Quality Mesh Generation Research Articles

Guaranteed-quality higher-order triangular meshing of 2D domains

We present a guaranteed quality mesh generation algorithm for the curvilinear triangulation of planar domains with piecewise polynomial boundary. The resulting mesh consists of higher-order triangular elements which are not only regular (i.e., with injective geometric map) but respect strict bounds on quality measures like scaled Jacobian and MIPS distortion. This also implies that the curved triangles' inner angles are bounded from above and below. These are key quality criteria, for instance, in the field of finite element analysis. The domain boundary is reproduced exactly, without geometric approximation error. The central idea is to transform the curvilinear meshing problem into a linear meshing problem via a carefully constructed transformation of bounded distortion, enabling us to leverage key results on guaranteed-quality straight-edge triangulation. The transformation is based on a simple yet general construction and observations about convergence properties of curves under subdivision. Our algorithm can handle arbitrary polynomial order, arbitrarily sharp corners, feature and interface curves, and can be executed using rational arithmetic for strict reliability.

Large eddy simulation of aircraft at affordable cost: a milestone in computational fluid dynamics

Abstract While there have been numerous applications of large eddy simulations (LES) to complex flows, their application to practical engineering configurations, such as full aircraft models, have been limited to date. Recently, however, advances in rapid, high quality mesh generation, low-dissipation numerical schemes and physics-based subgrid-scale and wall models have led to, for the first time, accurate simulations of a realistic aircraft in landing configuration (the Japanese Aerospace Exploration Agency Standard Model) in less than a day of turnaround time with modest resource requirements. In this paper, a systematic study of the predictive capability of LES across a range of angles of attack (including maximum lift and post-stall regimes), the robustness of the predictions to grid resolution and the incorporation of wind tunnel effects is carried out. Integrated engineering quantities of interest, such as lift, drag and pitching moment will be compared with experimental data, while sectional pressure forces will be used to corroborate the accuracy of the integrated quantities. Good agreement with experimental $C_L$ data is obtained across the lift curve with the coefficient of lift at maximum lift, $C_{L,max}$ , consistently being predicted to within five lift counts of the experimental value. The grid point requirements to achieve this level of accuracy are reduced compared with recent estimates (even for wall modelled LES), with the solutions showing systematic improvement upon grid refinement, with the exception of the solution at the lowest angles of attack, which will be discussed later in the text. Simulations that include the wind tunnel walls and aircraft body mounting system are able to replicate important features of the flow field noted in the experiment that are absent from free air calculations of the same geometry, namely, the onset of inboard flow separation in the post-stall regime. Turnaround times of the order of a day are made possible in part by algorithmic advances made to leverage graphical processing units. The results presented herein suggest that this combined approach (meshing, numerical algorithms, modelling, efficient computer implementation) is on the threshold of readiness for industrial use in aeronautical design.

Iterative conjugate heat transfer analysis for heat transfer enhancement of an externally cooled three‐phase induction motor

A novel iterative conjugate heat transfer method is proposed for thermal modelling of a drill pump motor which is a constant speed three-phase induction motor. The major advantage of this technique is that it enables computational fluid dynamics (CFD) and heat transfer analysis of the rotor and the stator in a segregated manner. The two are then coupled in a separate annulus model, which represents the air gap, via boundary conditions on the annulus walls. This greatly reduces the total number of computational cells and enables good quality mesh generation - a pre-requisite for accurate CFD predictions. To validate this method, a baseline CFD and heat transfer analysis was done using FLUENT and the maximum temperature prediction was found to be within 1.75% of the previously done experiments on the existing design of the machine. Further, this method was applied to develop a heat transfer enhancement solution which reduced the maximum temperature in the drill motor from 203.5 °C to 172.9 °C.

