Automatic Mesh Generation Research Articles

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Purpose Modern CAD systems facilitate the creation of any surface geometry imaginable, and complex surfaces for free-form grid shells are often represented by a set of Non-Uniform Rational B-Splines surface patches. But it remains an intractable issue how to generate high-quality grids on complex surfaces efficiently. To solve this issue, an automatic triangular mesh generation method is presented, based on bubble dynamics simulation and a modified Delaunay method. Design/methodology/approach A moderate amount of points are first distributed on a given surface. Next, by regarding the points as elastic bubbles with the same size and introducing the forces acting on bubbles, the motion control equations of bubbles are established. The equilibrium state of the bubble system is found by Verlet algorithm. Then, the Voronoi diagram on the surface is obtained by calculating the intersection between the surface and the three-dimensional (3D) Voronoi diagram of the centers of bubbles. Finally, a triangular mesh, Delaunay triangulation on the surface, is determined based on the dual change of the Voronoi diagram. Findings This method generates meshes on the surface directly, unlike mapping-based methods, avoiding the mapping distortion. Examples are given to demonstrate the successful execution of this method. The result also illustrates that this method is applicable to various surfaces in high automation level and resultant meshes are highly uniform and well-shaped. Originality/value Thus, this method provides the convenience for the geometry design of complex free-form grid structure.

Multilevel design optimization of hydraulic turbines based on hierarchical metamodel-assisted evolutionary algorithms

In this paper, an efficient hydraulic optimization procedure is presented and applied to the design of hydraulic turbines. For computationally expensive industrial design optimization problems, an advanced optimization tool (EASY software) and a fast CFD evaluation tool are required. EASY optimization software is a Hierarchical Metamodel-Assisted Evolutionary Algorithm (HMAEA) that can be used in both single-(SOO) and multi-objective optimization (MOO) problems. In order to minimize the CFD solver calls during the optimization design, the MAEA rely on local metamodels, trained on the fly, that are used to identify the most promising members in each population and then only these are to be re-evaluated by the CPU costly CFD solver. For additional economy in the CPU cost, the hierarchical (two-level) optimization scheme is used in this paper, where at each level, a different evaluation tool, a low and a high fidelity specific software, can be linked. The low level utilizes a low-CPU cost and low-accuracy tool to explore the design space with a minimum impact to the wall clock time and the high level, using the high fidelity, high-CPU cost tool is used to exploit the information from the low level. For the applications presented in this paper, the high fidelity model is an incompressible Navier-Stokes equation solver and the low fidelity model is based on the solution of the incompressible Euler equations. In order to optimize the geometry of hydraulic machines, an in-house automatic geometry and mesh generation tool has been integrated in the optimization tool chain. In what follows, 2 three-objective design optimization problems of 3D Francis hydraulic turbines are presented. The optimization objective functions concern the ‘quality’ of the runner outlet velocity profile, the cavitation behavior and efficiency of the runner. The optimization results of the hydraulic turbine components along with the performance of the presented optimization procedure are shown in the paper.

Shape-Optimizing and Illumination-Smoothing Image Stitching

Image stitching is usually subject to projective distortion and color difference problems. This paper presents an illumination-smoothing image stitching method based on the shape-optimizing hybrid transformation. An automatic mesh generation strategy is especially designed to reduce the calculation of the hybrid transformation within a reasonable range and guarantee the accuracy of image alignment. We consider stitching multiple images while constraining the distortion with the hybrid transformation and alleviate the color difference. In this paper, the method of color correction is adapted according to the characteristics of image stitching so as to achieve illumination-smoothing results. Moreover, the triangulation of the matching feature points is used to partition the color regions of the image and then more abundant color information is obtained for the calculation of the color transformation model. For general horizontal images, our method can achieve better results with less distortion in comparison with state-of-the-art methods. Various experimental results validate our new method.

