Hexahedral Mesh Generation Research Articles

Surrogate-based integrated design optimization for aerodynamic/stealth performance enhancements

The shape optimization considering both aerodynamic and radar stealth performances has been a considerable attention area for next-generation aircraft, with challenges involving balancing design contradictions and improving optimization efficiency. This paper develops a surrogate-based integrated design optimization method coupling Computational Fluid Dynamics (CFD) and Computational Electromagnetics (CEM) for aerodynamic/stealth performance enhancements. The topology-based 3D hexahedral mesh generation and 2D triangular mesh generation with adaptive refinement provide efficient preprocessing for CFD/CEM solvers. The surrogate-based optimization algorithm with parallel infill-sampling strategy and adaptive design space expansion is employed to search the global optimum and improve optimization efficiency while filtering out numerical noise. The Weighted Sum method is employed to address design contradictions in different disciplines. Optimizations considering aerodynamic, stealth, and aerodynamic/stealth performance of a flying wing aircraft are conducted to verify the effectiveness of the developed method. The optimization results indicate that exclusive consideration of a singular discipline leads to a significant deterioration in the performance of the other discipline. Balanced performance is achieved through coupling optimization. The numerical noise in the stealth discipline is markedly higher than in the aerodynamics discipline. The results demonstrate that the developed method is capable of addressing aerodynamic/stealth design optimization problems and significantly reducing the number of CFD/CEM evaluations while maintaining global optimization effectiveness.

Automatic decomposition of protrusion volumes on thin-shell models for hexahedral mesh generation

Automatic decomposition of protrusion volumes on thin-shell models for hexahedral mesh generation

A metrics-based polycube construction method for hexahedral mesh generation

A metrics-based polycube construction method for hexahedral mesh generation

Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing

We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.

Meso‐Skeleton Guided Hexahedral Mesh Design

AbstractWe present a novel approach for the generation of hexahedral meshes in a volume domain given its meso‐skeleton. This compact representation of the topology and geometry, composed of both curve and surface parts, is used to produce a raw decomposition of the domain into hexahedral blocks. Analysis of the different local configurations of the skeleton leads to the construction of a set of connection surfaces that are used as a scaffold onto which the hexahedral blocks are assembled. These local configurations of the skeleton completely determine the singularities of the final mesh, and by following the skeleton, the geometry of the produced mesh naturally follows the geometry of the domain. Depending on the end user needs, the obtained mesh can be further adapted, refined or optimized, for example to better fit the boundary of the domain. Our algorithm does not involve the resolution of any global problem, most decisions are taken locally and it is thus highly suitable for parallel processing. This efficiency allows the user to stay in the loop for the correction or edition of the meso‐skeleton for which a first sketch can be given by an existing automatic extraction algorithm.

Generation of adaptive hexahedral meshes from surface and voxel geometric models

We present a modification of the developed hexahedral mesh generator from voxel data which allows constructing adaptive computational meshes. Construction of the refinement field is based on geometry features of the described model when it has a large thickness difference in dimensions or small and thin areas. A universal criterion for cells refinement is proposed which gives the possibility of its use in the case of volumetric (voxel) and surface (STL) representations of the model geometry. The refinement templates that provide conformal mesh closure are described. The results of the algorithm performance are given.

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.

Automated geometry and hexahedral mesh generation for kilometer-scale atmospheric flow simulations

This article introduces a methodology for automatic generation of geometries and meshes for kilometer-scale Atmospheric Boundary Layer (ABL) flow simulations, with topography and elevation. The proposed programmatic (hence automatable) \emph{template morphing approach} facilitates interpolation of scattered point cloud terrain data on a template geometry domain, morphing a high-quality quadrilateral template mesh for the interpolated geometry, and setup as well as execution of Computational Fluid Dynamics (CFD) flow simulation. The proposed method specifically addresses the previously reported problems of sustaining an ABL structure across the simulation domain by imposing the velocity and turbulence properties on all vertical surfaces. We present a validation study for the proposed method on an artificial Gaussian hill terrain. A real-world localized wind forecast application from the Turku Archipelago, Finland, is also presented, using open terrain data from National Land Survey of Finland. Such localized wind forecasts aim to assist ships in autonomous navigation and maneuvering in complex port or fairway environments, which is the motivation for this study.

An Interactive Modeling Method for Complex Hexahedral Mesh Generation with Volumetric Subdivision

The existing methods are difficult to construct hexahedral meshes. To address this problem, an interactive construction method of complex hexahedral mesh model based on volumetric subdivision is presented. The user firstly needs to interactively construct the model skeleton, by placing cubes at the nodes of the skeleton structure, and performing interactive operations such as rotation, translation, and scaling of the node cubes. Then, through the connection between the nodes and the topological split operation, the initial control mesh can be constructed. Further, interpolatory Catmull-Clark volumetric subdivision method is used to generate hexahedral meshes with different resolutions. Finally, the padding operation is used to eliminate the degraded elements at the boundary and improve the quality of the hexahedral mesh elements to obtain the final hexahedral mesh. The results of numerical example show that the method can easily and efficiently generate hexahedral meshes interactively, and eliminates the intermediate steps of generating volume meshes from surface meshes. It has some practical applications in finite element analysis, isogeometric analysis and geometric modeling in animation.

