Mesh Quality Improvement Research Articles

Hexahedral Mesh Quality Improvement with Geometric Constraints

Hexahedral Mesh Quality Improvement with Geometric Constraints

Regular Position-Oriented Method for Mesh Smoothing

Mesh smoothing is an essential technique for the improvement of mesh quality in finite element analysis, due to the fact that mesh quality has a large impact on the convergence of the computational scheme and the accuracy of the numerical results. A novel mesh smoothing method based on regular-position-guided operations is presented in this paper. The method introduced here contains two main stages: The first stage computes the regular position of each vertex based on the shape of the element and conducts regular-position-oriented-based element transformations independently; the second stage determines the finial position of each vertex according to its surrounding elements with an assembly strategy. This method is not limited to planar triangular mesh, but applicable to surface polygonal mesh. Numerical experiments on various mesh models demonstrate the effectiveness and potential of this method.

Computational aeroacoustic prediction of trailing edge noise for small wind turbines

The study of aeroacoustic noise generated by small wind turbines is important to increase acceptance and implementation of the technology. Small wind turbines have unique challenges due to the low Reynolds number (Re) flow the blades experience, which introduces a potential for tonal noise. Computational aeroacoustics can be applied during the design stage of the turbine blades to improve acoustic performance. This work aims to validate a fully analytical aeroacoustic model by analyzing a SD 7037 blade segment at static angles of attack, with comparison to experimental flow and acoustic data. The Ffowcs-Williams and Hawkings (FW-H) acoustic model is used in combination with Large Eddy Simulation (LES). The following simulation parameters were examined: mesh quality, mesh density, inlet turbulence and spanwise boundary condition. These parameters change the boundary layer (BL) transition process and the formation of the laminar separation bubble on the suction side of the blade segment, both of which impact the aeroacoustic noise prediction. It was found that improvement in mesh quality and density on the surface of the blade segment resulted in improved BL simulation and tonal noise prediction. Alteration of the inlet turbulence and spanwise boundary condition did not have as large of an effect.

Building Geometry Simplification for Improving Mesh Quality of Numerical Analysis Model

Numerical analysis, especially the finite volume method (FVM), is one of the primary approaches employed when evaluating a building environment. A complicated geometry can degrade the mesh quality, leading to numerical diffusions and errors. Thus, this study develops and evaluates an automatic building geometry simplification method based on integrating similar surfaces for the geometry of an indoor space. A regression model showed that the complexity of the simplified geometry and its similarity to the original geometry decreased linearly with the threshold of the method. The mesh quality was significantly improved by the simplification. In particular, the maximum skewness decreased exponentially with the threshold of the method. It is expected that the simplification method and regression model presented in this study can be used to quantitatively control the mesh quality.

Approximating isosurfaces by guaranteed‐quality triangular meshes

AbstractWe describe a new method for approximating an implicit surface F by a piecewise‐flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh that gives a piecewise‐differentiable approximation of F, with angles between 35.2 and 101.5 degrees. As the mesh size approaches 0, the mesh converges to F through surfaces that are isotopic to F.

Simulation-driven optimization of high-order meshes in ALE hydrodynamics

In this paper we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible shock hydrodynamic applications. The mesh optimization process is driven by information provided by the simulation which uses the optimized mesh, such as shock positions, material regions, known error estimates, etc. These simulation features are usually represented discretely, for instance, as finite element functions on the Lagrangian mesh. The discrete nature of the input is critical for the practical applicability of the algorithms we propose and distinguishes this work from approaches that strictly require analytical information. Our methods are based on node movement through a high-order extension of the Target-Matrix Optimization Paradigm (TMOP) of [1]. The proposed formulation is fully algebraic and relies only on local Jacobian matrices, so it is applicable to all types of mesh elements, in 2D and 3D, and any order of the mesh. We discuss the notions of constructing adaptive target matrices and obtaining their derivatives, reconstructing discrete data in intermediate meshes, node limiting that enables improvement of global mesh quality while preserving space-dependent local mesh features, and appropriate normalization of the objective function. The adaptivity methods are combined with automatic ALE triggers that can provide robustness of the mesh evolution and avoid excessive remap procedures. The benefits of the new high-order TMOP technology are illustrated on several simulations performed in the high-order ALE application BLAST [2].

