Mesh Generation Algorithm Research Articles

A parametric approach for creating finite element models from point clouds for steel superstructure components in steel girder bridges

Finite element (FE) analysis is widely used to evaluate the conditions of existing bridges. However, the creation of high-fidelity FE models (FEM) for existing bridges is often a challenging task. In view of the ability of 3D laser scanning to capture detailed geometrical information, this study proposes a direct scan-to-FEM strategy specifically for steel bridge superstructure and hence to facilitate the creation of high-fidelity FE models for existing steel girder bridges. Parametric representations are proposed to address partial occlusions in the point clouds as well as to reinforce the connectivity and alignment between the superstructure elements. Mesh generation algorithms are developed to automatically convert the parametric representations into all-hexahedron FE mesh assembly that can be used directly for FE analysis without any mesh verification or editing. Experimental validations are carried out to evaluate the effectiveness of proposed method in term of both mesh quality and analysis accuracy.

Finite element mesh transition for local–global modeling of composite structures

This study presents an automatic mesh generation algorithm designed to address computational challenges in simulating small-scale defects within large composite structures. The algorithm seamlessly transitions from a coarse mesh, corresponding to the global structure, to a highly refined mesh in targeted local regions of interest. The transition element number and shape can be adjusted by the specified parameters. Tailored to complement this method for non-homogeneous composite models, which include multiple materials such as cohesive layers representing interlayer properties, a volume fraction calculator is integrated to automatically assign the mixture material property in each transition element. Entire processes are fully automated using a MATLAB script, eliminating the need to open the FEA software interface. The validation studies of the reconstructed two-dimensional models, assembled with the wrinkle-defect model, demonstrate their feasibility. The performance of the model is examined in terms of strain and displacement at the connecting boundaries, load–displacement curve, and interlayer failure prediction. The mesh transition model achieves agreeable results compared to a fully fine mesh model, and a 92% reduction in computational time in stress analysis, showing the efficiency of the mesh transition for local–global modeling of composite structures.

Geometry import into virtual reality visualization engine for HEP experiments at BM@N

Modern visualization and multimedia platforms, such as Unity, provide immersive interaction for HEP experiment data analysis. In this work, we present the method for importing the detector geometry, solids hierarchy, and materials from GDML format directly to Unity. This method is based on parsing files in GDML format and generating the geometry using mesh generation algorithms and Constructive Solid Geometry methods. The provided method is applied to the BM@N experiment at NICA accelerator complex in Joint Institute of Nuclear Research and can be used in virtual reality and augmented reality applications for data analysis and outreach events in high energy physics experiments.

An improved dynamic bidirectional coupled hydrologic–hydrodynamic model for efficient flood inundation prediction

Abstract. To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction.

Microstructure generation and full-field multi-scale analyses for short fiber reinforced thermoplastics: Application to PA66GF composites

Short Fiber Reinforced Thermoplastics (SFRTs) like PA66GF composites are highly heterogeneous materials with a rather complex microstructure such that the characterization and the prediction of their mechanical behavior remain quite challenging. So far, most of the research efforts have employed phenomenological and mean-field multi-scale models to deal with SFRTs. The present contribution rather focuses on a full-field multi-scale approach that incorporates advanced techniques in terms of microstructural representation and material modeling, allowing a deep insight of the dominating deformation mechanisms occurring in PA66GF composites. The proposed approach is based on an automatic periodic mesh generation algorithm for matrix-inclusion Representative Volume Elements (RVE) with randomly positioned fibers that follow a given Orientation Distribution Function (ODF). At the microscopic scale, while the fibers are assumed to be elastic, the behavior of the thermoplastic matrix is described by a phenomenological multi-mechanism constitutive model accounting for viscoelasticity, viscoplasticity and ductile damage. It results an advanced multi-scale model that enables to visualize the local deformation and degradation mechanisms occurring at the microscopic scale while simultaneously analyzing their influence on the macroscopic response of the composite upon monotonic, persistent and cyclic loading. The potential of the proposed approach is further evaluated by comparing the predicted responses against experimental data.