3D finite element study of the fatigue damage of Ti–6Al–4V in presence of fretting wear

Fretting damage analysis is carried out for several 3D contact geometries (cylinder-on-plane and punch-on-plane) under different slip regimes. A robust numerical environment is implemented to simulate the consequences of fatigue-fretting, in terms of wear or fatigue crack initiation. The numerical model allows to characterize the abrasive wear phenomena observed experimentally, and introduces specific damage post-processing to predict crack initiation. The numerical process includes an automatic mesh generation for updating the geometry due to wear effect. The difference between 2D and 3D cases is highlighted. Cases where a 3D numerical approach appears to be mandatory to obtain a quantitative agreement between simulation and experiment are mentioned.

Automatic and high-quality surface mesh generation for CAD models

In this paper, we present a fully automatic framework that tessellates industrial computer-aided design (CAD) models into high-quality triangular meshes. In contrast to previous approaches that are purely parametric or performed directly in 3D space, our method is based on a remeshing algorithm that can achieve accuracy and high-quality simultaneously. Given an input standard CAD model, which is represented by B-rep format,we first rebuild the parametric domain for each surface patch according to an initial triangulation, and then the boundaries of the parametric domain are retriangulated by exploiting the Constrained Delaunay Triangulation (CDT). In the second stage, the 2D triangulation is projected back to the 3D space, and a modified global isotropic remeshing process is applied, which further improves the regularity and angle quality of the tessellated meshes. Experiments demonstrate the validity of the proposed approach and its ability to generate high-quality meshes. Moreover, we evaluate our technique and compare it with state-of-the-art CAD model tessellation approaches.

Development of high precise similar sub-part search technique for automatic mesh generation reusing proven models

Development of high precise similar sub-part search technique for automatic mesh generation reusing proven models

Development of the model for a diesel engine catalytic converter

One of the key issues of the modern engine development is to comply with today’s stringent emission standards. It forces the manufacturers to enhance in-engine and after treatment emission reduction technologies continuously. The selective catalytic reduction (SCR) is still the most effective technique for nitrogen oxides removal from exhaust gases of vehicles with diesel engines. Numerical modelling is widely used for SCR systems development and assessment. In this paper, a simplified one-dimensional numerical model of diesel SCR catalyst, which was implemented in Matlab, is described. The algorithm for automatic mesh generation describing real cross-section geometry of the catalyst block and the calculation procedure allowing to take into account non-uniform distribution of the gas flow parameters at the catalyst inlet are presented. Model was validated by the experimental data available in the literature. Numerical simulations for the full-scale modern SCR catalyst were carried out. The effect of the gas velocity non-uniformity at the catalyst inlet on the overall NOx reduction efficiency was evaluated.

On the effect of salinity and nano-particles on polymer flooding in a heterogeneous porous media: Experimental and modeling approaches

In this study, polymer flooding process was simulated using COMSOL Multiphysics® modeling software. Navier–Stokes and phase field equations were solved simultaneously using finite element approach. Effects of salinity, viscosity, and nano-particles were studied on displacement efficiency of oil sample in the heterogeneous porous media. Modeling results for oil recovery factor and breakthrough time were obtained and compared to experimental outputs of another study. Results indicated that there exists a proper accommodation between the results. Errors ranged from 3% to 7% for oil recovery factor and 0.5%–0.9% for the breakthrough time in various injection scenarios. Using predefined structure of the under test micromodel, star-like meshes were developed in this software for the first time. This unstructured mesh is more likely to the pore structures of the sandstone reservoirs. To increase the validity of the results, a boundary layer was designated in the fluid flow path and mesh generation was performed manually in a complicated pore space instead of automatic mesh generation. Experimental and modeling results for the residual oil saturation as a function of dimensionless time were compared. Mesh dependency studies were performed to obtain the best number of mesh elements in which the most accurate results were obtained in the minimum required time. Finally, sensitivity analysis studies were performed as a function of injection rate, mobility ratio, and viscosity and the operating conditions were analyzed in terms of capillary number. All the polymer injection scenarios led to reasonable range for this parameter which verifies the accuracy of the selected operating parameters and the modeling approach.

