Automatic three-dimensional mesh generation by the modified-octree technique

An approach for the fully automatic generation of three-dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.     

Automatic mesh generation over intersecting surfaces

A fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets. By carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections, pieces of surfaces can be arbitrarily combined and merged. A great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections. The new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces. In fact, it is a powerful surface mesh manipulator, and through the repeated use of the process, complex structures can be rapidly and accurately constructed.     

Automatic mesh generation with tetrahedron elements

To reduce the manual work involved in the application of the FEM in practice, preprocessors can be applied for the construction of network structures, which are complicated in generation strategy and do not form any optimum discrete structure. The time necessary for generation can be minimized even more by the application of only one element type within the whole network structure. A technique for the automatic generation of 3D-network structures with tetrahedron elements is presented in this paper. In this proposed technique, the nodal points of the network structure must be defined manually before the generation procedure, since a random positioning of points is usually undesirable for FEM calculation. The nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices. After the generation, the element sides forming any part of the boundary surface of the network structure can be automatically identified. If necessary, the network structure can be automatically refined.     

Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high‐quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high‐quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user‐specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk‐through algorithm, an efficient sizing‐value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing‐function approach enables accurate and fully automatic surface mesh generation. Copyright © 2016 John Wiley & Sons, Ltd.     

Automatic two- and three-dimensional mesh generation based on fuzzy knowledge processing

This paper describes the development of a novel automatic FEM mesh generation algorithm based on the fuzzy knowledge processing technique.A number of local nodal patterns are stored in a nodal pattern database of the mesh generation system. These nodal patterns are determined a priori based on certain theories or past experience of experts of FEM analyses. For example, such human experts can determine certain nodal patterns suitable for stress concentration analyses of cracks, corners, holes and so on. Each nodal pattern possesses a membership function and a procedure of node placement according to this function. In the cases of the nodal patterns for stress concentration regions, the membership function which is utilized in the fuzzy knowledge processing has two meanings, i.e. the closeness of nodal location to each stress concentration field as well as nodal density. This is attributed to the fact that a denser nodal pattern is required near a stress concentration field. What a user has to do in a practical mesh generation process are to choose several local nodal patterns properly and to designate the maximum nodal density of each pattern. After those simple operations by the user, the system places the chosen nodal patterns automatically in an analysis domain and on its boundary, and connects them smoothly by the fuzzy knowledge processing technique. Then triangular or tetrahedral elements are generated by means of the advancing front method. The key issue of the present algorithm is an easy control of complex two- or three-dimensional nodal density distribution by means of the fuzzy knowledge processing technique.To demonstrate fundamental performances of the present algorithm, a prototype system was constructed with one of object-oriented languages, Smalltalk-80 on a 32-bit microcomputer, Macintosh II. The mesh generation of several two- and three-dimensional domains with cracks, holes and junctions was presented as examples.     

Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples

In this paper, a new metric advancing front surface mesh generation scheme is suggested. This new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept. The target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model. While the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously, a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model. As a result, the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry. Numerical experience indicates that, by using the proposed mesh generation scheme, high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low‐end PC. Finally, by using the pseudo‐curvature element‐size controlling metric to impose the curvature element‐size requirement in an implicit manner, the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately. Copyright © 2003 John Wiley & Sons, Ltd.     

Automatic quadrilateral/triangular free-form mesh generation for planar regions

Automation of finite element mesh generation holds great benefits for mechanical product development and analysis. In addition to freeing engineers from mundane tasks, automation of mesh generation reduces product cycle design and eliminates human-related errors. Most of the existing mesh generation methods are either semi-automatic or require specific topological information. A fully automatic free-form mesh generation method is described in this paper to alleviate some of these problems. The method is capable of meshing singly or multiply connected convex/concave planar regions. These regions can be viewed as crosssectional areas of 2 1/2 D objects analysed as plane stress, plane strain or axisymmetric stress problems. In addition to being fully automatic, the method produces quadrilateral or triangular elements with aspect rations near one. Moreover, it does not require any topological constraints on the regions to be meshed; i.e. it provides free-form mesh generation. The input to the method includes the region's boundary curves, the element size and the mesh grading information. The method begins by decomposing the planar region to be meshed into convex subregions. Each subregion is meshed by first generating nodes on its boundaries using the input element size. The boundary nodes are then offset to mesh the subregion. The resulting meshes are merged together to form the final mesh. The paper describes the method in detail, algorithms developed to implement it and sample numerical examples. Results on parametric studies of the method performance are also discussed.     