An efficient unstructured quadrilateral-dominated surface mesh generation method for arbitrary geometry with tiny features or crack defects in DiBFM

An efficient unstructured quadrilateral-dominated surface mesh generation algorithm is presented to generate high-quality surface elements for arbitrary geometry with tiny features or crack defects. For complex entities with proximity features, a novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. The algorithm also works for regions with proximity features, as well as for arbitrary geometry with one or multiple cracks. The procedure incorporates aspects of well-known meshing techniques, but includes some original and efficient processes. The refinement field is constructed according to mesh size, boundary curvature, surface curvature and other geometry features. In order to effectively generate the core mesh, a fast intersection algorithm between topological elements and the solid boundary is established, which improves the efficiency of intersection calculation. The geometry-based techniques are employed for boundary matching of the core mesh. The method has been successfully employed in conjunction with the dual interpolation boundary face method (DiBFM). Several realistic geometries with cracks or proximity features are applied to demonstrate the accuracy and validity of the proposed approach.

Algorithmic analysis and application of structural tessellation in design and optimization

This paper explores the application of structural tessellation in architectural and structural design, where surfaces or spaces are divided into smaller repeating shapes or units to create aesthetic and functional structures. Structural tessellation offers various advantages, including improved stability, increased load-bearing capacity, and enhanced aesthetic appeal. The growing use of digital tools and advanced numerical algorithms has facilitated the creation of complex and intricate tessellations that can be tailored to suit specific project requirements. This research focuses on algorithmic methods for generating tessellations and their utilization in structural engineering and design optimization. Diverse patterns and configurations of tessellation are investigated through mesh generation algorithms, parametric approaches, and pattern gradation and repetitions, with data visualization accomplished using computing scripts and Grasshopper. The tessellation elements are employed to discretize the design domain in structural optimization and create initial patterns. The paper demonstrates the feasibility of proposed frameworks for structural design and application through the examination of various numerical examples. In conclusion, the strategic use of structural tessellation proves to be effective in producing unique and functional structures that seamlessly combine visual appeal with material and resource efficiency.

A node moving-based structural topology optimization method in the body-fitted mesh

The work presents a node-moving algorithm for topology optimization (NMTO) in the arbitrarily shaped design domain. Also, we further enhanced a body-fitted mesh generation algorithm to express smooth boundaries more efficiently. In each optimization iteration, a narrowband offset from the structural profile is established, based on which a signed-distance function is constructed to determine the node-moving direction. At the same time, the magnitude of node velocity is derived from the shape derivative of the objective function - the sum of mean compliance and mean curvature. After the signed-distance function is updated based on the new position of the nodes within the narrowband with the abovementioned velocity, boundaries implicitly represented by its zero-level contour are obtained naturally. Such a forward Euler updating scheme is much more efficient than the well-known upwind algorithm for the body-fitted mesh as it avoids the interpolation of triangular nodes to the rectangular nodes and a small time step. Compared with other methods, benchmark numerical examples demonstrate that the proposed method can produce elegant structures with smoother boundaries and better objective functions for optimization problems seeking maximal stiffness or displacement at a prescribed node. In addition, the proposed approach prevents, to a large extent, useless void parts from being included in the time-consuming finite element analysis.

Wake characteristics of a balloon wind turbine and aerodynamic analysis of its balloon using a large eddy simulation and actuator disk model