Application of automated cubic-order mesh generation for efficient energy transfer using parabolic arcs for microwave problems

This paper aims to offer an efficient, simple and accurate cubic-order subparametric finite element technique utilizing 2-D automated mesh generator for microwave applications. The proposed technique utilizes the best discretization procedure, the finest quadrature rule and an excellent subparametric finite element algorithm for obtaining the numerical solutions of the Helmholtz equation. The high-quality automated mesh generator MATLAB code developed for the present work using HOmesh2d.m and CurvedHOmesh2d.m are provided. This approach utilizes up to cubic-order triangular mesh for arbitrary waveguide structures. The meshes with one side curved cubic-order triangular elements are proposed with parabolic arcs for curved waveguide structures. For regular waveguide structures with sharp edges having singularities, the utilization of unstructured cubic-order triangular meshes with refinement for the technique is proposed. The method is demonstrated for six different waveguide structures and the outcomes obtained are compared with the best available numerical or analytical results. The results show that the proposed technique produces an efficient and most accurate finite element results for the finite element analysis performed for waveguide structures with singularities and curved geometries as there is no curvature loss. Thus, the proposed subparametric finite element technique with the automated mesh generator is verified to yield a viable approach for getting the most precise numerical result for the 2-D Helmholtz equation in distinct waveguide cross-sections. Therefore, this approach can be used to produce the most efficient energy transfer for microwave applications.

An adaptive remeshing technique for predicting the growth of irregular crack fronts using p-version finite element analysis

An adaptive remeshing technique using p-version finite element analysis was developed to predict the growth of cracks with highly irregular crack front geometries. In order to represent the shape of the crack front, the commonly used ellipse was replaced by a high-resolution spline. This enabled the growth of irregular crack fronts with local changes in curvature, convex and concave regions and small radii of curvature to be simulated iteratively using automatic mesh generation. The method was demonstrated for an irregular corner crack at a notch and the predicted crack front geometry was shown to be in good agreement with experimental results.

A parametric morphing method for generating structured meshes for marine free surface flow applications with plane symmetry

Abstract This article introduces a method for morphing a parametric, rectangular and structured 3D template mesh such that it embodies: (1) a given (half) hull surface properly aligned with a pre-defined air-water interface zone, (2) a high-quality boundary layer region near the hull, and (3) a smooth transition of the mesh to the template mesh structure away from the hull. The performance of the proposed method is successfully validated on three widely studied benchmark cases, namely the parabolic Wigley hull, the Series 60 hull and the DTMB 5415 combatant hull. The proposed automated mesh generation method is useful in shape optimization for computational fluid dynamics, among others. Highlights A new method for creating structured meshes for marine CFD applications is presented. The proposed method is parametric and thus fully programmable. The method includes an automatic resolution of CAD geometry errors. The resulting meshes are strictly orthogonal near the inter-phase zone and the hull. The main application of the proposed method is in CFD-based shape optimization.

Nonlocal damage modelling by the scaled boundary finite element method

Summary The progressive damage of structures is fruitfully simulated by using the semi-analytical scaled boundary finite element method (SBFEM). The integral-type nonlocal model combined with the isotropic damage model is extended to eliminate the mesh sensitivity concerning the strain localization. An automatic and efficient quadtree mesh generation algorithm is employed to refine the localized damage process zone (DPZ) and reduce the number of degrees of freedom (DOFs). Owing to the salient advantage of the SBFEM in using arbitrary polygonal subdomains, side-effects associated with hanging nodes can be eliminated. Furthermore, the computational effort of strain/stress field and damage variables can be considerably saved in the framework of the SBFEM. Four numerical benchmarks with regular-shaped domain and a porous plate with irregular holes are simulated to demonstrate the effectiveness and robustness of the proposed approach.

Automated homogenization-based fracture analysis: Effects of SVE size and boundary condition

To model the sample-to-sample variations and the effect of microscale inhomogeneities on fracture response, statistical volume elements (SVEs) are employed to homogenize the elastic and fracture properties of ZrB2-SiC, a two-phase particulate composite often used as a thermal coating. In the mesoscale analysis, 2D finite element models are generated using a non-iterative, automated mesh generation algorithm named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR). The analysis of SVEs under mixed, traction, and minimal kinematic boundary conditions yields their angle-dependent tensile and shear fracture strengths and elastic stiffnesses. This study shows that homogenized fracture strengths are highly dependent on the SVE size and the particular geometric distribution of inclusions (even for similar volume ratios), whereas elastic properties are mainly a function of the volume fraction. Moreover, mean values of strength and bulk modulus, respectively, decrease and remain almost constant as the SVE size increases. For the macroscale analysis, an isotropic, inhomogeneous field of fracture strength is generated from the homogenization of SVEs. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is subsequently employed for fracture analysis under uniaxial tensile and thermal strain loadings.

