Hex-dominant Mesh Research Articles

Computational investigation of plasma arc welding process for aluminium alloys

Thermal stress is a very common phenomenon that occurs at the welded joint. Determination of the same at the joint is however difficult due to inhomogeneity of the weld joint metals and spreading of heat to the surroundings from the Heat Affected Zone (HAZ). Thermal stress induced at the welded joint changes the microstructure of grains which affects the mechanical properties of the welded material. Due to this, cracks may appear in the joint leading to failure of the weld. In the present study, three-dimensional model of two types of welded joint, i.e., Tee Joint and lap joint of two plates having dimensions 100 mm × 75 mm × 5 mm are prepared using ANSYS Workbench 2020 R2. Hex dominant meshing is chosen in order to have clear picture of the spread of temperature over the entire region. The change of Residual stress with variation of welding current and keeping welding voltage constant is also observed for weld joint made of Aluminium Alloy. In this study, conduct steady-state thermal analysis and structural analysis on an aluminium alloy 6063 to assess von Mises stress, von Mises strain, and deformation distribution induced by heating. Evaluate various welding joints to identify the most effective technique.

Hybrid Base Complex: Extract and Visualize Structure of Hex-dominant Meshes.

Hex-dominant mesh generation has received significant attention in recent research due to its superior robustness compared to pure hex-mesh generation techniques. In this work, we introduce the first structure for analyzing hex-dominant meshes. This structure builds on the base complex of pure hex-meshes but incorporates the non-hex elements for a more comprehensive and complete representation. We provide its definition and describe its construction steps. Based on this structure, we present an extraction and categorization of sheets using advanced graph matching techniques to handle the non-hex elements. This enables us to develop an enhanced visual analysis of the structure for any hex-dominant meshes.We apply this structure-based visual analysis to compare hex-dominant meshes generated by different methods to study their advantages and disadvantages. This complements the standard quality metric based on the non-hex element percentage for hex-dominant meshes. Moreover, we propose a strategy to extract a cleaned (optimized) valence-based singularity graph wireframe to analyze the structure for both mesh and sheets. Our results demonstrate that the proposed hybrid base complex provides a coarse representation for mesh element, and the proposed valence singularity graph wireframe provides a better internal visualization of hex-dominant meshes.

Metric-Driven 3D Frame Field Generation.

Controlling the size and shear of elements is crucial in pure hex or hex-dominant meshing. To this end, non-orthonormal frame fields that are almost everywhere integrable (except for the singularities) can play a key role. However, it is often challenging or impossible to generate such a frame field under the tight control of a general Riemannian metric field. Therefore, we propose to solve a relatively weaker problem, i.e., generating such a frame field for a Riemannian metric field that is flat away from singularities. Such a metric field admits a local isometry to 3D Euclidean space. Applying Cartans first structural equation to the associated rotation field, i.e., the rotation part of the frame field, we show that the rotation field must have zero covariant derivatives under the 3D connection induced by the metric field. This observation leads to a metric-aware smoothness measure, equivalent to local integrability. The use of such a measure can be justified on meshes associated with locally flat metric fields. We also propose a method to generate smooth metric fields under a few intuitive constraints. On cuboid shapes, our method generates singularities aware of the metric fields, which makes the parameterization match the input metric fields better than the conventional methods. For generic shapes, while our method generates visually similar results to those using boundary frame fields to guide the metric field generation, the integrability and consistency of the metric fields are still improved, as reflected by the statistics.

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.

LoopyCuts

We present a new fully automatic block-decomposition algorithm for feature-preserving, strongly hex-dominant meshing, that yields results with a drastically larger percentage of hex elements than prior art. Our method is guided by a surface field that conforms to both surface curvature and feature lines, and exploits an ordered set of cutting loops that evenly cover the input surface, defining an arrangement of loops suitable for hex-element generation. We decompose the solid into coarse blocks by iteratively cutting it with surfaces bounded by these loops. The vast majority of the obtained blocks can be turned into hexahedral cells via simple midpoint subdivision. Our method produces pure hexahedral meshes in approximately 80% of the cases, and hex-dominant meshes with less than 2% non-hexahedral cells in the remaining cases. We demonstrate the robustness of our method on 70+ models, including CAD objects with features of various complexity, organic and synthetic shapes, and provide extensive comparisons to prior art, demonstrating its superiority.

Computational fluid dynamics simulation to compare large volume irrigation and continuous spraying during nasal irrigation.