Automatic three-dimensional finite element mesh generation via modified ray casting

Three-dimensional (3-D) finite element mesh generation has been the target of automation due to the complexities associated with generating and visualizing the mesh. A fully automatic 3-D mesh generation method is developed. The method is capable of meshing CSG solid models. It is based on modifying the classical ray-casting technique to meet the requirements of mesh generation. The modifications include the utilization of the element size in the casting process, the utilization of 3-D space box enclosures, and the casting of ray segments (rays with finite length). The method begins by casting ray segments into the solid. Based on the intersections between the segments and the solid boundary, the solid is discretized into cells arranged in a structure. The cell structure stores neighbourhood relations between its cells. Each cell is meshed with valid finite elements. Mesh continuity between cells is achieved via the neighbourhood relations. The last step is to process the boundary elements to represent closely the boundary. The method has been tested and applied to a number of solid models. Sample examples are presented.     

Automatic and efficient hybrid viscous mesh generation based on clipped Voronoi diagrams

The commonly used advancing layers method to generate hybrid meshes suffers from many drawbacks. The generation of isotropic meshes for far-field domains with irregular and complex boundary subdivisions after boundary layers advancing is time consuming and, in some cases, is not robust in 3D. To address these difficulties, this paper presents a novel method to generate hybrid polygonal meshes in 2D and polyhedral meshes in 3D for viscous flow simulations. In the proposed method, first, we generate a full Voronoi diagram for the appropriate distribution of generators that avoids the extra mesh generation required for the remaining holes in the advancing layers method. To recover the inner solid boundaries, we implement a robust boundary cell cutting process. Because the generators are located layer by layer near the boundaries, there is no requirement to consider all of the Voronoi cells. Only the first layer Voronoi cells must be cut, making the calculation very efficient. We have generated hybrid meshes using the present method for many viscous flow cases. The results show close agreement between the computations and the experimental results, thus indicating the reliability and effectiveness of the hybrid mesh generated by our method.     

Automatic mesh generation from solid models based on recursive spatial decompositions

This paper introduces a two-stage algorithm for the automatic conversion of solid models into finite element meshes. In Stage 1 the solid is approximated by a collection of variably sized cells generated by recursive spatial decomposition and stored in a logical tree. In Stage 2 the approximating cell structure, which includes cells that are wholly inside the solid (IN) as well as cells that are neither inside nor outside (NIO), is transformed into a finite element model. IN cells are directly mapped into finite elements while NIO cells are decomposed according to their topologically complexity through either template mapping or recursive element extraction. Although specifically designed for adaptive remeshing, the algorithm is of general use and can be implemented in any Solid Modelling System that supports Boolean operations on solids and maintains a complete boundary representation. Core algorithms for Stages i and 2 are rigorously developed to insure their applicability within a genuinely automatic procedure. Specific issues related to boundary evaluation and decomposition procedures are identified and discussed. The implementation of the algorithm into an experimental system based on the PADL-2 solid modeller is described. The paper concludes with a comparative study of existing meshing algorithms based on recursive spatial decompositions.     

Fully automatic two dimensional mesh generation using normal offsetting

A technique, based on a normal offsetting procedure, for the fully automatic generation of two dimensional meshes suitable for finite element analysis is presented. The method positions nodes by first meshing the geometric entities that compose the object boundary, then offsetting those nodal locations along vectors normal to the boundary geometry. The offset row of nodes is processed to ensure a good nodal spacing appropriate for generating well shaped elements. Following processing, the new row is offset again and the cycle is repeated until the entire area is filled with nodes. The boundary based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases. Nodal locations are calculated based on local parameters avoiding the higher order time complexities associated with global calculations. A technique for controlling mesh density by overlaying an independent mesh density function on the geometry is also presented as part of the method. This approach allows mesh density to be automatically controlled by a variety of factors, such as previous analysis results, that are external to the actual mesh generation process. The independent nature of the function method allows different sources of density information to be used interchangeably without modification to the mesh generation procedure.     