Multi-Objective Genetic Algorithm Assisted by an Artificial Neural Network Metamodel for Shape Optimization of a Centrifugal Blood Pump.

A centrifugal blood pump is a common type of the pump used as a left ventricular assist device (LVAD) in the medical industries. The reduction of the LVADs hemolysis level to reduce the blood damage is one of the major concerns in designing of such devices. Also, the enhancement of the LVADs efficiency to decrease the battery size is another design requirement. The blood damage critically depends on the state of the blood being pumped. Besides the blood state, the blood damage also depends on the pump impeller and volute geometries. In this research, a multi-objective optimization of a centrifugal blood pump is performed. A complete 3D-optimization platform is established for both impeller and volute of a centrifugal blood pump consisting of parametric modeling, automatic mesh generation, computational fluid dynamics (CFD) simulation, and optimization strategy. A vast number of cases with various impeller and volute shapes are numerically simulated. Three different metamodels are created using artificial neural networks (ANNs) in order to approximate the pump hydraulic efficiency, hemolysis index (HI), and pressure head. The inverse of the relative pressure head is defined as the first objective and the summation of relative hemolysis index and the inverse of the relative efficiency is assumed as the second objective. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to find the Pareto Front. A set of optimal points is selected. Finally, for the physiological flow conditions, the optimum design that provides 11.9% HI reduction and 7.2% efficiency enhancement is selected.

ES-PIM applied to buckling of variable angle tow laminates

The increasing need for automatic mesh generation has led to the development of efficient triangulation algorithms that are able to discretize any 2D or 3D domain. Modern finite element formulations based on strain smoothing techniques (SFEM) provide enhanced convergence properties, preventing yet the stiffening behavior of triangular meshes. Recent research has shown that meshless methods based on triangular mapping of the integration domain can be used to produce even better convergence properties than SFEM. The present study explores the Edge-based Smoothed Point Interpolation Method (ES-PIM) as a meshless solution to investigate linear buckling on variable angle tow (VAT) laminates. Such advanced composite structures show a heterogeneous distribution of constitutive properties and thickness, presenting additional challenges to the numerical solution. Important aspects related to the transverse shear correction herein adopted are investigated, leading to interesting conclusions regarding the possibility to use the ES-PIM for conservative estimates of the critical buckling load of VAT laminates.

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

SummaryThe 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.

Modeling a dry running twin-screw expander using a coupled thermal-fluid solver with automatic mesh generation

Understanding the details of the internal flow processes in screw compressors and expanders is very important for their efficient and robust design. Computational fluid dynamics (CFD) provides full access to a modeled three dimensional flow field and its variation in time. However, the application of CFD to screw compressors and expanders can be difficult because of the complicated geometries involved and the need to supply the computational grid on which the modeled equations are solved over a large number of time steps. While the majority of previous research on CFD applications to screw machines features inventive techniques for generating meshes that adequately resolve the flows in the small clearances, an alternate approach is demonstrated in this work. The screw expander SE 51.2 from TU Dortmund University is analyzed here through a CFD model which generates the grid automatically based on a modified Cartesian cut-cell approach. The grid is then adaptively refined based on local gradients of velocity and temperature. At each time step, the grid is regenerated based on the geometry motion. As opposed to resolving the flow in the clearances, a model is applied so that the cells in the clearance can remain relatively large. The detailed measurements of the screw expander are used to validate the model. The operating conditions investigated include the expansion of dry air at a four-to-one pressure ratio for four different rotational speeds. The measured internal chamber pressures are compared to the results from the model, as are the average mass flow rate, indicated power, and outlet temperature. A coupled thermal-fluid approach is used to model the rotor temperatures and corresponding thermal deformation of the rotors and housing. In this approach, the fluid and solid temperatures are solved together; to deal with the problem of the disparate time scales between the fluid and solid heat transfer, the solids are periodically solved to steady state using heat transfer coefficients and near-wall temperatures computed from an energy conserving averaging over several cycles. The effects of the various leakage flow paths in the model, including the rotor-to-rotor, rotor-tip-to-housing, and bearing leakage are demonstrated and quantified. Finally, simulation and experimental results are compared in terms of different rotor-tip-to-housing clearance heights. The model considering the appropriate thermal deformation of the rotors is shown to yield the best agreement with the measurements, however there is work remaining to reduce the model calculation time, especially at low rotational speeds.

