numerical methods in computational fluid dynamics. The mesh optimisation approach is appealing and significant as it can naturally produce anisotropic meshes to optimally represent the directional information often present in high Reynolds number fluid flow. Some examples of the dynamical structures one may wish to represent with adaptive methods include boundary layers, turbulent eddies, vorticity filaments, etc. In this talk we will review our underlying three-dimensional Navier-Stokes finite element solver, parallel load-balanced mesh optimisation algorithm and extensions to couple this with mesh movement methods. We will then show some examples of their use in classical CFD problems, in engineering fluids applications, and in environmental/geophysical fluid dynamics. The latter applications provide the main impetus for this work and include the dispersal of pollutants in turbulent boundary layer flow over urban canopies, and a wide range of multi-scale oceanographic problems.

The development of Gmsh has been under way for a decade now. Recently, Gmsh has encountered a major evolution. In this talk, we will present Gmsh 2.0 and detail some of its innovative features :

• Adaptive mesh generation algorithms applied to hybrid 3D models (STEP-IGES-Gmsh Native...),
• Mesh generation applied to ocean modelling,
• Efficient visualization of high order finite element solutions

We will also share our experience in the development of an open source mesh generator and detail the perspectives for the future of Gmsh.

We develop two new methods for creating high-quality tetrahedral meshes: one with guaranteed good dihedral angles, and one that in practice produces far better dihedral angles than any prior method. The isosurface stuffing algorithm fills an isosurface with a uniformly sized tetrahedral mesh whose dihedral angles are bounded between 10.7 degrees and 165 degrees. The algorithm is whip fast, numerically robust, and easy to implement because, like Marching Cubes, it generates tetrahedra from a small set of precomputed stencils. Our angle bounds are guaranteed by a computer-assisted proof. Our second contribution is a mesh improvement method that uses optimization-based smoothing, topological transformations, and vertex insertions and deletions to achieve extremely high quality tetrahedra.

3D Boundary recovery is a fundamental problem in mesh generation. Theoretical questions of this problem like complexity, optimality, and output size are either NP-complete or still open. We discuss a practical and robust approach for solving this problem. Our approach is based on the construction of a constrained Delaunay tetrahedralization (CDT) for a set of constraints (segments and facets). Additional points (Steiner points) on the constraints are allowed in order to guarantee the existence of a CDT. While these points can be removed later. We give analysis on the complexity and the output size of our approach.