scholarly journals Optimal Dual Schemes for Adaptive Grid Based Hexmeshing

2022 ◽  
Vol 41 (2) ◽  
pp. 1-14
Author(s):  
Marco Livesu ◽  
Luca Pitzalis ◽  
Gianmarco Cherchi
Keyword(s):  
Adaptive Grids ◽  
Hexahedral Mesh ◽  
Entry Barrier ◽  
Numerical Resolution ◽  
Prior Art ◽  
Hexahedral Meshes ◽  
Technical Details ◽  
Combinatorial Space ◽  
Valid Solution ◽  
Refined Grid

Hexahedral meshes are a ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the ability to restore the all hex property around the hanging nodes that arise at the interface between cells having different size. The most advanced tools to accomplish this task are based on mesh dualization. These approaches use topological schemes to regularize the valence of inner vertices and edges, such that dualizing the grid yields a pure hexahedral mesh. In this article, we study in detail the dual approach, and propose four main contributions to it: (i) We enumerate all the possible transitions that dual methods must be able to handle, showing that prior schemes do not natively cover all of them; (ii) We show that schemes are internally asymmetric, therefore not only their construction is ambiguous, but different implementative choices lead to hexahedral meshes with different singular structure; (iii) We explore the combinatorial space of dual schemes, selecting the minimum set that covers all the possible configurations and also yields the simplest singular structure in the output hexmesh; (iv) We enlarge the class of adaptive grids that can be transformed into pure hexahedral meshes, relaxing one of the tight topological requirements imposed by previous approaches. Our extensive experiments show that our transition schemes consistently outperform prior art in terms of ability to converge to a valid solution, amount and distribution of singular mesh edges, and element count. Last but not least, we publicly release our code and reveal a conspicuous amount of technical details that were overlooked in previous literature, lowering an entry barrier that was hard to overcome for practitioners in the field.

A Face Clustering Method for a Hexahedral Meshing

2003 ◽  
Author(s):  
Jun Doi ◽  
Atsushi Yamada ◽  
Keisuke Inoue
Keyword(s):  
Manufacturing Industry ◽  
Dimensional Space ◽  
Difficult Problem ◽  
Hexahedral Mesh ◽  
Element Analysis ◽  
Intermediate Model ◽  
3 Dimensional ◽  
Face Clustering ◽  
Hexahedral Meshes

Finite element analysis has become a key technology for a design process of manufacturing industry. A hexahedral mesh is focused, because using a hexahedral mesh increases the quality of analysis. However it is very difficult problem to generate high quality hexahedral meshes, and there are many challenging research topics. Our goal is to develop a method to generate hexahedral meshes automatically to general volumes. Our method uses an intermediate model to recognize the input volume. The intermediate model is defined in the integer 3-dimensional space, and faces of the intermediate model are vertical to coordinate axes. Hexahedral mesh is generated by dividing the intermediate model into integer grids, and blocks of grids are projected into original volume. In this paper, we describe the method to generate a topology of the intermediate model. We use face clustering technique to generate the topology of the intermediate model. The faces of the input volume are clustered into 6 types; according to 3 coordinate axes and its direction, and clustered faces will be the faces of the intermediate model.

Semi-Automated Patient Specific Hexahedral Mesh Generation of Articular Cartilage

2009 ◽  
Author(s):  
Srinivas C. Tadepalli ◽  
Kiran H. Shivanna ◽  
Vincent A. Magnotta ◽  
Nicole M. Grosland
Keyword(s):  
Articular Cartilage ◽  
Chemical Properties ◽  
Image Data ◽  
Patient Specific ◽  
Joint Mechanics ◽  
Hexahedral Mesh ◽  
Low Friction ◽  
Uniform Distance ◽  
Hexahedral Mesh Generation ◽  
Hexahedral Meshes