Failure Process Simulation of Interlayered Rocks under Compression

Anisotropy in strength and deformation of rock mass induced by bedding planes and interlayered structures is a vital problem in rock mechanics and rock engineering. The modified rigid block spring method (RBSM), initially proposed for modeling of isotropic rock, is extended to study the failure process of interlayered rocks under compression with different confining pressures. The modified rigid block spring method is used to simulate the initiation and propagation of microcracks. The Mohr–Coulomb criterion is employed to determine shear failure events and the tensile strength criterion for tensile failure events. Rock materials are replaced by an assembly of Voronoi-based polygonal blocks. To explicitly simulate structural planes and for automatic mesh generation, a multistep point insertion procedure is proposed. A typical experiment on interlayered rocks in literature is simulated using the proposed model. Effects of the orientation of bedding planes with regard to the loading direction on the failure mechanism and strength anisotropy are emphasized. Results indicate that the modified RBSM model succeeds in capturing main failure mechanisms and strength anisotropy induced by interlayered structures and different confining pressures.

Three-dimensional damage analysis by the scaled boundary finite element method

A novel and effective approach within the framework of the scaled boundary finite element method (SBFEM) is proposed for the damage analysis of structures in three dimensions. The integral-type nonlocal model is extended to SBFEM to eliminate the mesh sensitivity concerning the strain localization. In order to reduce the number of degrees of freedoms (DOFs), an automatic mesh generation algorithm using octree decomposition is employed to refine the localized damage process zone (DPZ), but no extra effort is required to deal with hanging nodes existing between adjacent subdomains with different sizes. A double-notched tension beam is simulated with two different meshes to illustrate the mesh-independence. Three benchmarks are modelled to further verify the effectiveness and robustness of the proposed approach. It is shown that the proposed computational approach is capable of accurately capturing the damage evolution under complicated boundary conditions, and the results agree well with the experimental observations and prior numerical simulations reported in the literatures.

Exploring Mesh Generation and Quality Enhancement with Open Source Codes

The finite element method is a very reliable and precise technique for solving partial differential equations in three-dimensional domains, with relevant applications in several areas. However, 3D simulations by FEM require computer programs for solid modeling and automatic mesh generation and there are few examples of open source codes available and dedicated to these tasks. Unfortunately, these open source codes are not usually conceived to operate together in an integrated fashion, showing distinct life cycles and different origins, which may result in contradictory specifications. In this study, a method is proposed to integrate solid modeling and automatic mesh generation with focus on open source codes and how the quality of FEM simulations can be improved by the improvement of the mesh. The method was structured in desired features for the solid construction and in integration strategies for an automatic mesh generation. The approach was tested in nontrivial domains and with known relevance for studies focused on computational electromagnetics. Meshes were generated with millions of tetrahedral elements and the results were compared to the quality values commonly discussed in literature focused on FEM. Complex geometries were meshed in a few seconds, with consistent values of aspect ratios (more than 90% of the tetrahedral elements were constructed with values at most 5) and dihedral angles (the values were bounded between 5.9 to 166.7°C, with a peak value around 90°C). Finally, in order to show the relation among highly refined meshes and quality criteria which can be explored by proposed method, the Laplace's equation was simulated by FEM in order to analyze the equipotential lines of a parallel-plate capacitor. The results show how the quality of a simulation can be improved, especially concerning the increasing number of tetrahedra in the mesh with proper aspect ratio.