Mesh smoothing algorithm based on exterior angles split.

Since meshes of poor quality give rise to low accuracy in finite element analysis and kinds of inconveniences in many other applications, mesh smoothing is widely used as an essential technique for the improvement of mesh quality. With respect to this issue, the main contribution of this paper is that a novel mesh smoothing method based on an exterior-angle-split process is proposed. The proposed method contains three main stages: the first stage is independent element geometric transformation performed by exterior-angle-split operations, treating elements unconnected; the second stage is to offset scaling and displacement induced by element transformation; the third stage is to determine the final positions of nodes with a weighted strategy. Theoretical proof describes the regularity of this method and many numerical experiments illustrate its convergence. Not only is this method applicable for triangular mesh, but also can be naturally extended to arbitrary polygonal surface mesh. Quality improvements of demonstrations on triangular and quadrilateral meshes show the effectiveness of this method.

A Data-Driven Approach for Simultaneous Mesh Untangling and Smoothing Using Pointer Networks

Poorly-shaped and/or inverted elements negatively affect numerical simulation accuracy and efficiency. Most current approaches consider mesh quality improvement and mesh untangling problems as numerical optimization problems and solve them using nonlinear optimization. However, these optimization-based approaches require users to set and solve complex numerical optimization problems with no guarantee that the output meshes are valid meshes with good element qualities. Therefore, this paper proposes a data-driven approach for simultaneous mesh untangling and smoothing using a Pointer network. The proposed approach generates various triangular meshes and employs a novel sequence generation algorithm to train the Pointer network and predicts competitive approximate solutions using the trained network. The strength of the proposed framework lies in its simplicity to predict the best free vertex candidate, providing high-quality output meshes, since it does not require solving complex numerical optimization for prediction. Experimental results show that the proposed framework successfully eliminates inverted elements on the meshes and improved average and worst element quality up to 85.9% and 97.8%, respectively, compared to current optimization-based methods.

Efficient Parallel Algorithms for 3D Laplacian Smoothing on the GPU

In numerical modeling, mesh quality is one of the decisive factors that strongly affects the accuracy of calculations and the convergence of iterations. To improve mesh quality, the Laplacian mesh smoothing method, which repositions nodes to the barycenter of adjacent nodes without changing the mesh topology, has been widely used. However, smoothing a large-scale three dimensional mesh is quite computationally expensive, and few studies have focused on accelerating the Laplacian mesh smoothing method by utilizing the graphics processing unit (GPU). This paper presents a GPU-accelerated parallel algorithm for Laplacian smoothing in three dimensions by considering the influence of different data layouts and iteration forms. To evaluate the efficiency of the GPU implementation, the parallel solution is compared with the original serial solution. Experimental results show that our parallel implementation is up to 46 times faster than the serial version.

Anisotropic Surface Remeshing without Obtuse Angles

AbstractWe present a novel anisotropic surface remeshing method that can efficiently eliminate obtuse angles. Unlike previous work that can only suppress obtuse angles with expensive resampling and Lloyd‐type iterations, our method relies on a simple yet efficient connectivity and geometry refinement, which can not only remove all the obtuse angles, but also preserves the original mesh connectivity as much as possible. Our method can be directly used as a post‐processing step for anisotropic meshes generated from existing algorithms to improve mesh quality. We evaluate our method by testing on a variety of meshes with different geometry and topology, and comparing with representative prior work. The results demonstrate the effectiveness and efficiency of our approach.

Improved Simultaneous Mesh Untangling and Quality Improvement Methods of 2D Triangular Meshes

Few inverted or poor quality elements can ruin both the accuracy and efficiency of numerical solutions. This paper proposes improved mesh untangling and quality improvement methods using the modified mesh quality metric for 2D triangular meshes. The new mesh quality metric ensures highly inverted elements assign higher penalty when the signed area of the element is negative, and also produces more accurate signed areas for valid elements. Therefore, the proposed methods can quickly remove inverted elements and also improve worst element qualities compared with the existing methods. We also combine Delaunay-based edge flip with optimization-based mesh untangling and quality improvement methods to further improve worst element qualities. Numerical results show that the proposed methods yield better quality meshes for improvement of the worst quality and are faster than existing methods.

