Quadrilateral Mesh Generation with Deferred Constraint Insertion

A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.

An ANN-based element extraction method for automatic mesh generation

Generation of quadrilateral meshes on free-form surfaces

Quadrilateral meshes offer certain advantages compared to triangular ones, such as reduced number of elements and alignment with problem-specific directions. We present a pipeline for the generation of quadrilateral meshes on complex geometries. It is based on two key components: robust surface meshing and efficient indirect conversion of a triangular mesh to an all-quad one. The input is a valid geometric surface mesh, i.e., a triangulation that accurately represents the geometry of the model. A right-angled triangular surface mesh is initially created by continuously modifying the input mesh while always preserving its topological validity. The main advantages of our local mesh modification-based approach are to (i) allow the generation of meshes that are globally aligned with a given direction field and (ii) to reliably handle non-manifold feature edges (in multi-volume models) and small features. The final quadrilateral mesh is obtained by merging pairs of triangles into quadrilaterals. We develop a novel bipartite labeling scheme in order to identify and correct inconsistent pairings. The procedure is based on local operations and is much more efficient than previous global strategies for tri-to-quad conversion. The whole pipeline is tested on a large number of models with diverse characteristics.

In this paper we present a fast and reliable method for generation of molecular surfaces. While the method is readily applicable to van der Waals surface generation, we shall be focusing on solvent-accessible surfaces (SAS) and solvent-excluded surfaces (SES) of a molecule. A list-based method is utilized to represent and generate the union of multiple spheres with arbitrary radii, with which we are able to produce the SAS and SES of a molecule in a very efficient way. The surface generated is represented by a quadrilateral mesh, which can be easily converted into a triangular mesh if needed. Some results will be provided to demonstrate the speed and quality of our mesh generation algorithms.

A new scheme for the generation of a graded quadrilateral mesh

Purpose Automatic mesh generation is still a challenge problem for combustion fluid dynamics simulations because of the high-quality requirement and complexity of geometries. This paper aims to find an efficient automatic analysis model creation and mesh generation method to save the time for pre-processing in numerical simulations. Design/methodology/approach Based on the previous work, we explore effective model processing and mesh generation methods from practical engineering applications. Considering the automation and high quality requirement, we construct an automatic mesh generation procedure for combustion fluid dynamics problems. Findings The numerical results show that the procedure we proposed in this paper can automatically generate high quality mesh for combustion fluid dynamics simulations. The strategy of fluid model construction is time-saving and with high-precision. The mesh generation method in our procedure is automatic and efficient. Practical implications The procedure proposed in this paper is applicable to the practical engineering application model, such as aircraft simulation, aeroengine simulation and so on. The procedure has been integrated into an numerical simulation software. Originality/value The method proposed in this paper has very practical application value. It can be used in the practical application and saves a lot of manual processing time for numerical stimulation specialists.

A new approach to mesh generation for general 3D domain is proposed. A prototype mesh generator which utilizes octree for easy manipulation of 3D structures, is developed. It shows that well-fitted tetrahedral mesh can be constructed assuming that an appropriate triangular mesh upon the boundary is given. There is a good chance that adaptive meshing and moving boundary will be managed well in this mesh generation method.

A fuzzy logic knowledge-based approach, FUZZYMESH, for finite element mesh generation and analysis is presented. The proposed approach initiates the adaptive process with a high quality initial mesh that is more refined around the critical points/regions in the problem domain. In order to create high quality initial meshes, the heuristic knowledge, past experience, common sense, and ad hoc methods of finite element specialists are incorporated into the knowledge base of the fuzzy system. Using the linguistic variable concept and approximate reasoning techniques, the fuzzy system makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes the determination of priority of critical points/regions and the prediction of mesh sizes for them. According to the mesh size information, a near-optimal initial mesh is created with an automatic mesh generator that is based on the advancing front mesh generation technique. The performance of the proposed approach was measured and evaluated in terms of efficiency and accuracy. The evaluation included comparison between the results of a code based on the proposed fuzzy logic knowledge-based approach, FUZZYMESH, and the conventional approach, which starts the finite element analysis with different meshes, by solving various problems. The global as well as local errors of different solutions were examined and compared. The CPU times for different approaches to achieve a particular accuracy were also measured and compared. The results showed that due to better quality of initial meshes, FUZZYMESH results in lower levels and more accurate error estimates. In turn, the proposed approach is able to solve the problem with a more accurate solution at less cost.

2D automatic body-fitted structured mesh generation using advancing extraction method

The regular topological structure endows quadrilateral meshes with advantages such as high computational accuracy, reduced element requirements, and enhanced computational efficiency, granting them irreplaceable application value in high‐end engineering simulation domains. However, significant bottlenecks persist in the fully automatic generation technology of quadrilateral meshes for complex geometric models. Existing methods often encounter key issues such as high mesh distortion rates and insufficient algorithm stability when handling high‐curvature boundaries and multiscale feature regions, limiting their widespread application in engineering simulations. This article proposes a quad‐dominant mesh generation method based on gradient fields. Firstly, the three‐dimensional triangular mesh is transformed into a two‐dimensional parametric domain through conformal mapping. Subsequently, based on the compression ratio measured from three‐dimensional to two‐dimensional, the direction and size of the advancing front are calculated to draw contour lines in the parametric domain. A threshold is set to automatically generate high‐quality grids. Based on the extracted contour lines, high‐quality quadrilateral grids are generated pairwise along the gradient field directions. For regions that do not meet the threshold requirements, triangular mesh filling is employed to generate a two‐dimensional quad‐dominant grid. Due to the bijective nature of the mapping, the quad‐dominant surface mesh is obtained through the inverse transformation from the 2D parametric domain back to the 3D space.

Parallel and distributed adaptive quadrilateral mesh generation

The Modified Direct Method: An Iterative Approach for Smoothing Planar Meshes

Automatic generation of quadrilateral finite element meshes

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (MUSCL approach) followed by an upwind step (Roe's flux-difference splitting). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the Nessyahu-Tadmor (N-T) scheme and the CE/SE method with epilson = 1/2. The upwind scheme is extended to the case of two spatial dimensions (2D) in a straightforward manner. The N-T and CE/SE schemes are extended in a manner similar to the 2D extensions of the CE/SE scheme by Wang and Chang for a triangular mesh and by Zhang, Yu, and Chang for a quadrilateral mesh. The slope estimates, however, are simplified. Fourier stability and accuracy analyses are carried out for these schemes for the standard 1D and the 2D quadrilateral mesh cases. In the nonstandard case of a triangular mesh, the triangles must be paired up when analyzing the upwind and N-T schemes. An observation resulting in an extended N-T scheme which is faster and uses only one-third of the storage for flow data compared with the CE/SE method is presented. Numerical results are shown. Other improvements to the schemes are discussed.