Advancing Front Technique Research Articles

A three-dimensional advancing front technique to generate grids based on the neural networks

A three-dimensional advancing front technique to generate grids based on the neural networks

A new strain-based pentagonal membrane finite element for solid mechanics problems

Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modeling arbitrary shapes compared to triangles. In this study, a pentagonal membrane element was developed with the strain approach for the first time. The element possesses invariance, and the equilibrium constraint was applied to the assumed strain field using corrective coefficients. Inspired by the advancing front technique, a pentagonal mesh was generated, and the mesh quality was enhanced with Laplacian smoothing. The performance of the developed pentagonal element was assessed in a few numerical tests, and the results revealed its suitability in modeling the bending of beams. Besides, the numerical results are enhanced when pentagonal elements are used in mesh transitions along boundaries to smoothen curved edges and capture distributed loads.

Advancing Front Mesh Generation on Dirty Composite Surfaces

Computer-aided design (CAD) models usually contain many errors between neighboring surfaces, such as slivers, gaps, and overlaps. To clean up such models, virtual operations have been suggested to merge multiple neighboring CAD surfaces into a single composite surface. However, it remains a challenge to generate a quality mesh on thereby formed dirty composite surfaces. In this paper, we propose a novel advancing front technique (AFT) that can treat such composite surfaces by developing two new schemes to enhance the traditional AFT. Firstly, for each composite surface, we define a parametric plane by using a combined set of the tessellation on this composite surface. Simplicial complex augmentation framework reparameterization approach is suggested since it can treat tessellations containing gap and overlap after introducing a pre-processing step. Meanwhile, this approach can ensure a bijective mapping between the parametric and physical space. The front intersection check can thus be performed on the parametric plane robustly. Secondly, the indirect and direct approaches are alternatively employed to calculate ideal points in different circumstances. In the circumstance that the possible new element is completely contained in one single CAD surface, the ideal point is calculated on the intrinsic parametric plane of the surface; otherwise, the ideal point is directly calculated on the physical space. We avoid using the geometry defined on the tessellation since we prefer to getting a mesh respecting the original CAD model rather than its tessellation counterpart. Presently, the developed new schemes have been incorporated into our in-house surface mesher, and their efficiency and effectiveness have been demonstrated through a comparison with state-of-the-art commercial tools (e.g., COMSOL Multiphysics) and AFT algorithm, using CAD models of industry-level complexity.

Stochastic ice accretion model using an unstructured advancing front technique

Stochastic ice accretion model using an unstructured advancing front technique

A Front Advancing Adaptive Triangular Mesh Dynamic Generation Algorithm and Its Application in 3D Geological Modeling

The traditional advancing front technique algorithm encounters many problems due to the complex geometric characteristics of the front edge shape. These problems include poor quality, a slow algorithm, low robustness, and the inability of the mesh unit to converge. To address these problems, an optimized adaptive triangular mesh dynamic generation algorithm called R-TIN is proposed and applied to 3D engineering geological modeling in this study. Firstly, all the shapes involved in advancing the front edge inward were classified into four types, and then the optimal triangular unit was constructed by using the candidate mesh point heuristic algorithm. Then, the robustness of this algorithm could be maintained by the graded concession of the included angle threshold in the adjacent front-line segments. Finally, based on 160 engineering geological boreholes in the study area, the 3D engineering geological model was constructed and the accuracy and visualization effect of the overall geological model have been greatly improved, which can better present the spatial distribution of strata and lithological characteristics. At the same time, this algorithm can be used in geoscience information services to support the regional or national exploration of resources and energy, sustainable development and utilization, environmental protection and the prevention of geological disasters.

SAFT: Shotgun advancing front technique for massively parallel mesh generation on graphics processing unit

AbstractLarge‐scale numerical simulations need efficient parallel mesh generation schemes. Several parallel advancing front algorithms were proposed in the past decades, most of which require domain decomposition. In this article, we present a shotgun algorithm for parallel advancing front mesh generation. Our algorithm is front‐based, therefore does not require domain decomposition. We've implemented the algorithm on GPU, which has thousands of CUDA cores. Different from traditional volume‐based parallelization, each CUDA thread handles one face at a time. We deal with conflicts by discarding illegal new elements which intersect with each other. We name this proposed method “SAFT”, which stands for “shotgun advancing front technique”. Its performance, as well as scalability, has been evaluated on a laptop equipped with one NVIDIA Geforce RTX2060 graphics card. We have been able to generate high‐quality 2D meshes efficiently (233k elements per second).