Surface mesh quality improvement by weighted inscribed circle method

Surface mesh quality is one of key factors in finite element applications, since it affects the accuracy and efficiency of finite element simulation and influences the quality of subsequently generated solid mesh. In this paper, we proposed a novel surface mesh smoothing algorithm which aims to produce a more regular mesh from a given input mesh, while accurately preserving its sharp features such as edges and corners. The mesh quality is improved by a combination of surface node classification and node relocation, while the new position of the vertex is obtained by weighted average of the centers of inscribed circles of the surrounding polygon, and projecting the averaged position to lie in space near the input surface mesh. The procedure above is repeated until the maximal change of mesh quality is less than a pre-defined threshold. Finally, several experimental results are presented to demonstrate the effectiveness and practicability of our method.

A Deviation-Based Dynamic Vertex Reordering Technique for 2D Mesh Quality Improvement

We propose a novel deviation-based vertex reordering method for 2D mesh quality improvement. We reorder free vertices based on how likely this is to improve the quality of adjacent elements, based on the gradient of the element quality with respect to the vertex location. Specifically, we prioritize the free vertex with large differences between the best and the worst-quality element around the free vertex. Our method performs better than existing vertex reordering methods since it is based on the theory of non-smooth optimization. The downhill simplex method is employed to solve the mesh optimization problem for improving the worst element quality. Numerical results show that the proposed vertex reordering techniques improve both the worst and average element, compared to those with existing vertex reordering techniques.

A combined use of embedded and cohesive elements to model damage development in fibrous composites

In recent years the embedded element (EE) technique, which is based on the superposition of meshes, has been introduced into finite element (FE) modelling of composite materials. When compared to conventional approaches employing a single continuous mesh this technique has a number of advantages, among which are simplicity in the model creation and improved mesh quality. However, due to the absence of physical interfaces, simulation of interfacial damage with this technique presents a real challenge. In this work we propose an approach in which the EE technique is combined with the cohesive zone model with the purpose to model interfacial damage in fibrous composites. The new hybrid method is validated against conventional FE models in four case studies. Among others the methodology is applied to predict mechanical properties of nanocomposites reinforced by carbon nanotubes showing good agreement with experimental data.

Surface Mesh Quality Improvement Based on Medial Axis

Surface Mesh Quality Improvement Based on Medial Axis

STUDY OF MESH QUALITY IMPROVEMENT FOR CFD ANALYSIS OF AN AIRFOIL

ABSTRACT: Airfoils generate lift in engineering applications such as for airplanes, wind turbines, automotive spoilers, etc. For accurate CFD analysis of airfoils, the quality of the mesh is of paramount importance, especially when dealing with turbulent flows commonly encountered in real life applications. Currently there are different tools that are available to improve the quality of the mesh required for CFD studies. This paper describes a study to assess the significant of the quality of the mesh on CFD analyses of NACA 23012 airfoil by using selected open source tools. The turbulence is modeled using the well-known k-ω Shear Stress Transport model. For validation, results have been compared with experimental datasets which were obtained from “TAG Stuttgart #1” tunnel.
 ABSTRAK: Sayap pesawat dapat menghasilkan daya angkat dalam aplikasi kejuruteraan seperti kapal terbang, turbin angin, spoiler automotif, dan sebagainya. Kualiti pada jaringan adalah amat penting bagi mendapatkan analisa CFD yang tepat pada sayap pesawat, terutamanya apabila berhadapan situasi aliran turbulen sebenar. Pada masa ini terdapat pelbagai perisian bagi meningkatkan mutu jaringan dalam kajian CFD. Kertas kerja ini membentangkan satu kajian bagi menilai kepentingan kualiti jaringan pada analisis CFD bagi sayap pesawat NACA 23012 dengan menggunakan sumber terpilih perisian terbuka. Model turbulen dibangunkan mengguna pakai model k-ω Shear Stress Transport (SST) yang terkenal. Bagi pengesahan, keputusan uji kaji telah dibandingkan dengan set data yang diperoleh dari terowong "TAG Stuttgart #1”."