Articular cartilage is a critical component in the movement of one bone against another. It possesses unique chemical properties allowing it to serve as a bearing surface, capable of transferring loads from one bone to another while simultaneously allowing the load bearing surfaces to articulate with low friction. Patient-specific finite element (FE) models incorporating articular cartilage provide insight into articular joint mechanics [1, 2]. To date, the methods/tools available to create accurate FE mesh definitions of the articular cartilage are limited. Semi-automated morphing methods have been developed, but many intermediate steps have to be performed to get the final cartilage mesh definition [3]. Commercially available software [4] is capable of generating tetrahedral/shell/pyramid element based meshes of the cartilage from the underlying bony surface, but hexahedral meshes are preferred over tetrahedral meshes [5]. IA-FEMesh currently provides the ability to project a pre-defined set of elements a uniform distance [6]. This technique has been adopted in several models [1, 2]. Cartilage does not necessarily exist as such; rather the thickness of the cartilage is non-uniform and varies over the surface. Consequently an accurate representation of the articular cartilage is crucial for an accurate contact FE analysis. The goal of this study was to develop an algorithm that will aid in the generation of anatomically accurate cartilage FE mesh definitions in a reliable manner based on patient-specific image data.

On the Development of Strategies for an Efficient Semi-Automated Hex-Meshing Process of Complex Jet Engine Component Assemblies

2015 ◽  
Author(s):  
H. Böhm ◽  
A. Hornig ◽  
A. Langkamp ◽  
M. Gude ◽  
A. Keskin
Keyword(s):  
Significant Proportion ◽  
Work Effort ◽  
Hexahedral Mesh ◽  
Geometry Model ◽  
Design Changes ◽  
Hexahedral Meshing ◽  
Hexahedral Meshes ◽  
Complex Structural ◽  
Meshing Process

A significant proportion of the work effort for a whole engine analysis is spent for prep-processing tasks especially for component assemblies and complex structural components. With respect to the generation of a pure hexahedral mesh, the work effort increases due to the absence of an automatic method to generate high quality hexahedral meshes for an arbitrary geometry. In addition, the time-consuming hexahedral meshing process contains numerous, repetitive tasks for large and complex assemblies due to similar and identical components. In this work a modular strategy for hexahedral meshing of large and complex assemblies was explored with the aim to reduce and to simplify the development process due to a prospective semi-automation of time-consuming routines. The procedure bases on an initial identification and classification of each component of the whole assembly regarding e.g. overall meshing complexity. Meshing relevant parameters were identified for geometry preparation and hexahedral meshing itself. Furthermore, for semi-automation the software package NX (Siemens NX Software), in particular the incorporated automation tool Product Template Studio (PTS) was investigated which enables an automated re-meshing of the geometry model in case of design changes.

scholarly journals Grid Type Impact on the Results of the Volume of Fluid Method in the Free Surface Flow Calculations Around Ship Hull

2018 ◽  
Vol 1 (1) ◽  
pp. 151-157
Author(s):  
Karol Sugalski ◽  
Tomáš Skrúcaný
Keyword(s):  
Free Surface ◽  
Fluid Dynamic ◽  
Free Surface Flow ◽  
Triangular Mesh ◽  
Surface Flow ◽  
Ship Hull ◽  
Hexahedral Mesh ◽  
Two Phase ◽  
Advantages And Disadvantages ◽  
Hexahedral Meshes

Abstract This article presents results of the free surface flow around ship hull on two different types of computational grid. Each type of mentioned grid has its own advantages and disadvantages in particular cases, mostly in one phase simulation. Omitting cases with capitation, there is no free surface involved in one phase simulation. Multiphase simulations are crucial in the ship design process and optimization. Recreating free surface on the triangular mesh causes difficulties, in contrast to the hexahedral meshes, where calculated surface is more aligned to the physical border of the fluids. In this paper, results from the triangular mesh were compared to results from hexahedral mesh. Conclusions about triangular meshes in two phase simulation are presented. The computational fluid dynamic toolbox OpenFOAM is used to perform calculations of the total resistance of work boat in calm water.

