Automatic Mesh Generation Research Articles

Automatic triangulated mesh generation of pulmonary airways from segmented lung 3DCTs for computational fluid dynamics.

Computational fluid dynamics (CFD) of lung airflow during normal and pathophysiological breathing provides insight into regional pulmonary ventilation. By integrating CFD methods with 4D lung imaging workflows, regions of normal pulmonary function can be spared during treatment planning. To facilitate the use of CFD simulations in a clinical setup, a robust, automated, and CFD-compliant airway mesh generation technique is necessary. We define a CFD-compliant airway mesh to be devoid of blockages of airflow and leaks in the airway path, both of which are caused by airway meshing errors that occur when using conventional meshing techniques. We present an algorithm to create a CFD-compliant airway mesh in an automated manner. Beginning with a medial skeleton of the airway segmentation, the branches were tracked, and 3D points at which bifurcations occur were identified. Airway branches and bifurcation features were isolated to allow for automated and careful meshing that considered their anatomical nature. We present the meshing results from three state-of-the-art tools and compare them with the meshes generated by our algorithm. The results show that fully CFD-compliant meshes were automatically generated for an ideal geometry and patient-specific CT scans. Using an open-source smoothed-particle hydrodynamics CFD implementation, we compared the airflow using our approach and conventionally generated airway meshes. Our meshing algorithm was able to successfully generate a CFD-compliant mesh from pre-segmented lung CT scans, providing an automatic meshing approach that enables interventional CFD simulations to guide lung procedures such as radiotherapy or lung volume reduction surgery.

Hovering efficiency optimization of the ducted propeller with weight penalty taken into account

The ducted propeller is superior to the open propeller in hovering efficiency. However, the overall system efficiency of a ducted propeller is reduced due to its heavy structure. If the weight penalty is taken into account, will the ducted propeller still be superior to an open propeller? And in this scenario, how will a ducted propeller with better efficiency than an open propeller be designed? This paper investigates these questions by parametric analysis based on experiments and then parametric optimization that involves hovering efficiency and structural weight in objective functions. Both multi-disciplinary design optimization and multi-objective programming are performed by surrogate-based optimization. An in-house automatic structured mesh generation module is developed to deal with significant geometry variation in design space. Finally, the optimization results are validated by post-optimization experiments. The results of experiment and optimization indicate that the effects of weight penalty play a leading role at low disk loading and hence in this case, the one with lighter structure is superior. But at high disk loading, as thrust gets higher, the leading factor turns into aerodynamic hovering efficiency, therefore the one with higher aerodynamic hovering efficiency prevails. The multi-objective optimization produces an L-shaped Pareto front, and the optimum of multi-disciplinary optimization is quite close to the Pareto front knee point. The designs in this region encounter limited aerodynamic hovering efficiency loss but gain significant weight reduction. Therefore, we can obtain a ducted propeller superior to an open propeller in system efficiency with pretty low disk loading, although the weight penalty is considered. These designs feature a relatively large inner lip radius, a small outer lip radius, and a short or even no diffuser. This means that the inner lip radius contributes the most to the aerodynamic hovering efficiency, followed by the diffuser and outer lip. These designs have very low height to diameter ratio therefore they can be easily integrated into aircraft structure.

Novel Hybridization of Parameter and Topology Optimizations: Application to Permanent Magnet Motor

This article introduces novel hybridization of parameter optimization (PO) and topology optimization (TO) methods. The proposed method is applied to the optimization of a permanent magnet motor. The magnet shape and topology of the flux barrier of the rotor core are optimized by performing PO and TO simultaneously. In the optimization, automatic mesh generation is adopted to improve the resolution of the shape representation. It is shown that the increase in the average torque resulting from the proposed hybrid optimization is larger than that obtained by the conventional TO in which only the topology of the flux barrier is optimized. The decomposition of the total torque to the magnet and reluctance torques suggests that the reluctance torque is effectively generated in the rotor optimized by the proposed method.