A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs

Flows in fractured media have been modeled with many different approaches in order to get reliable and efficient simulations for many critical applications. The common issues to be tackled are the wide range of scales involved in the phenomenon, the complexity of the domain, and the huge computational cost. In this paper we introduce residual-based “a posteriori” error estimates for a formulation of the flow in the discrete fracture networks based on a constrained optimization approach (see Berrone, Pieraccini, and Scialò [SIAM J. Sci. Comput., 35 (2013), pp. B487--B510], [SIAM J. Sci. Comput., 35 (2013), pp. A908--A935], [J. Comput. Phys., 256 (2014), pp. 838--853]), suitable to overcome all the difficulties related to a good quality mesh generation with conformity requirement.

Automatic Curvilinear Quality Mesh Generation Driven by Smooth Boundary and Guaranteed Fidelity

The development of robust high-order finite element methods requires the construction of valid high-order meshes for complex geometries without user intervention. This paper presents a novel approach for automatically generating a high-order mesh with two main features: first, the boundary of the mesh is globally smooth; second, the mesh boundary satisfies a required fidelity tolerance. Invalid elements are eliminated. Example meshes demonstrate the features of the algorithm.

New software developments for quality mesh generation and optimization from biomedical imaging data

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit.

A quality and efficient tetrahedral mesh generation method

A method of unstructured tetrahedral mesh generation for general three-dimensional domain of arbitrary shape is presented. The method consists of two steps. First, generating the boundary tetrahedral mesh by the classic Delaunay method, then, using the advancing front method to create internal points and inserting them into the mesh by the Delaunay kernel procedure. The algorithm combines the advantages of the high point placement quality of the advancing front method and the high efficiency and convergence guaranty of the Delaunay algorithm. To get better efficiency, a new front identification and field point generation method is proposed and applied. Several examples have demonstrated the computational efficiency of our method and the high quality of meshes that generated within a reasonable time limit.

DELAUNAY REFINEMENT ALGORITHMS FOR ESTIMATING LOCAL FEATURE SIZE IN 2D AND 3D

We present Delaunay refinement algorithms for estimating local feature size on the input vertices of a 2D piecewise linear complex and on the input vertices and segments of a 3D piecewise linear complex. These algorithms are designed to eliminate the need for a local feature size oracle during quality mesh generation of domains containing acute input angles. In keeping with Ruppert's algorithm, encroachment in these algorithms can be determined through only local information in the current Delaunay triangulation. The algorithms are practical to implement and several examples are given.

THE EFFECTS OF MESH STYLE ON THE FINITE ELEMENT ANALYSIS FOR ARTIFICIAL HIP JOINTS

In this paper, a good quality mesh generation for the finite element method is investigated for artificial hip joint simulations. In general, bad meshes with a large aspect ratio or mixed elements can give rise to excessively long computational running times and extremely high errors. Typically, hexahedral elements outperform tetrahedral elements during three-dimensional contact analysis using the finite element method. Therefore, it is essential to mesh biologic structures with hexahedral elements. Four meshing schemes for the finite element analysis of an artificial hip joint are presented and compared: (1) tetrahedral elements, (2) wedge and hexahedral elements, (3) open cubic box hexahedral elements, and (4) proposed hexahedral elements. The proposed meshing scheme is to partition a part before seeding so that we have a high quality three-dimensional mesh which consists of only hexahedral elements. The von Mises stress distributions were obtained and analyzed. We also performed mesh refinement convergence tests for all four cases.

A prototype mesh generation tool for CFD simulations in architecture domain

Computational Fluid Dynamics (CFD) has been introduced to the architectural engineering and HVAC (Heating Ventilation and Air Conditioning) industry for decades. However, the mesh generation process is complicated and time consuming, especially for free form geometric artifacts, e.g., human bodies in the room or buildings in complex terrains. This paper presents an effort to apply quality mesh generation for CFD simulations in the architectural context. A prototype meshing tool is developed to construct adaptive quadrilateral meshes from two-dimensional image data, e.g., architecture drawings. First the quadtree based isocontouring method is utilized to generate initial uniform quadrilateral meshes in the immediate region of the objects. Meshes are further decomposed into finer quads adaptively near the surface of the object without introducing any hanging nodes. Boundary layers are then generated using the pillowing technique and the thickness of the boundary layer is controlled to achieve the desired y + values for different near wall turbulence models. Finally, meshes are extended to the ambient domain with desired sizes, where flow fields are assumed to be relatively steady. The developed tool has been employed to generate meshes for CFD simulations of scenarios commonly existing in the indoor and outdoor environment.