Automatic mesh generation for computing symmetric local stresses by 2d-viscoplastic BEM with modified transfinite method

This paper presents a scheme of automatic mesh generation for computing the local stresses by 2D-viscoplastic boundary element method (BEM) with modified transfinite mapping method. The advanced techniques for mesh spacing and region of transfinite mapping method in BEM are studied. The applications demonstrate that the method in BEM gives high computational efficiency and precise modelling of boundaries. This reduces the time and effort required of the analyst to set up a nonlinear model, the amount of input data required is reduced greatly. The numerical examples are given in a later section.     

Simultaneous surface and tetrahedron mesh adaptation using mesh‐free techniques

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

Towards automatic structured multiblock mesh generation using improved transfinite interpolation

The quality of any numerical flowfield solution is inextricably linked to the quality of the mesh used. It is normally accepted that structured meshes are of higher quality than unstructured meshes, but are much more difficult to generate and, furthermore, for complex topologies a multiblock approach is required. This is the most resource‐intensive approach to mesh generation, since block structures, mesh point distributions, etc., need to be defined before the generation process, and so is seldom used in an industrial design loop, particularly where a novice user may be involved. This paper considers and presents two significant advances in multiblock mesh generation: the development of a fast, robust, and improved quality interpolation‐based generation scheme and a fully automatic multiblock optimization and generation method. A volume generation technique is presented based on a form of transfinite interpolation, but modified to include improved orthogonality and spacing control and, more significantly, an aspect ratio‐based smoothing algorithm that removes grid crossover and results in smooth meshes even for discontinuous boundary distributions. A fully automatic multiblock generation scheme is also presented, which only requires surface patch(es) and a target number of mesh cells. Hence, all user input is removed from the process, and a novice user is able to obtain a high‐quality mesh in a few minutes. It also means the code can be run in batch mode, or called as an external function, and so is ideal for incorporation into a design or optimization loop. To demonstrate the power and efficiency of the code, multiblock meshes of up to 256 million cells are presented for wings and rotors in hover and forward flight. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive tetrahedral mesh generation by constrained Delaunay refinement

This paper presents a tetrahedral mesh generation method for numerically solving partial differential equations using finite element or finite volume methods in three‐dimensional space. The main issues are the mesh quality and mesh size, which directly affect the accuracy of the numerical solution and the computational cost. Two basic problems need to be resolved, namely boundary conformity and field points distribution. The proposed method utilizes a special three‐dimensional triangulation, so‐called constrained Delaunay tetrahedralization to conform the domain boundary and create field points simultaneously. Good quality tetrahedra and graded mesh size can be theoretically guaranteed for a large class of mesh domains. In addition, an isotropic size field associated with the numerical solution can be supplied; the field points will then be distributed according to it. Good mesh size conformity can be achieved for smooth sizing informations. The proposed method has been implemented. Various examples are provided to illustrate its theoretical aspects as well as practical performance. Copyright © 2008 John Wiley & Sons, Ltd.     

Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

This paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluid–structure interaction with complex geometry. First, a new stabilized three‐field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the Navier–Stokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluid–solid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time‐dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight. Copyright © 2013 John Wiley & Sons, Ltd.     

A mesh adaptation procedure for periodic domains

In this paper, an original technique is developed in order to build adaptive meshes on periodic domains. The new approach has the important property that it is code‐reused. The procedure is used against three different algorithms, namely, MAdLib ( Int. J. Numer. Meth. Engng 2000; in press), mmg (Proc. 17th Int. Meshing Roundtable, 2008) and the couple Yams (Rapport Technique RT‐0252, 2001) /Ghs3d (Proc. 8th Int. Meshing Roundtable, 1999). None of the latter algorithms needs to be adapted before it is applied to periodic domains. Some examples of adaptation are presented based on analytical, isotropic and anisotropic mesh‐size fields. Periodicity in translation and rotation both are considered. Finally, the mesh adaptation strategy is used in order to reduce the computational cost of a prediction of strain heterogeneity throughout a periodic polycrystalline aggregate deforming by dislocation slip. Copyright © 2011 John Wiley & Sons, Ltd.