Nasal irrigation is now widely recognized as a treatment for chronic rhinosinusitis and during the postoperative period. However, there are no guidelines for performing irrigation. This study used computational fluid dynamics (CFD) simulation objective physical parameters to optimize and increase the efficiency of nasal irrigation and to compare large-volume, manual, and gravity pressure irrigation vs small-volume continuous spraying. A 3-dimensional (3D) sinonasal model was constructed from a healthy adult high-resolution computed tomography (CT) scan. The 3D nasal model was constructed using a tetrahedral and hex-dominant mesh grid with TGRID™ 16 (ANSYS Inc., Villeurbanne, France) software. A structured hex mesh was created inside the domain using the Hexcore meshing method. The final mesh had a total of 9.6 × 106 cells with an average size of 0.29 mm3 , or an average volume of 2.42 × 10-2 mm3 . Navier-Stokes equations were resolved with the standard k - ε model. Large-volume irrigation (15 mL/s) covered all zones (136 to 310 cm2 ) rapidly with strong shear stress and prolonged contact time (310 mPa 3.26 seconds for gravity mode and 280 mPa 3.35 seconds for manual pressure mode). Continuous spraying (3 mL/second) covered all areas (76 to 310 cm2 ) but with far less volume, more slowly, with low shear stress (50 mPa), and with shorter contact time (1.84 seconds). The surface wetted by time in contact was 135.4, 113.9, and 46.6 cm2 for gravity, manual pressure mode, and continuous spraying, respectively. CFD simulation visualizes the circulation of water during nasal irrigation and makes it possible to determine objective parameters to decide which mode of irrigation may be used.

Identifying combinations of tetrahedra into hexahedra: A vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra, prisms and pyramids. In this paper we introduce an algorithm that performs this identification and builds the set H of all possible combinations of tetrahedral elements of an input mesh T into hexahedra, prisms, or pyramids. All identified cells are valid for engineering analysis. First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed. The subset of tetrahedra of T triangulating each potential cell is then determined. Quality checks allow to early discard poor quality cells and to dramatically improve the efficiency of the method. Each potential hexahedron/prism/pyramid is computed only once. Around 3 millions potential hexahedra are computed in 10 s on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.

Hex-dominant meshing: Mind the gap!

We propose a robust pipeline that can generate hex-dominant meshes from any global parameterization of a tetrahedral mesh. We focus on robustness in order to be able to benchmark different parameterizations on a large database. Our main contribution is a new method that integrates the hexahedra (extracted from the parameterization) into the original object. The main difficulty is to produce the boundary of the result, composed of both faces of hexahedra and tetrahedra. Obviously, this surface must be a good approximation of the original object but, more importantly, it must be possible to remesh the volume bounded by this surface minus the extracted hexahedra (called void). We enforce these properties by carefully tracking and eliminating all possibilities of failure at each step of our pipeline.We tested our method on a large collection of objects (200+) with different settings. In most cases, we obtained results of very good quality as compared to the state-of-the-art solutions. To ease reproducing our results and benchmarks, we provide a C++ implementation of the pipeline in the supplemental materials.

Robust hex-dominant mesh generation using field-guided polyhedral agglomeration

We propose a robust and efficient field-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding fields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The field design phase of our method relies on a compact quaternionic representation of volumetric octa-fields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses field-guided mesh simplification to convert the optimized fields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the benefits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results.

Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra. In this paper we introduce an algorithm that performs this identification and builds the set H of all possible combinations of tetrahedral elements of an input mesh T into hexahedra. All identified hexahedral elements are valid for engineering analysis. The new method first computes all combinations of eight vertices whose connectivity in T matches the connectivity of a hexahedron. The subset of tetrahedra of T triangulating each potential hexahedron is then determined. Quality checks allow to early discard poor quality hexahedra and to dramatically improve the efficiency of the method. Each potential hexahedron is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes H built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.

Frame field smoothness-based approach for hex-dominant meshing

An indirect approach for building hex-dominant meshes is proposed: a tetrahedral mesh is constructed at first and is recombined to create a maximum amount of hexahedra. The efficiency of the recombination process is known to significantly depend on the quality of the sampling of the vertices. A good vertex sampling depends itself on the quality of the underlying frame field that has been used to locate the vertices. An iterative procedure to obtain a high quality three-dimensional frame field is presented. Then, a new point insertion algorithm based on a frame field smoothness is developed. Points are inserted in priority in smooth frame field regions. The new approach is tested and compared with simpler strategies on various geometries. The new method leads to hex-dominant meshes exhibiting either an equivalent or a larger volume ratio of hexahedra (up to 20%) compared to the frontal point insertion approach.

LayTracks3D: A new approach for meshing general solids using medial axis transform

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.

Statics Aware Grid Shells

AbstractWe introduce a framework for the generation of polygonal gridshell architectural structures, whose topology is designed in order to excel in static performances. We start from the analysis of stress on the input surface and we use the resulting tensor field to induce an anisotropic nonEuclidean metric over it. This metric is derived by studying the relation between the stress tensor over a continuous shell and the optimal shape of polygons in a corresponding gridshell. Polygonal meshes with uniform density and isotropic cells under this metric exhibit variable density and anisotropy in Euclidean space, thus achieving a better distribution of the strain energy over their elements. Meshes are further optimized taking into account symmetry and regularity of cells to improve aesthetics. We experiment with quad meshes and hexdominant meshes, demonstrating that our gridshells achieve better static performances than stateoftheart gridshells.