Automatic Regular Hexahedral Mesh Generation by Regular Volume Decomposition

1997 ◽  
Author(s):  
Bih-Yaw Shih ◽  
Hiroshi Sakurai
Keyword(s):  
Mesh Generation ◽  
Complex Shape ◽  
Solid Model ◽  
Hexahedral Mesh ◽  
Solid Models ◽  
Hexahedral Mesh Generation ◽  
Volume Decomposition ◽  
Hexahedral Meshes ◽  
The Way

Abstract A method has been developed to generate regular hexahedral meshes automatically from arbitrary solid models by volume decomposition. This method first decomposes a solid model having a complex shape into volumes having simple shapes. Then, shape-specific meshing methods like mapping are applied to generate regular hexahedral meshes from these volumes. Finally, all regular hexahedral meshes of these volumes are combined into a regular hexahedral mesh of the original solid model. Thus the method generates regular hexahedral meshes automatically in a way similar to the way a human does interactively. This is in contrast to the previous methods of automatic hexahedral mesh generation, which try to generate hexahedral meshes from solid models directly.

CFD Predictions of Single Row Film Cooling With Inclined Holes: Influence of Hole Outlet Geometry

2010 ◽  
Author(s):  
Habeeb Idowu Oguntade ◽  
Gordon E. Andrews ◽  
Alan Burns ◽  
Derek Ingham ◽  
Mohammed Pourkashanian
Keyword(s):  
Film Cooling ◽  
Turbulence Models ◽  
Experimental Results ◽  
Hexahedral Mesh ◽  
Mesh Structure ◽  
Film Cooling Effectiveness ◽  
Single Row ◽  
Narrow Angle ◽  
Hexahedral Meshes ◽  
Outlet Hole

A CFD investigation of a single row of round inclined film cooling holes in a crossflow has been carried out with the view of investigating the discrepancies in the literature between predicted and measured results. The experimental results of Sinha et al. [1], Kohli et al. [40], Pedersen et al. [3] and others form the data base for validation of the CFD prediction of film cooling. Previous work in the literature is reviewed to show that CFD has had difficulty in obtaining agreement with these basic experimental film cooling results. However, most previous work has used tetrahedral meshes which gave poor agreement with experiments in the near hole region. In the present work it is shown by direct comparison of tetrahedral and hexahedral meshes, using the FLUENT code, with the same turbulence models, that only hexahedral meshes give good agreement with the experimental results in the near hole region. It is postulated that the reason is that the mesh structure is aligned with the flow and has more computational nodes in the important film cooling boundary layer. The hexahedral mesh was used with five turbulence models, which showed the standard k-epsilon model consistently gave the best agreement with experimental data for narrow angle film cooling. This CFD methodology was shown to be capable of predicting the influence on film cooling effectiveness of trench hole and larger diameter outlet hole geometries.

Adaptive FEM Analysis Technique Using Multigrid Method for Unstructured Hexahedral Meshes

2006 ◽  
Vol 306-308 ◽  
pp. 565-570 ◽  
Author(s):  
Yoshitaka Wada ◽  
Jun'ichi Shinbori ◽  
Masanori Kikuchi
Keyword(s):  
Mesh Generation ◽  
Large Scale ◽  
Multigrid Method ◽  
Fem Analysis ◽  
Preconditioned Conjugate Gradient ◽  
Hexahedral Mesh ◽  
Practical Applications ◽  
Analysis Technique ◽  
Hexahedral Meshes ◽  
Intensive Work

MG (multigrid) method is one of the most promising solvers for large scale problems. Hexahedral mesh generation and its adaptation are not enough to use for practical applications, because its mesh generation is very difficult and still labor intensive work by hand. We have developed hexahedral local refinement technique controlled by posterior error estimation. We have proposed a MG technique for unstructured hexahedral meshes with local mesh refinement. In this paper, the proposed technique is evaluated to check its performance and severe analyses of bending cantilevers. Performance of MG for unstructured hexahedral meshes is compared with that of the PCG (preconditioned conjugate gradient) through several benchmark examples of 3-D static elastic analysis. Proposed MG is faster than PCG for all problems as number of freedoms increases. Finally limitation of the proposed technique is presented.

scholarly journals Hexahedral Mesh Quality Improvement with Geometric Constraints