Hex-Mesh Generation and Processing: A Survey

In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post-processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.

Hex Me If You Can.

HexMe consists of 189 tetrahedral meshes with tagged features and a workflow to generate them. The primary purpose of HexMe meshes is to enable consistent and practically meaningful evaluation of hexahedral meshing algorithms and related techniques, specifically regarding the correct meshing of specified feature points, curves, and surfaces. The tetrahedral meshes have been generated with Gmsh, starting from 63 computer-aided design (CAD) models from various databases. To highlight and label the diverse and challenging aspects of hexahedral mesh generation, the CAD models are classified into three categories: simple, nasty, and industrial. For each CAD model, we provide three kinds of tetrahedral meshes (uniform, curvature-adapted, and box-embedded). The mesh generation pipeline is defined with the help of Snakemake, a modern workflow management system, which allows us to specify a fully automated, extensible, and sustainable workflow. It is possible to download the whole dataset or select individual meshes by browsing the online catalog. The HexMe dataset is built with evolution in mind and prepared for future developments. A public GitHub repository hosts the HexMe workflow, where external contributions and future releases are possible and encouraged. We demonstrate the value of HexMe by exploring the robustness limitations of state-of-the-art frame-field-based hexahedral meshing algorithm. Only for 19 of 189 tagged tetrahedral inputs all feature entities are meshed correctly, while the average success rates are 70.9% / 48.5% / 34.6% for feature points/curves/surfaces.

The 3D Motorcycle Complex for Structured Volume Decomposition

AbstractThe so‐called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2‐manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi‐structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three‐dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher‐dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T‐spline construction.

Simulation of primary current distribution in Tesla-type pulse generators.

In a Tesla-type pulse generator, self-inductance of the primary coil is a crucial parameter to determine the final oscillating condition. However, the accurate value of this inductance might be changed due to the uneven primary current distribution caused by practical configuration of the primary side. Consequently, in order to precisely design the transformer, it is helpful to evaluate the primary inductance based on electromagnetic simulation instead of conventional approximate calculation. In this paper, a simulation model based on the finite integration technique is established to solve the uneven primary current problem. A primary coil with multiple contacting points is designed, and hexahedral mesh generation of the coil is also discussed. Hence, a series of verification tests using different primary structures are performed to support the results of simulation. Both results of the simulation model and the verification test presented that the variation of the primary inductance will affect the performance of the generator, and the number of contacting points is the main cause to determine the maximum current density of the coil.

A novel 3D anisotropic Voronoi microstructure generator with an advanced spatial discretization scheme

At the microstructural scale, Voronoi tessellations are commonly used to represent a polycrystalline morphology. However, due to spherical growth of nuclei, an anisotropic tessellation with spatially varying elongated grain directions, which is present in many applications, cannot be obtained. In this work, a novel 3D anisotropic Voronoi algorithm is presented, together with its implementation and two application cases. The proposed algorithm takes into account preferred grain growth directions, aspect ratios and sizes in the definition of an ellipsoidal growth velocity field defined per grain. For applications in which a predetermined mesh is used, e.g. voxel-mesh based simulations, the grains are extracted in a straight-forward manner. In cases where a fully grain conforming discretization is desired, e.g. finite element simulations, a hexahedral mesh generator is incorporated to arrive at a discretization which can be directly used in microstructural modeling simulations. Two application cases are studied (a wire + arc additively manufactured and a magnesium alloy microstructure) in which the algorithm’s capability for curved, non-convex, periodic domains is shown. Furthermore, the resulting grain morphology is compared to experimental data in terms of grain size, grain aspect ratio and grain columnar direction distribution. In both cases, the algorithm adequately produces a representative volume element with convincing representativeness of the experimental data. The 3D anisotropic Voronoi algorithm is highly versatile in a wide range of application cases, specifically suitable for the generation of polycrystalline microstructures that include grains with spatially varying elongated directions.