Optimization Design and Experimental Study of S-shaped Inlet

Lip and diffuser are two important parts of S-shaped inlet, which are difficult to balance in the optimization design of S-shaped inlet. This paper presents an optimization method for S-shaped inlet. Firstly, the parametric models of the lip and the diffuser are established. Combining with automatic mesh generation technology, numerical simulation and genetic algorithm, an optimization platform of s-shaped inlet design based on Isight is established. Aiming at the design of inlet for an unmanned aerial vehicle (UAV), compared with the prototype, the total pressure recovery coefficient of the optimized inlet obtained by this optimization method is increased by 1.5%, and the steady-state circumferential distortion is reduced by 58.6%. The wind tunnel experiment is carried out to obtain the aerodynamic performance of the inlet, and the experimental results are in good agreement with the numerical simulation results.

Automatic sizing functions for unstructured mesh generation revisited

PurposeSizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.Design/methodology/approachA practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.FindingsThe local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.Originality/valueTheoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Gridding and Segmentation Method for DNA Microarray Images

This article mainly explores meshing and segmentation techniques for microarray image analysis. The term "grid" refers to dividing an image into subgrids of dots and then dividing them into point detection. Most of the existing methods depend on input parameters such as the number of rows / columns, the number of points in each row / column, the size of the subarrays, etc. This article proposes a fully automatic mesh generation algorithm. This can remove any initialized parameter without any manual intervention. In the segmentation step, clustering algorithms are used because they do not consider the size and shape of the spots, do not depend on the initial state of the pixels, and do not require post-processing. In this article, a new method is proposed to estimate the initial parameters (centroid and number of clusters) required by any clustering algorithm. Qualitative and quantitative analysis shows that the algorithm can perform grid processing on microarray images well, and improves the performance of the clustering algorithm.

An open-source ABAQUS implementation of the scaled boundary finite element method to study interfacial problems using polyhedral meshes

The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis pipeline in the standard finite element method (FEM). In this paper, we implement polyhedral elements based on the SBFEM into the commercial finite element software ABAQUS. To this end, user elements are provided through the user subroutine UEL. Detailed explanations regarding the data structures and implementational aspects of the procedures are given. The focus of the current implementation is on interfacial problems and therefore, element-based surfaces are created on polyhedral user elements to establish interactions. This is achieved by an overlay of standard finite elements with negligible stiffness, provided in the ABAQUS element library, with polyhedral user elements. By means of several numerical examples, the advantages of polyhedral elements regarding the treatment of non-matching interfaces and automatic mesh generation are clearly demonstrated. Thus, the performance of ABAQUS for problems involving interfaces is augmented based on the availability of polyhedral meshes. Due to the implementation of polyhedral user elements, ABAQUS can directly handle complex geometries given in the form of digital images or stereolithography (STL) files. In order to facilitate the use of the proposed approach, the code of the UEL is published open-source and can be downloaded from https://github.com/ShukaiYa/SBFEM-UEL.

A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes

Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and transient solvers are required. To this end, a parallel explicit solver exploiting the advantages of balanced octree meshes is introduced. To avoid the hanging nodes problem encountered in standard finite element analysis (FEA), the scaled boundary finite element method (SBFEM) is deployed as a spatial discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral elements are straightforwardly generated. Considering the scaling and transformation of octree cells, the stiffness and mass matrices of a limited number of unique cell patterns are pre-computed. A recently proposed mass lumping technique is extended to 3D yielding a well-conditioned diagonal mass matrix. This enables us to leverage the advantages of explicit time integrator, i.e., it is possible to efficiently compute the nodal displacements without the need for solving a system of linear equations. We implement the proposed scheme together with a central difference method (CDM) in a distributed computing environment. The performance of our parallel explicit solver is evaluated by means of several numerical benchmark examples, including complex geometries and various practical applications. A significant speedup is observed for these examples with up to one billion of degrees of freedom and running on up to 16,384 computing cores.