2021 ◽  
Author(s):  
wei peng ◽  
Xinguang Wu ◽  
Yidong Bao ◽  
Chaoyang Zhang ◽  
Weixi Ji
Keyword(s):  
Quality Improvement ◽  
Geometric Constraints ◽  
Mesh Quality ◽  
Quality Improvements ◽  
Hexahedral Mesh ◽  
Different Types ◽  
Hexahedral Meshes ◽  
Improvement Method ◽  
Quality Improvement Method

Abstract Hexahedral mesh is of great value in the analysis of mechanical structure, and the mesh quality has an important impact on the efficiency and accuracy of the analysis. This paper presents a quality improvement method for hexahedral meshes, which consists of node classification, geometric constraints based single hexahedron regularization and local hexahedral mesh stitching. The nodes are divided into different types and the corresponding geometric constraints are established in single hexahedron regularization to keep the geometric shapes of original mesh. In contrast to the global optimization strategies, we perform the hexahedral mesh stitching operation within a few local regions surrounding elements with undesired quality, which can effectively improve the quality of the mesh with less consuming time. A number of mesh quality improvements for hexahedral meshes generated by a variety of methods are introduced to demonstrate the effectiveness of our method.

Edge-Based Quadrilateral Mesh Fitting Using Normal Vector Diffusion

2015 ◽  
Vol 9 (6) ◽  
pp. 756-764
Author(s):  
Yusuke Imai ◽  
◽  
Seungki Kim ◽  
Hiroyuki Hiraoka ◽  
Hiroshi Kawaharada ◽  
...  
Keyword(s):  
Boundary Surface ◽  
Cnc Machining ◽  
Numerical Control ◽  
Normal Vector ◽  
Boundary Edge ◽  
Hexahedral Mesh ◽  
Target Shape ◽  
Laplacian Energy ◽  
Hexahedral Meshes ◽  
Normal Vectors

Nowadays, many manufacturers use computer-aided design (CAD) for processes such as computer numerical control (CNC) machining, simulations, and press working. They use CAD models for their simulations because the cost of performance simulations is lower than that of actual product testing. In this paper, we consider hexahedral meshes for finite element analysis because simulations using such meshes are more accurate than those using tetrahedral meshes. Our aim is to automatically generate hexahedral meshes with sharp features that precisely represent the corresponding features of the target shape. Our hexahedral mesh generation algorithm is voxel-based, and thus in our previous studies, we fitted the surface of voxels to the target surface using Laplacian energy minimization. We used normal vectors during the fitting to preserve any existing sharp features. Each face of the boundary surface of a hexahedral mesh is a quadrilateral face, which we consider to consist of four triangles. Herein, we assume that an edge of a quadrilateral surface has four normal vectors of four connected triangles. Here, we diffuse normal vectors of the target shape after extracting them to accurately preserve the shape features. Moreover, for the Laplacian energy, we add a term that matches the normal vector of the target shape with the four normal vectors of a boundary edge. Finally, we present some experimental results using our method.

scholarly journals Quadrilateral mesh fitting that preserves sharp features based on multi-normals for Laplacian energy

2014 ◽  
Vol 1 (2) ◽  
pp. 88-95 ◽  
Author(s):  
Yusuke Imai ◽  
Hiroyuki Hiraoka ◽  
Hiroshi Kawaharada
Keyword(s):  
Energy Minimization ◽  
Computer Aided Design ◽  
Performance Testing ◽  
Target Surface ◽  
Hexahedral Mesh ◽  
Element Analysis ◽  
Laplacian Energy ◽  
Hexahedral Meshes ◽  
Normal Vectors ◽  
The Cost

Abstract Because the cost of performance testing using actual products is expensive, manufacturers use lower-cost computer-aided design simulations for this function. In this paper, we propose using hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. We propose automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fit the surface of the voxels to the target surface using Laplacian energy minimization. We used normal vectors in the fitting to preserve sharp features. However, this method could not represent concave sharp features precisely. In this proposal, we improve our previous Laplacian energy minimization by adding a term that depends on multi-normal vectors instead of using normal vectors. Furthermore, we accentuate a convex/concave surface subset to represent concave sharp features.

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