Abstract. In the realm of novel technologies for generating electricity from renewable resources, an emerging category of wind energy converters called airborne wind energy systems (AWESs) has gained prominence. These pioneering systems employ tethered wings or aircraft that operate at higher atmospheric layers, enabling them to harness wind speeds surpassing conventional wind turbines' capabilities. The balloon wind turbine is one type of AWESs that utilizes the buoyancy effect to elevate the turbine to altitudes typically ranging from 400 to 1000 m. In this paper, the wake characteristics and aerodynamics of a balloon wind turbine were numerically investigated for different wind scenarios. Large eddy simulation, along with the actuator disk model, was employed to predict the wake behavior of the turbine. To improve the accuracy of the simulation results, a structured grid was generated and refined by using an algorithm to resolve about 80 % of the local turbulent kinetic energy in the wake. Results contributed to designing an optimized layout of wind farms and stability analysis of such systems. The capabilities of the hybrid large eddy simulation and actuator disk model (LES–ADM) when using the mesh generation algorithm were evaluated against the experimental data on a smaller wind turbine. The assessment revealed a good agreement between numerical and experimental results. While a weakened rotor wake was observed at the distance of 22.5 diameters downstream of the balloon turbine, the balloon wake disappeared at about 0.6 of that distance in all the wind scenarios. Vortices generated by the rotor and balloon started to merge at the tilt angle of 10∘, which intensified the turbulence intensity at 10 diameters downstream of the turbine for the wind speeds of 7 and 10 m s−1. By increasing the tilt angle, the lift force on the wings experienced a sharper increase with respect to that of the whole balloon, which signified a controlling system requirement for balancing such an extra lift force.

An Interface-Fitted Fictitious Domain Finite Element Method for the Simulation of Neutrally Buoyant Particles in Plane Shear Flow

In this paper, an interface-fitted fictitious domain finite element method is developed for the simulation of fluid–rigid particle interaction problems in cases of rotated particles with small displacement, where an interface-fitted mesh is employed for the discrete scheme to capture the fluid–rigid particle interface accurately, thereby improving the solution accuracy near the interface. Moreover, a linearization and decoupling process is presented to release the constraint between velocities of fluid and rigid particles in the finite element space, and to make the developed numerical method easy to be implemented. Our numerical experiments are carried out using two different moving interface-fitted meshes; one is obtained by a rotational arbitrary Lagrangian–Eulerian (ALE) mapping, and the other one through a local smoothing process among interface-cut elements. A unified velocity is defined in the entire domain based on the fictitious domain method, making it easier to develop an interface-fitted mesh generation algorithm in a fixed domain. Both show that the proposed method has a good performance in accuracy for simulating a neutrally buoyant particle in plane shear flow. This approach can be easily extended to fluid–structure interaction problems involving fluids in different states and structures in different shapes with large displacements or deformations.

Auto Mesh generation algorithm for the convex domain with the triangular elements

Mesh creation is one of the primary tasks in implementing the Finite Element Method (FEM) to solve two- and three-dimensional boundary value problems. However, the whole procedure becomes tedious and problematic when higher-order finite elements are employed to construct mesh and prepare corresponding element data. In this study, we strive to develop a versatile algorithm for discretizing the two-dimensional domain using linear, quadratic, and cubic triangular finite elements. The algorithm is developed based on n vertices (actual or more in number) that constitute the boundary of the domain, along with a computed (n+1)-th point such as the centroid. The algorithm, using this input, generates an initial mesh consisting of n triangular elements. Then, in every subsequent step, the algorithm increases the number of triangles in the mesh fourfold compared to the previous step. The algorithm we present here can employ (a) straight-sided (linear, quadratic, and cubic) triangular elements to generate the mesh for domains with polygonal boundaries and (b) both straight-sided and curved (quadratic and cubic) triangular elements with two straight sides and one curved side to generate meshes for domains with curved boundaries. Thus, the algorithm generates the desired meshes if the vertices are specified once at the initial step. Additionally, the inclusion of the mathematical expression of the curved boundary enables the algorithm to generate the fine mesh for the curved domain utilizing higher-order curved and straight-sided triangular elements. We also present a computer code in MATLAB incorporating the algorithm to create the mesh, prepare the element's data, and determine the element's connectivity.
 GANIT J. Bangladesh Math. Soc. 43.1 (2023) 017- 035

Locally Meshable Frame Fields

The main robustness issue of state-of-the-art frame field based hexahedral mesh generation algorithms originates from non-meshable topological configurations, which do not admit the construction of an integer-grid map but frequently occur in smooth frame fields. In this article, we investigate the topology of frame fields and derive conditions on their meshability, which are the basis for a novel algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 58%, when compared on the challenging HexMe dataset [Beaufort et al. 2022]. The source code of our implementation and the data of our experiments are available at https://lib.algohex.eu.