Numerical Analysis and Verification of the Gas Jet from Aircraft Engines Impacting a Jet Blast Deflector

The process of the gas jet from aircraft engines impacting a jet blast deflector is not only a complex fluid–solid coupling problem that is not easy to compute, but also a safety issue that seriously interferes with flight deck environment. The computational fluid dynamics (CFD) method is used to simulate numerically the impact effect of gas jet from aircraft engines on a jet blast deflector by using the Reynolds-averaged Navier-Stokes (RANS) equations and turbulence models. First of all, during the pre-processing of numerical computation, a sub-domains hybrid meshing scheme is adopted to reduce mesh number and improve mesh quality. Then, four different turbulence models including shear-stress transport (SST) k-w, standard k-w, standard k-ε and Reynolds stress model (RSM) are used to compare and verify the correctness of numerical methods for gas jet from a single aircraft engine. The predicted values are in good agreement with the experimental data, and the distribution and regularity of shock wave, velocity, pressure and temperature of a single aircraft engine are got. The results show that SST k-w turbulence model is more suitable for the numerical simulation of compressible viscous gas jet with high prediction accuracy. Finally, the impact effect of gas jet from two aircraft engines on a jet blast deflector is analyzed based on the above numerical method, not only the flow parameters of gas jet and the interaction regularity between gas jet and the jet blast deflector are got, but also the thermal shock properties and dynamic impact characteristics of gas jet impacting the jet blast deflector are got. So the dangerous activity area of crew and equipments on the flight deck can be predicted qualitatively and quantitatively. The proposed research explores out a correct numerical method for the fluid–solid interaction during the impact process of supersonic gas jet, which provides an effective technical support for design, thermal ablation and structural damage analysis of a new jet blast deflector.

Mesh smoothing of complex geometry using variations of cohort intelligence algorithm

Several approaches including optimization based methods were developed for mesh quality improvement using only node movement, keeping intact the element connectivity. In this research, a socio-inspired optimization approach referred to as cohort intelligence (CI) was investigated for mesh smoothing. Minimization of summation of condition numbers of all elements was the final aim. The geometrical boundaries of the object defined the surface and edge constraints for movement of external nodes. Movement of internal nodes was completely governed by variations of CI algorithm, viz. roulette wheel, follow best, follow better, alienation and random selection, follow worst and follow itself. The approach was demonstrated with pentagonal prism, hexagonal prism and hexagonal prism with hole. The performance of follow best and roulette wheel variations of CI algorithm was observed to be satisfactory as compared to other variations of the algorithm.

GETOpt mesh smoothing: Putting GETMe in the framework of global optimization-based schemes

We present a novel approach to mesh smoothing, called GETOpt, by using a variation of the Geometric Element Transformation Method (GETMe) which falls within the framework of global optimization-based schemes and mesh quality improvement methods. We introduce a global mesh quality measure, which is inspired by rigorous convergence results concerning the size of the geometric elements (non-degeneracy and comparable sizing) and whose gradient flow yields a combination of GETMe and Laplace smoothing. Under this scheme, it can be shown rigorously that the tetrahedral mesh never degenerates. Furthermore, numerical tests show that the sizing of the mesh elements become more comparable and that the FEM gives better approximations in case the PDE problem being solved demonstrates isotropic physical behavior. More specifically, we present in this article an example where the mesh is used to solve Poisson's equation using the standard Galerkin finite element method with piecewise linear and order 2 functions on the low-order mesh.

(Re-) Meshing using interpolative mapping and control point optimization

Abstract This work proposes a simple and fast approach for re-meshing the surfaces of smooth-featured geometries prior to CFD analysis. The aim is to improve mesh quality and thus the convergence and accuracy of the CFD analysis. The method is based on constructing an interpolant based on the geometry shape and then mapping a regular rectangular grid to the shape of the original geometry using that interpolant. Depending on the selected interpolation algorithm the process takes from less than a second to several minutes. The main interpolant discussed in this article is a Radial Basis Function with cubic spline basis, however other algorithms are also compared. The mesh can be optimized further using active (flexible) control points and optimization algorithms. A range of objective functions are discussed and demonstrated. The difference between re-interpolated and original meshes produces a metric function which is indicative of the mesh quality. It is shown that the method works for flat 2D surfaces, 3D surfaces and volumes. Highlights RBF Map is created between key points on an arbitrary shape and an ideal equivalent. The rest of the points are recreated using reverse transformation to the original. Control points are automatically selected based on k-mean clustering. Optimization of the control points position based on desired mesh quality metrics. The method is shown to work both on 2D and 3D shapes as well as 3D surfaces.