Quality mesh generation for molecular skin surfaces using restricted union of balls

Quality surface meshes for molecular models are desirable in the studies of protein shapes and functionalities. However, there is still no robust software that is capable to generate such meshes with good quality. In this paper, we present a Delaunay-based surface triangulation algorithm generating quality surface meshes for the molecular skin model. We expand the restricted union of balls along the surface and generate an ε-sampling of the skin surface incrementally. At the same time, a quality surface mesh is extracted from the Delaunay triangulation of the sample points. The algorithm supports robust and efficient implementation and guarantees the mesh quality and topology as well. Our results facilitate molecular visualization and have made a contribution towards generating quality volumetric tetrahedral meshes for the macromolecules.

Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams

In this paper, we propose a generic framework for 3D surface remeshing. Based on a metric-driven Discrete Voronoi Diagram construction, our output is an optimized 3D triangular mesh with a user defined vertex budget. Our approach can deal with a wide range of applications, from high quality mesh generation to shape approximation. By using appropriate metric constraints the method generates isotropic or anisotropic elements. Based on point-sampling, our algorithm combines the robustness and theoretical strength of Delaunay criteria with the efficiency of entirely discrete geometry processing . Besides the general described framework, we show experimental results using isotropic, quadric-enhanced isotropic and anisotropic metrics which prove the efficiency of our method on large meshes, for a low computational cost.

Shape reconstruction from medical images and quality mesh generation via implicit surfaces

AbstractThe ability of automatically reconstructing physiological shapes, of generating computational meshes, and of calculating flow solutions from medical images is enabling the introduction of computational fluid dynamics (CFD) techniques as an additional tool to aid clinical practice.This article presents a set of procedures for the shape reconstruction and triangulation of geometries derived from a set of medical images representing planar cross sections of the object. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is an iso‐surface of the implicit function that is approximated by a triangulation extracted by the method of marching cubes. The quality of this triangulation is often neither suitable for mesh generation nor for flow solution. We discuss the use of mesh enhancement techniques to maximize the quality of the triangulation together with curvature adaption to optimize mesh resolution.The proposed methodology is applied to the reconstruction and discretization of two physiological geometries: a femoral by‐pass graft and a nasal cavity. Copyright © 2006 John Wiley & Sons, Ltd.

Parallel Guaranteed Quality Delaunay Uniform Mesh Refinement

We present a theoretical framework for developing parallel guaranteed quality Delaunay mesh generation software that allows us to use commercial off‐the‐shelf sequential Delaunay meshers for two‐dimensional geometries. In this paper, we describe our approach for constructing uniform meshes, that is, the meshes in which all elements have approximately the same size. Our uniform distributed‐ and shared‐memory implementations are based on a simple (block) coarse‐grained mesh decomposition. Our method requires only local communication, which is bulk and structured as opposed to fine and unpredictable communication of the other existing practical parallel guaranteed quality mesh generation and refinement techniques. Our experimental data show that on a cluster of more than 100 workstations we can generate about 0.9 billion elements in less than 5 minutes in the absence of work‐load imbalances. Preliminary results for this paper were presented in [A. N. Chernikov and N. P. Chrisochoides, “Practical and efficient point insertion scheduling method for parallel guaranteed quality Delaunay refinement,” in Proceedings of the 18th Annual International Conference on Supercomputing, ACM Press, New York, 2004, pp. 48–57]. Our work in progress includes extending the presented approach, which can efficiently generate only uniform meshes, to nonuniform graded meshes.