A Fully Meshless Approach to the Numerical Simulation of Heat Conduction Problems over Arbitrary 3D Geometries

One of the goals of new CAE (Computer Aided Engineering) software is to reduce both time and costs of the design process without compromising accuracy. This result can be achieved, for instance, by promoting a “plug and play” philosophy, based on the adoption of automatic mesh generation algorithms. This in turn brings about some drawbacks, among others an unavoidable loss of accuracy due to the lack of specificity of the produced discretization. Alternatively it is possible to rely on the so called “meshless” methods, which skip the mesh generation process altogether. The purpose of this paper is to present a fully meshless approach, based on Radial Basis Function generated Finite Differences (RBF-FD), for the numerical solution of generic elliptic PDEs, with particular reference to time-dependent and steady 3D heat conduction problems. The absence of connectivity information, which is a peculiar feature of this meshless approach, is leveraged in order to develop an efficient procedure that accepts as input any given geometry defined by a stereolithography surface (.stl file format). In order to assess its performance, the aforementioned strategy is tested over multiple geometries, selected for their complexity and engineering relevance, highlighting excellent results both in terms of accuracy and computational efficiency. In order to account for future extensibility and performance, both node generation and domain discretization routines are entirely developed using Julia, an emerging programming language that is rapidly establishing itself as the new standard for scientific computing.

Automatic Finite Element Mesh Generation on 3D Surfaces Based on STEP

Computer Aided Engineering (CAE) have a vital value in die and mould manufacturing. For the purpose of enhancing the modelling ability of the existing CAE analysis system and improving the mesh generation quality and working efficiency, a system for automatic finite element mesh generation on 3D surfaces is designed and implemented. Applying the neutral mechanism for product information sharing provided by STEP, product model import and reconstruction process is first implemented. And then product model information extraction module is developed aims at preparing geometrical and topological information for finite element mesh generation. An improved strategy for automatic triangular mesh generation over 3D surface is adopted to realize the mesh generation of the system. Implemented results indicate that the presented system helps to improve the mesh quality and at the same time increase the process efficiency and reduce the time cost.

Efficient Mesh Generation and Deformation for Aerodynamic Shape Optimization

Mesh generation and deformation are critical elements in gradient-based aerodynamic shape optimization (ASO). Improperly generated or deformed meshes may contain bad-quality cells that degrade the accuracy of computational fluid dynamics (CFD) solvers. Moreover, an inefficient mesh deformation method can become the bottleneck for the entire ASO process. To perform practical ASO, mesh generation and deformation methods need to be automated, scalable, robust, and computationally efficient. This paper tackles these challenges by developing an efficient approach for generating high-quality structured meshes in a semi-automatic manner. An automatic mesh generation approach is also proposed to handle intersections of multiple structured meshes with the overset mesh approach. In addition to mesh generation, a flexible mesh deformation method is developed, along with an efficient approach for computing mesh deformation derivatives using automatic differentiation. Finally, the performance of the proposed approaches is evaluated in terms of speed, scalability, and robustness. The mesh generation approach scales up to 100 million cells and 256 CPU cores. In addition, the robust mesh deformation approach enables a large range of valid mesh deformations, which gives more freedom to explore the design space in ASO. Moreover, the mesh deformation and the computation of its derivatives require only 0.1% of the CFD runtime. The mesh generation and deformation approaches have been implemented in the pyHyp and IDWarp software packages, which are publicly available under open-source licenses. The proposed approaches are useful tools to handle general ASO problems for aircraft, turbomachinery, and ground vehicles.

Direct boundary method toolbox for some elliptic problems in FreeHyTE framework

FreeHyTE Direct Boundary Method Toolbox is a new computational framework for the solution of interior and exterior boundary value problems in two dimensions using three classes of direct methods: the Boundary Element Method, the Method of Fundamental Solutions and the Trefftz-Herrera Method. The toolbox, currently including solvers for Laplace and Helmholtz boundary value problems, is straightforward to use, featuring a simple graphical user interface and automatic mesh generators, and amenable to extension, as it provides modular computational procedures, directly applicable to other types of boundary elements and differential equations. The toolbox supports the definition of simply or multiply-connected domains, boundary elements of any order, complex wavenumbers, and Dirichlet, Neumann and Robin boundary conditions. FreeHyTE Direct Boundary Method Toolbox is freely distributed under the GNU General Public License and supported by manuals to quickly get new users started.

Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.

3D hybrid mesh generation with an improved vertical stretch algorithm for geometric models with pinch-out features

Aiming at the infeasibility of using quadrilateral-prisms to describe sharp shapes, an improved vertical stretch algorithm was proposed to generate three-dimensional (3D) hybrid meshes based on the quadrilateral mesh converted from triangles to discretize the geometric models with pinch-out features. A robust and automatic mesh generator was developed, which served as a preprocessing tool for simulating metal forming, water flows and transports. An initial mixed mesh composed of cuspate hexahedra, quadrilateral- and triangular-prisms was constructed to capture the sharp features of pinch-out regions effectively. Five splitting templates were established to divide the 3D elements derived from pinch-out sub-domains into tetrahedra and triangular-prisms. The concept of splitting points was defined, based on which the appropriate implementation mode of each splitting template could be determined, so as to achieve the conformity and consistency of common faces and edges between different kinds of elements. Two topological optimization templates were established to improve the quality of degenerated triangular-prisms and tetrahedra. A new pinch-out boundary quadrilateral insertion method was proposed to avoid the generation of cuspate hexahedra, which simplified the conformity treatment strategies and improved the quality of the resulting mesh to a certain extent. Practical applications confirmed that the hybrid mesh generation methods proposed in this paper could discretize the geometric models with pinch-out features precisely. The requirements on mesh conformity and refinement were also able to be fully satisfied.

A Scaled Boundary Approach for Inelasticity of Fibre‐Reinforced Composites

AbstractAs versatile materials with elevated mechanical properties, short fibre reinforced composites (SFRCs) are currently used in many applications. To enhance the mechanical properties, e.g. the ductility, or to reduce crack propagation, short fibres are added to a matrix material, such as polymers or concrete. In the case of concrete, for example, the composite might contain additional aggregates as well. Although the addition of fibres improves the mechanical properties in general, it is well‐known that many matrix materials exhibit creep deformations under constant long‐term loads.The contribution at hand discusses a scaled boundary approach to model the inelastic behaviour of SFRCs. To allow for an efficient and automated mesh generation, the scaled boundary finite element method (SBFEM) is used in conjunction with the quadtree/octree decomposition algorithm. Within this framework, the fibres are modelled in a discrete manner, and the mesh of the matrix is generated independently of the fibres. Applying a novel embedding method, the meshes of the matrix and the fibres are combined, which results in a compatible mesh without requiring additional constraints. Furthermore, it is straightforward to combine the discussed techniques with image‐based mesh generation, e.g. based on computed tomography scans. The current contribution presents various 2D and 3D examples illustrating the efficiency and adaptability of the proposed framework.In addition, we present a methodology to incorporate non‐linear constitutive models into the SBFEM. Separate constitutive equations are formulated for the matrix, aggregates, and fibres. Whereas the mechanical behaviour of the aggregates and the fibres can be modelled within the framework of elasticity, one must make use of non‐linear approaches to account for the rate‐dependent inelastic deformation of the matrix under multiaxial stress and deformation states. Overall, this method allows for the simulation of creep in SFRCs, while considering the complex microstructure of these materials in detail. This provides the basis for a realistic estimation of the effect of long‐term loading on SFRC components.

A comparative study of numerical approaches for the computation of effective properties of micro‐heterogeneous materials

AbstractThe paper presents a comparative study of the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for the numerical evaluation of the volume‐averaged stress of composites. Two‐dimensional meso‐scale models of concrete represented by digital images and discretized using an automatic mesh generation algorithm are considered. The different computational approaches are discussed and compared with respect to accuracy and efficiency for both scenarios.