Reynolds stresses and turbulent heat fluxes in fan-shaped and cylindrical film cooling holes

Large eddy simulation (LES) is carried out to predict the thermal performance, unsteady flow patterns, and turbulence characteristics of the fan-shaped hole and the cylindrical hole cooling films. Velocity fields, Reynolds stresses, and turbulent heat flux distributions are the factors that ultimately determine the film cooling effectiveness by deciding the concentration of coolant and heat near the surface. Accurate prediction of these processes can provide a reliable data set for the design of film cooling systems. It can also help solve difficulties of improving RANS-based simulations in terms of their inaccuracies in matching measured flow rates for a given pressure drop across the film and the mixing process once the coolant is ejected from the film. Credible estimates and modest costs of the current LES originate from the multiblock hexahedra meshing, the turbulence inflow generator, and the numerical schemes implemented. Multiblock hexahedra meshes are adopted and generated by a quasi-automatic mesh generation algorithm utilizing template-based multi-block construction followed by elliptic smoothing. Computational resources are utilized in a way that mesh refinement exists only near cooling decorations of small size and wall boundaries, without the need for associated clustering in the far field which is commonly used in commercial packages. The high orthogonality and continuous smoothness throughout the computational domain are maintained to facilitate turbulence capturing. The synthetic inflow generator produces a random field matching a realistic set of two-point statistics based on eigen-reconstruction in a computationally inexpensive processing step. To prove that the current LES simulations of modest cost can reproduce with high accuracy, the discharge characteristics, velocity, and turbulence intensity profiles of cylindrical and fan-shaped cooling films are compared with published measured data on the same flow configurations. Results reveal that the set of modeling methodologies is valid for calculating film-cooling performance within an acceptable range of accuracy. The energy-carrying turbulence structures in and near the cooling holes are shown and their behaviors are linked to turbulent Reynolds stresses. Reynolds stresses and turbulent heat fluxes are compared for different blowing ratios and two types of cooling holes in the parametric study. Similarity patterns of velocity profiles, non-dimensional temperature profiles, Reynolds stress and turbulent heat flux profiles are discussed.

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det⁡∇ψ(x,t)=G∘ψ(x,t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near-identity deformations of a reference mesh. Then, we formulate a new version of the deformation method [21] that results in a simple, fast, and high-order accurate numerical scheme and a dynamic SAM algorithm that is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging 2D and 3D mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22,18], while running approximately 200 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2D gas dynamics. Specifically, we implement the C-method [64,65] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs.

Robo-vision! 3D mesh generation of a scene for a robot for planar and non-planar complex objects.

This paper presents a novel architecture to generate a world model in terms of mesh from a continuous image stream with depth information extracted from a robot's ego-vision camera. We propose two algorithms for planar and non-planar mesh generation. A Cartesian grid-based mesh fitting algorithm is proposed for mesh generation of planar objects. For mesh generation of non-planar objects, we propose a Self Organization Map based algorithm. The proposed algorithm better approaches the boundary and overall shape of the objects compared to State-Of-the-Art (SOA). Extensive experiments done on three public datasets show that our method surpasses SOA both qualitatively and quantitatively.

MatFEA: Efficient Finite Element Framework for Analyzing Pavement Structures With Nonlinear Unbound Materials