Recent progress in robust and quality Delaunay mesh generation

In this paper, some current issues of Delaunay mesh generation and optimization are addressed, with particular emphasis on the robustness of the meshing procedure and the quality of the resulting mesh. We also report new progress on the robust conforming and constrained boundary recovery in three dimensions, along with the quality mesh generation based on Centroidal Voronoi tessellations. Applications to the numerical solution of differential equations and integrations with other softwares are discussed, including a brief discussion on the joint mesh and solver adaptation strategy.

In-cylinder airflow of automotive engine by quasi-direct numerical simulation

A Computational Fluid Dynamics (CFD) program for in-cylinder airflow analysis has been developed by the authors. The feature of the developed program is that it treats turbulence flow with the quasi-direct numerical simulation (Quasi-DNS). So it is possible to present transient turbulence eddy motions in detail. For fast and high quality mesh generation, the Voxel method was employed. The computational domain is discretized by uniform cubic cells in this method. The simulation results were verified by two benchmark tests. One of them in common use is a backward step flow test, the other is an in-cylinder flow test that supposed the engine induction stroke. Good agreement was obtained between the simulation and the experimental results of these benchmark tests.

Approximate Shape Quality Mesh Generation

We present two techniques for simplifying the list processing required in standard iterative refinement approaches to shape quality mesh generation. The goal of these techniques is to gain simplicity of programming, efficiency in execution, and robustness of termination. ‘Shape quality’ for a mesh generation method usually means that, under suitable conditions, a mesh with all angles exceeding a prescribed tolerance is generated. The methods introduced in this paper are truncated versions of such methods. They depend on the shape improvement properties of the terminal-edge LEPP-Delaunay refinement technique; we refer to them as approximate shape quality methods. They are intended for geometry-based preconditioning of coarse initial meshes for subsequent refinement to meet data representation needs. One technique is an algorithm re-organization to avoid maintaining a global list of triangles to be refined. The re-organization uses a recursive triangle processing strategy. Truncating the recursion depth results in an approximate method. Based on this, we argue that the refinement process can be carried out using a static list of the triangles to be refined that can be identified in the initial mesh. Comparisons of approximate to full shape quality meshes are provided.

Quality mesh generation

Many physical phenomena in science and engineering can be modeled by partial differential equations (PDEs) and solved by means of the Finite Element Method (FEM). Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. Mesh quality is a key-point for the accuracy of numerical simulation. In this paper, we are concerned with the generation of quality (or regular) meshes. This question is a particular occurrence of a more general mesh generation issue which aims to complete meshes conforming to a pre-specified size map (such meshes being referred to as `unit' meshes). We propose a method that makes this mesh construction possible. It is based on a Delaunay advancing-front combined method: the field points are defined using an advancing-front method and are connected using a generalized Delaunay type method. Some optimization methods are also discussed.

Quality Mesh Generation in Higher Dimensions

We consider the problem of triangulating a d-dimensional region. Our mesh generation algorithm, called QMG, is a quadtree-based algorithm that can triangulate any polyhedral region including nonconvex regions with holes. Furthermore, our algorithm guarantees a bounded aspect ratio triangulation provided that the input domain itself has no sharp angles. Finally, our algorithm is guaranteed never to overrefine the domain, in the sense that the number of simplices produced by QMG is bounded above by a factor times the number produced by any competing algorithm, where the factor depends on the aspect ratio bound satisfied by the competing algorithm. The QMG algorithm has been implemented in C++ and is used as a mesh generator for the finite element method.

A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation

We present a simple new algorithm for triangulating polygons and planar straightline graphs, It provides "shape" and "size" guarantees: •All triangles have a bounded aspect ratio.•The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for the finite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The technique we use-successive refinement of a Delaunay triangulation-extends a mesh generation technique of Chew by allowing triangles of varying sizes. Compared with previous quadtree-based algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles. We also discuss an implementation of the algorithm and evaluate its performance on a variety of inputs.