A new Simulation Model for Grate Firing Systems in OpenFOAM

A grate firing system can be seen as a multiphase flow problem. High volume fractions of solid fuel particles travel over the grate of a power plant, while heterogeneous reactions occure at the surface of the particles in combination with homogeneous combustion reactions inside the flue gas. Up to now, grate firing systems are still difficult to simulate with standard computational fluid dynamics (CFD). The movement of the solid particles inside the fuel bed and their heterogeneous reactions are difficult to combine with the homogeneous reactions of the gas phase species and the heat transfer. The emitted radiation from the gas has to be coupled with the heat balance inside the fuel bed.To solve this problem, we integrated a new library into a open source CFD code for coupling radiation models with the solids phase. We describe how to handle the workflow of the new library and present simulation results for two different furnace designs. An automatic mesh generator was developed. The work closes with simulation results for two different grate firing systems. Heterogeneous reactions and homogeneous reactions, as well as temperature fields inside the phase are presented. A validation of the simulations against measurement data is given.

자동격자생성 알고리듬을 이용한 주름관을 갖는 배관계의 효율적 진동 분석

In this study, an automatic mesh generation algorithm was developed for efficient finite shell element modeling of piping systems with bellows. For pre-processing of finite element analysis, a pipe geometry should be modeled using meshing software. However, the finite element meshing process requires time-consuming efforts for complicated piping systems such as bellows. Therefore, this study proposed an algorithm that can efficiently generate finite shell elements automatically. To generate the finite shell element model of the pipe, this algorithm only needs the information of the centerline of the pipe and the corresponding radius that is identical to the finite beam element. Additionally, effects of bellows on the dynamic characteristics of a curved pipe were discussed. The variation of the natural frequencies and dynamic stiffness of the piping system with respect to the change of the location, height and width of the bellows were investigated. The suggested automatic mesh algorithm is advantageous for the modeling of pipes having complex shapes such as bellows. Hence, it has the potential to be useful in designing optimal bellows in piping systems that require numerous finite element analysis calculations.

Automatic mesh generator for the non-linear homogenized analysis of double curvature masonry structures

An automatic full 3D mesh generator for the non-linear 3D homogenized discrete FE analysis of masonry double curvature structures is presented. The method can reproduce the main features exhibited by masonry, preserving the orthotropy and accounting for the influence of membrane loads on the flexural behavior. Previous homogenization procedures allow reducing the number of variables, leading to non-linear analyses with a low computational burden. In the approach proposed, masonry is modeled through an assemblage of elastic cells joined by non-linear interfaces with finite thickness. The latter are modeled as brick elements with softening replicated by a damage constitutive relationship (known in Abaqus - the commercial FE code used - as Concrete Damage Plasticity). The discrete mesh is obtained automatically by means of an ad-hoc routine which transforms a standard 2D homogeneous FE mesh into a 3D orthotropic elastic model with non-linear interfaces connecting contiguous elastic elements (cells). The proposed method is applied to a hemispherical dome and a cloister vault, with abundant experimental and numerical data available in the literature to compare with. Sensitivity analyses are conducted in order to have an insight into the reliability of the method, which proved excellent predictivity capabilities, as far as both the peak load and the activated failure mechanism are concerned.

NNW-GridStar: Interactive structured mesh generation software for aircrafts

The structured meshes are widely utilized in the aircraft industry because of their efficiency in achieving accurate solutions, especially for viscous flows of complex configurations. However, they are usually generated by engineers through enormous and tedious interaction with the graphical user interface of mesh generation software. To address this issue, we implement one piece of interactive structured mesh generation software called NNW-GridStar. First, we present its design details, including the software architecture and data structure. Second, we demonstrate its implementation and emphasize on the accelerated techniques proposed in our software, which consist of automatic boundary-layer mesh generation, rapid block assembly, multiblock stretching, and O-type block stretching. Finally, we perform a deep comparison between the developed NNW-GridStar and another two pieces of well known commercial software, and then demonstrate the application of NNW-GridStar in the productional CFD simulations. Experimental results show that NNW-GridStar has an outstanding generation speed and can produce meshes with high quality.