An efficient 3D mesh generator based on geometry decomposition

13th Computational Fluid Dynamics Conference, 1997

The present paper describes an unstructured hexahedral mesh generator for viscous flow simulations around complex 3D configurations. The first step of this method is the geometric adaptation of an initial non-body-fitted mesh by grid embedding. The resulting octree mesh is then fitted to the actual boundaries of the domain and its main features, such as sharp edges and corners, are captured. Degenerated cells resulting from body-fitting are removed using a splitting strategy and by insertion of buffer layers. Finally, in vicinity of solid walls, layers of highly stretched cells are marched directly from the quadrilateral surface mesh that is a by-product of the body-fitting process. Interfacing between the layer and octree meshes only requires the deformation of the octree to insert the layers. The resulting method is highly automated and significantly reduces turn-around times. To illustrate its capabilities, both internal and external applications are presented.

1996

We present a new algorithm for the generation of hexahedral element meshes. The algorithm starts with an octree discretization of the interior of the input object which is converted to a conforming hexahedral element mesh. Then the isomorphism technique 9] is used to adapt the mesh to the object boundary. keywords. hexahedra, mesh generation, octree 1 Introduction The last decades have seen immense progress in the development of numerical algorithms for the simulation of technical and physical processes. Finite element, nite di erence and nite volume methods are now routinely used in engineering. Therefore interest has grown in reducing simulation turnaround time, and the development of powerful, easy-to-use mesh generation programs has become an important issue. Much work has been done on algorithms for the generation of triangular, quadrilateral and tetrahedral element meshes. The state of the art is reviewed in 1], online information can be found in 2] and 3]. Mesh generators of this type have been integrated in many commercial programs. Unfortunately, the situation is worse in the eld of hex meshing. Most existing programs use mapped-meshing and multiblock techniques which require much user interaction and are therefore very time-consuming. Algorithms for the automatic generation of hexahedral element meshes have come up only recently, in essence the following techniques are used:

Advanced Modeling and Simulation in Engineering Sciences, 2014

Background: Indirect quad mesh generation methods rely on an initial triangular mesh. So called triangle-merge techniques are then used to recombine the triangles of the initial mesh into quadrilaterals. This way, high-quality full-quad meshes suitable for finite element calculations can be generated for arbitrary two-dimensional geometries. Methods: In this paper, a similar indirect approach is applied to the three-dimensional case, i.e., a method to recombine tetrahedra into hexahedra. Contrary to the 2D case, a 100% recombination rate is seldom attained in 3D. Instead, part of the remaining tetrahedra are combined into prisms and pyramids, eventually yielding a mixed mesh. We show that the percentage of recombined hexahedra strongly depends on the location of the vertices in the initial 3D mesh. If the vertices are placed at random, less than 50% of the tetrahedra will be combined into hexahedra. In order to reach larger ratios, the vertices of the initial mesh need to be anticipatively organized into a lattice-like structure. This can be achieved with a frontal algorithm, which is applicable to both the two-and three-dimensional cases. The quality of the vertex alignment inside the volumes relies on the quality of the alignment on the surfaces. Once the vertex placement process is completed, the region is tetrahedralized with a Delaunay kernel. A maximum number of tetrahedra are then merged into hexahedra using the algorithm of Yamakawa-Shimada. Results: Non-uniform mixed meshes obtained following our approach show a volumic percentage of hexahedra that usually exceeds 80%. Conclusions: The execution times are reasonable. However, non-conformal quadrilateral faces adjacent to triangular faces are present in the final meshes.

Computational Geosciences

With huge data acquisition progresses realized in the past decades and acquisition systems now able to produce high resolution grids and point clouds, the digitization of physical terrains becomes increasingly more precise. Such extreme quantities of generated and modeled data greatly impact computational performances on many levels of high-performance computing (HPC): storage media, memory requirements, transfer capability, and finally simulation interactivity, necessary to exploit this instance of big data. Efficient representations and storage are thus becoming "enabling technologies" in HPC experimental and simulation science. We propose HexaShrink, an original decomposition scheme for structured hexahedral volume meshes. The latter are used for instance in biomedical engineering, materials science, or geosciences. HexaShrink provides a comprehensive framework allowing efficient mesh visualization and storage. Its exactly reversible multiresolution decomposition yields a hierarchy of meshes of increasing levels of details, in terms of either geometry, continuous or categorical properties of cells. Starting with an overview of volume meshes compression techniques, our contribution blends coherently different multiresolution wavelet schemes in different dimensions. It results in a global framework preserving discontinuities (faults) across scales, implemented as a fully reversible upscaling at different resolutions. Experimental results are provided on meshes of varying size and complexity. They emphasize the consistency of the proposed representation, in terms of visualization, attribute downsampling and distribution at different resolutions. Finally, HexaShrink yields gains in storage space when combined to lossless compression techniques. Keywords Compression • Corner point grid • Discrete wavelet transform • Geometrical discontinuities • Hexahedral volume meshes • High-performance computing • Multiscale methods • Simulation • Upscaling This work was partly presented in [1].