This paper reports the details of a computationally efficient finite element analysis code (called MatFEA), designed specifically for flexible pavements, where stress-dependent characteristics of unbound layers are considered. The stress-dependent nonlinearity of the unbound materials has been modeled in MatFEA through an iterative approach. MatFEA was mainly developed to improve the Mechanistic-Empirical Asphalt Pavement Analysis (MEAPA) web application with capability of analysis/design of nonlinear pavement structures. A specific-purpose mesh generation algorithm was developed for the MatFEA in which the mesh density was dynamically adjustable based on the expected stress magnitude. To verify the results of the MatFEA, 12,000 nonlinear pavement structures with different structural and loading properties were generated and analyzed with MatFEA. The same pavement structures were modeled in a general-purpose FE-based ABAQUS™ program. The results of this study showed that the critical pavement structural responses from the MatFEA were almost identical with those modeled by ABAQUS™ program. The average runtime of MatFEA for analyzing each pavement structure was about 1.13 s. Finally, it was concluded that application of the dynamically adjustable mesh generation algorithm in the MatFEA helped achieve a reasonably high accuracy as well as efficient runtime, which brings the advantage of implementing the MatFEA as a pavement structural response model in the mechanistic-empirical pavement analysis/design procedures.

Floating Point Genetic Algorithm Approach for Optimizing Unstructured Meshes

This paper presents a method for optimizing unstructured triangular meshes using a floating-point genetic algorithm. A mesh generation algorithm based on a modified advancing front method and sets of heuristic rules are used to generate the initial non-smooth triangular meshes for complex shapes. The developed mesh is then smoothed using a floating-point genetic algorithm that is more flexible than the usual binary genetic algorithms, and can handle non-smooth regions containing several local extrema. Three approaches are used in selecting the fitness function to be optimized in the genetic algorithm, namely, the triangle aspect ratio, the maximum angle at each node of the triangular mesh, and a weighted linear combination of both functions. The genetic algorithm has been tested and validated for a number of test cases covering a wide range of complex geometry applications. The results have shown a high degree of improvement in the quality of the smoothed meshes and an ability to handle non-convex regions.

An Unstructured Mesh Generation Algorithm for Arbitrary Geometry with Proximity Features

An Unstructured Mesh Generation Algorithm for Arbitrary Geometry with Proximity Features

On the Efficiency of the Advancing-Front Surface Mesh Generation Algorithm

An efficient advancing front algorithm is presented to create high-quality surface elements on CAD models. Various novel schemes are developed to improve the efficiency of the algorithm while not sacrificing its robustness and the resulting mesh quality. New features include a fast projection scheme that can perform robustly in case of badly defined surfaces, a procedure that computes the ideal point by an approach that can preserve the advantageous features of both the mapping and direct methods, and an octree data structure that can speed up the local search of all existing front nodes about the ideal point. To our knowledge, the proposed algorithm is one of the fastest algorithms for surface mesh generation. On an AMD Ryzen 5 3600 machine, the sequential version of the proposed algorithm can create a quality mesh at a speed of up to 100,000 elements per second. This speed is more than 3 times higher than a state-of-the-art code can achieve. Another advantage of the proposed algorithm is its ability to maintain its high efficiency when millions or more elements are created on one single surface. In this circumstance, the efficiency of some state-of-the-arts codes slows down by one or two orders. After parallelized based on the taskflow approach, the proposed algorithm can create more than 1.6 million elements on real-world configurations in 7 s by using 6 computer cores. This speed is higher than a state-of-the-art commercial code can achieve by one order. • An efficient surface mesh generator for large-scale triangular mesh generation of industrial CAD models, which is far faster than existing schemes. • The nonlinear calculation such as orthogonal projection and ideal point calculation is comprehensively improved. • Traditional surface mesh generation methods such as direct method and mapping method are combined. • The design of spatial index data structure (octree and AD tree) makes the algorithm have strong scalability.

Declarative Specification for Unstructured Mesh Editing Algorithms

We introduce a novel approach to describe mesh generation, mesh adaptation, and geometric modeling algorithms relying on changing mesh connectivity using a high-level abstraction. The main motivation is to enable easy customization and development of these algorithms via a declarative specification consisting of a set of per-element invariants, operation scheduling, and attribute transfer for each editing operation. We demonstrate that widely used algorithms editing surfaces and volumes can be compactly expressed with our abstraction, and their implementation within our framework is simple, automatically parallelizable on shared-memory architectures, and with guaranteed satisfaction of the prescribed invariants. These algorithms are readable and easy to customize for specific use cases. We introduce a software library implementing this abstraction and providing automatic shared-memory parallelization.