Curvature and Feature-Aware Print-Paths from Hexahedral Meshes for Additive Manufacturing

Recently proposed meshing techniques allow the generation of high-quality hexahedral meshes (hex-mesh) whose edges follow the surface feature and curvature-lines. This study investigates their use in additive manufacturing for the generation of curvature and feature-aware print-paths (tool-paths). A hex-mesh consists of 8-noded hexahedra (hex-cells) and a cuboid-like sub-volume is structured (i.e., valence for the inner edges is only four), which is represented using a three-dimensional (3D) array of hex-cells. All cuboid-like sub-volumes (called C-partitions) are first enumerated by growing them from singular-edges (i.e., a series of connected same-valence singular-edges that are not two on the boundary or four in the interior). These C-partitions are then selected one-by-one according to a cost function based on several criteria including alignment of print-paths along the feature curves and curvature directions. Remaining C-partitions are split if they intersect the (previously) selected C-partitions. The C-partitions are iteratively chosen and split until all hex-mesh is covered by the (selected) C-partitions. Print-paths are arranged along (predetermined) direction(s) in a C-partition, and tubes representing deposited material (in AM) around the print-path overlap at some locations. Thus, these tubes are repaired via tube adjustment operators, in which their location and material deposition radii at those locations are modified. As a proof of concept, curvature and feature-aware print-paths are finally validated using an AM simulator and machine.

A modification of the hexahedral mesh generator based on voxel geometry representation

We consider a modification of the previously developed voxel-based mesh algorithm to generate models given in STL-geometry format. Proposed hexahedral mesh generator belongs to the family of grid methods, and is general-purpose in terms of a capability to use as source data both volume (voxel) and STL-surface representation of model geometry. For now, the algorithm works with CAD models described in the well-known STL format. However, it also allows to handle higher-order surface patches defined in an arbitrary format if appropriate procedures for projection and intersection operations will be specified. To define the initial position of mesh nodes, a “signed distance field” volume data file, obtained from the STL-geometry, is used. A special projection technique was developed to adapt constructed orthogonal mesh on the model's boundary. It provides an approximation of sharp edges and corners and is performed before running any other operations with the mesh. Finally, to improve the quality of the mesh, additional procedures were implemented, including boundary layers insertion, bad quality cells splitting, and optimization-based smoothing technique. The algorithm has been tested on a sufficient number of models, some of which are given as examples.

Transient gear contact simulations using a floating frame of reference approach and higher-order ansatz functions

Gear drives are crucial components for a wide range of devices such as combustion engines and wind turbines. Predictions of durability, transmission errors, and noise emission are required already during early development. To that end, deformations, velocities, stresses, and contact forces can be analyzed using numerical simulations. For this, finite element analyses (FEA) or multibody system (MBS) simulations can be used. Yet, rigid MBS can be inaccurate since contact forces must be estimated using a heuristic force–displacement law since no deformations are available. Also, the need for elaborate manual tuning of contact parameters is a drawback. FEA, on the other hand, bring about long computation times that make them inappropriate for the analysis of transient phenomena. Further, a bottleneck of FEA for gears is the expensive human labor that is necessary to generate hexahedral meshes required for contact detection. Both quadratically and linearly interpolating tetrahedral meshes can be generated quickly and reliably. Tet4 elements, however, are not a viable option due to their inferior performance. Thus, as a remedy to (i) the parametrization issues and the inaccuracy inherent while using rigid MBS descriptions, (ii) the long simulation times of FEA, and (iii) the issue of expensive manual generation of hexahedral meshes, we propose using elastic multibody systems with quadratic tetrahedral meshes for dynamic contact simulations. The novelty of this contribution is the use of quadratic ansatz functions for the description of both geometry and contact calculation in combination with a floating frame of reference formulation and model order reduction.

Thermal Stress Analysis for High CRI LED Indoor Lighting Module

AbstractThis research is for developing a new light emitting diode (LED) indoor lighting module with high color rendering index greater than 95. When the LED is operated, electrical energy is generated and heat is released. The failing of heat dispersal degrades the performance and decreases the operating life. To manage the thermal problem effectively, several approaches have been tested in this research study. A heat sink is designed to absorb and transfer heat from the LED module. To analyze the heat flow and thermal stress of the designed LED products effectively, hexahedral mesh generation has been implemented. Heat transfer analysis was performed to find an optimal conductive material. The outcomes of this research study suggest the best material for LED products and show the result of thermal transfer simulation.

Hierarchical template-based hexahedral mesh generation

This work describes a hexahedral mesh generation algorithm ideally suited for transition subdomain meshes in the context of any domain decomposition meshing strategy. The algorithm is based on an automatic hierarchical region decomposition in which, in the last level, it is possible to generate hexahedral elements with a conventional mapping strategy. Templates usually impose restrictions on meshes on boundary surfaces of a subdomain to be meshed. The proposed hierarchical template scheme eliminates many of these restrictions, creating more options in surface meshes and mesh refinement as input boundary data. This work implements four basic templates for volumes that should be simplified by a unit box. The volume decomposition is performance using a cube-shaped parametric space in the local coordinate system. The algorithm decomposes hierarchically a volume until all volumes should be mappable to generate elements by the 3D mapping approach. Examples demonstrate that this idea may result in structured meshes in complex geometries.

Subject specific hexahedral Finite Element mesh generation of the pelvis from bi-Planar X-ray images

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. A full hexahedral subject-specific FE mesh was generated with an accurate surface representation.