2001

A new methodology to generate a hex-dominant mesh is presented. From a closed surface and an initial all-hex mesh that contains the closed surface, the proposed algorithm generates, by intersection, a new mostly-hex mesh that includes polyhedra located at the boundary of the geometrical domain. The polyhedra may be used as cells if the field simulation solver supports them or be decomposed into hexahedra and pyramids using a generalized mid-point-subdivision technique. This methodology is currently used to provide hex-dominant automatic mesh generation in the preprocessor pro*am of the CFD code STAR-CD.

Engineering with Computers, 1996

HEXAR, a new software product developed at Cray Research, Inc., automatically generates good quality meshes directly from surface data produced by computeraided design (CAD) packages. The HEXAR automatic mesh generator is based on a proprietary and parallel algorithm that relies on pattern recognition, local mesh refinement and coarsening, and variational mesh smoothing techniques to create all-hexahedral volume meshes. HEXAR generates grids two to three orders of magnitude faster than current manual approaches. Although approximate by design, the resulting meshes have qualities acceptable by many commercial structural and CFD (computational fluid dynamics) software. HEXAR turns mesh generation into an automatic process .for most commercial engineerin 9 applications.

Communications in Numerical Methods in Engineering, 1994

The paper demonstrates an approach to generate three-dimensional boundary-fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh-adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so-called 'Macro Command Language', a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced-e.g. a computational mesh for a two-valve cylinder head can be generated within a few hours.

2011

Recently, randomly close-packed Voronoi meshes have been proposed for simulating pervasive fracture processes in materials and structures by allowing fractures to grow only at the interelement faces of the polyhedral cells. The polyhedral cells are formulated as finite elements. A new meshing tool is presented here for creating randomly close-packed Voronoi meshes in nonconvex domains with internal surfaces. Applications using these meshes include blast and impact response of engineered structures as well as hydraulic fracturing in geostructures and the design of CO 2 sequestration processes to maintain the integrity of a reservoir caprock that contains preexisting fractures and joints.

This work presents a threedimensional unstructured mesh generator for the analysis of hydroelectric power plants reservoirs using finite element methods. In order to obtain an accurate simulation of the physical flow of interest, the discrete mesh needs to consider adequately the geophysical data employed for the definition of the domain, which usually comes from sources with different precision, type and structure. The proposed algorithm is practical, stable and able to deal with different types of geophysical input data producing well conditioned three-dimensional meshes.

Mathematics and Computers in Simulation, 2007

Mesh generation is a critical step in high fidelity computational simulations. High-quality and high-density meshes are required to accurately capture the complex physical phenomena. A robust approach for a parallel framework has been developed to generate large-scale meshes in a short period of time. A coarse tetrahedral mesh is generated first to provide the basis of block interfaces and then is partitioned into a number of sub-domains using METIS partitioning algorithms. A volume mesh is generated on each sub-domain in parallel using an advancing front method. Dynamic load balancing is achieved by evenly distributing work among the processors. All the sub-domains are combined to create a single volume mesh. The combined volume mesh can be smoothed to remove the artifacts in the interfaces between sub-domains. A void region is defined inside each sub-domain to reduce the data points during the smoothing operation. The scalability of the parallel mesh generation is evaluated to quantify the improvement on shared-and distributed-memory computer systems.

Concurrency and Computation: Practice and Experience, 2012

We show a parallel implementation and performance analysis of a linear octree-based mesh generation scheme designed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models. We present algorithms for the construction, 2:1 balancing and meshing large linear octrees on supercomputers. Our scheme uses efficient computer graphics algorithms for surface detection, allowing us to represent complex geometries. An isogranular analysis demonstrates good scalability. Our implementation is able to execute the 2:1 balancing operations over 3.4 billion octants in less than 10 s per 1.6 million octants per CPU core. .

. A new all-hexahedral meshing algorithm, referred to as "Geode", is described. This algorithm is the combination of hex/tet plastering, dicing, and a new 26-hex transition element template.The algorithm is described in detail, and examples are given of problems meshed with this algorithm. keywords. Geode; hexahedral mesh generation; transition template. 1. Introduction Finite element analysis is used to model physical phenomena in a wide variety of disciplines, including structural mechanics and dynamics, heat transfer, and computational fluid dynamics (CFD). To perform these analyses, the problem domain must first be discretized into one-, two- or three-dimensional elements. While the finite element method allows many types of elements, tetrahedra and hexahedra are typically used; furthermore, hexahedra are considered more accurate for a given cost for some types of analyses, particularly in the non-linear regime. However, generating all-hexahedral meshes for typical pro...

Proceedings of the 16th International Meshing Roundtable, 2008

This paper describes a distributed-memory, embarrassingly parallel hexahedral mesh generator, pCAMAL (parallel CUBIT Adaptive Mesh Algorithm Library). pCAMAL utilizes the sweeping method following a serial step of geometry decomposition conducted in the CUBIT geometry preparation and mesh generation tool. The utility of pCAMAL in generating large meshes is illustrated, and linear speed-up under load-balanced conditions is demonstrated.

Computers & Structures, 1988

Some recent efforts on the development of methods to ensun the robustness of automatic thracdimensional mesh generation techniques arc discuss& The topic arcas considered arc mesh entity classification, finite octrcc cell triangulation, and coarse mesh generation by element removal.