Indirect unstructured hex-dominant mesh generation using tetrahedra recombination

Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to generate a hex-dominant mesh conformal to 3D geological surfaces and well paths suitable for finite-element and control-volume finite-element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms, and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm (Meshkat and Talmor Int. J. Numer. Meth. Eng. 49(1-2), 17–30 2000) that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem (Bomze et al. 1999), known to be $\mathcal {N}\mathcal {P}$ -Complete. We propose several heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on 3D geological models including a faulted and folded model and a discrete fracture network.

A Comparison of High Order Interpolation Nodes for the Pyramid

The use of pyramid elements is crucial to the construction of efficient hex-dominant meshes [M. Bergot, G. Cohen, and M. Duruflé, J. Sci. Comput., 42 (2010), pp. 345--381]. For conforming nodal finite element methods with mixed element types, it is advantageous for nodal distributions on the faces of the pyramid to match those on the faces and edges of hexahedra and tetrahedra. We adapt existing procedures for constructing optimized tetrahedral nodal sets for high order interpolation to the pyramid with constrained face nodes, including two generalizations of the explicit warp and blend construction of nodes on the tetrahedron [T. Warburton, J. Engrg. Math., 56 (2006), pp. 247--262]. Comparisons between nodal sets show that the lowest Lebesgue constants are given by warp and blend nodes for order $N\leq 7$ and Fekete nodes for $N>7$, though numerical experiments show little variation in the conditioning and accuracy of all surveyed nonequidistant points.

Geometric Representation of Flow Features Using the Medial Axis for Mesh Generation

A method to represent complex flow features as geometric entities, using the medial axis for the purpose of generating flow-feature aligned meshes, is presented. These geometric entities are embedded into the domain to influence the generation of unstructured quad-dominant surface meshes in two and three dimensions. The resulting high-quality feature-aligned surface meshes can locally mimic the attributes of a structured grid. This paper also presents a method to extrude shock-aligned quad-dominant surface meshes beyond the boundary layer to cover the extent of transonic shock waves. The process provides a means to embed a high-quality hex-dominant mesh block, aligned with the transonic shock wave, into a hybrid volume mesh for viscous computations. Inclusion of the aligned mesh block is shown to enhance the ability of the hybrid mesh to resolve the shock wave, and thus, improve the numerical solution.

Cell packing structures

This paper is an overview of architectural structures which are either composed of polyhedral cells or closely related to them. We introduce the concept of a support structure of such a polyhedral cell packing. It is formed by planar quads and obtained by connecting corresponding vertices in two combinatorially equivalent meshes whose corresponding edges are coplanar and thus determine planar quads. Since corresponding triangle meshes only yield trivial structures, we focus on support structures associated with quad meshes or hex-dominant meshes. For the quadrilateral case, we provide a short survey of recent research which reveals beautiful relations to discrete differential geometry. Those are essential for successfully initializing numerical optimization schemes for the computation of quad-based support structures. Hex-dominant structures may be designed via Voronoi tessellations, power diagrams, sphere packings and various extensions of these concepts. Apart from the obvious application as load-bearing structures, we illustrate here a new application to shading and indirect lighting. On a higher level, our work emphasizes the interplay between geometry, optimization, statics, and manufacturing, with the overall aim of combining form, function and fabrication into novel integrated design tools.

LayTracks3D: A New Approach to Meshing General Solids using Medial Axis Transform

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex and hex- dominant meshes of 3D assembly models. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D are similar to tunnels with no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the result section. The paper also describes how this algorithm can be extended to produce all-hex meshes in general geometries.

Hex-Dominant Mesh Improving Quality to Tracking Hydrocarbons in Dynamic Basins

The proposed method regularizes as far as possible some verticals of a hex-dominant basin mesh; this regularization is used to optimize the numerical simulation of hydrocarbons flow in basins. The studied basins contain faults and constitute complex geometries. This mesh optimization is adapted for a new way to mesh basins called the Constrained Grid Method (CGM). Data constitutes some horizon surfaces; the surfaces contain tags to reconstruct the fault surfaces which represent in our case some constraints to generate a hexdominant mesh. To make a regular hex-dominant mesh, the following steps are applied: first, the borders of horizon surfaces are extracted and optimized to get the connections between the borders as vertical as possible; this means that the border nodes have approximately the same xy directions. Next, a Dirichlet equation is solved to apply a Laplacian smoothing 2D on xy directions for each horizon surface. And as the connected (x,y) between the borders are approximately the same, as well as the implied the harmonic solutions, then the positions on (x,y) are minimized.

Hex-dominant Meshing Approach based on Frame Field Smoothness

We propose here an indirect approach for building hex-dominant meshes, using the recombination of tetrahedra to create hexahedra. The efficiency of this recombination depends on the location of the initial points. A two-dimensional frame field is obtained on the boundaries by solving an elliptic PDE. We first propose a procedure to extend the two dimensional field inside the volume and to obtain a smooth three-dimensional frame field, used to insert new points. Then, we propose a point insertion algorithm based on a frame field smoothness estimator: new points are preferentially inserted in smooth frame field regions. The meshes obtained clearly exhibit a larger ratio of hexahedra, compared to more straightforward approaches.