Development of SFEM-Pre: A Novel Preprocessor for Model Creation for the Smoothed Finite Element Method

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

An extension of advancing front technique on new target surface after virtual topology operations

In this paper, an extension of advancing front technique (AFT) on new target surface (NTS) after virtual topology operations has been achieved in order to suitably represent CAD model and enhance the accuracy of numerical analyses. The extension of AFT has been accomplished through two stages. In the first stage, through analysis of the connection features of the intersecting lines with geometric continuity, a new notion of NTS is proposed. Based on the new notion, the topology of NTS is adjusted to generate meshes and meet the requirements of numerical analyses. In the second stage, AFT is extended accordingly in order to realize the topology of NTS. Specifically, based on the concise description of the front configuration of AFT, all of the subordinate aspects of AFT, including meshing order, generation of elements and nodes, and validity checking, are optimized. With the extension of AFT in this fashion, the target surfaces of AFT have been extended from the parametric surfaces to the composite surfaces. Finally, two examples are calculated with the extended AFT. The results of the calculation have verified that the topology of the composite surfaces is suitable and that the extended AFT is accurate and efficient.

A novel stencil selection method for the gradient reconstruction on unstructured grid based on OpenFOAM

For the unstructured finite volume algorithms, the stencil utilized for gradient reconstruction is important for the accuracy, efficiency and robustness. In this paper, we present a novel stencil selection method for the gradient reconstruction of the cell-centered finite volume methodology. In the novel stencil selection method, two local directions are generated for each control volume, and the stencil is generated based on the local directions. In this way, the characteristics of the structured grid are able to be reflected on the unstructured grid. To obtain the suitable local directions, an advancing front technique (AFT) is utilized to guide their generation. Through AFT, the direction of the boundary normal vector, along which the flow fields change dramatically, is obtained and propagated from the boundaries to the internal regions. Finally, the novel stencil extends in two directions, one of which is approximately aligned with the direction of the boundary normal vector. Hence, the gradient reconstruction methods with the new stencil are able to use the information along the boundary normal. In order to verify the validity of the new stencil, we present a new gradient reconstruction method, the structured least squares (struLSQR) method, by applying the new stencil to the least squares (LSQR) method. The performance of struLSQR, and two existing gradient reconstruction methods in OpenFOAM is tested by adopting the 2D channel flow and the 2D circular cylinder flow on both the quadrilateral and the triangular grids. A laminar flow past a flat plate is also adopted to verify the applicability of struLSQR to the viscous flow. The numerical results illustrate that the new stencil is able to solve the blow-up problem of LSQR. It can also obtain a higher order of accuracy compared to extLSQR. Moreover, the convergence speed of struLSQR can be up to 1.64 ∼ 2.60x of that of extLSQR.

High-quality mesh generation for human hip based on ideal element size: methods and evaluation

The objective of this work was to obtain high-quality mesh generation results for the human hip. This study adopted an edge-collapse algorithm based on quadric error metrics to simplify the hip model. The adjacent triangular areas and a cost function that considered the mean value of error were introduced to avoid error accumulation and ensure invariant geometric features. Local mesh refinement was achieved by constructing a comprehensive size field. Finally, high-quality surface and volume meshes were generated using the advancing-front technique (AFT) and Delaunay algorithms. Two human hipbones, 13 muscles, and one articular cartilage sample were modelled. The hip model was simplified and the mesh was generated using the method proposed in this study. The smallest angle of most surface mesh elements was greater than 45°, and the triangular numbers in this optimal angle interval were superior to those generated by the AFT algorithms. Eight quality evaluation parameters of the mesh model were tested using the check-elems tool. The femoral meshing results in this work were more accurate than those obtained with the AFT algorithms. The results of the vastus lateralis mesh generation were superior to the results obtained with the existing algorithm, except for the volume skew parameter. The proportions for the high-quality tetrahedral elements obtained using Wang’s algorithm for the femur and the vastuslateralis muscle were 17.81% and 24.50%, respectively. The proportions obtained using the hypermesh software were 16.31% and 22.87% for the femoral and vastuslateralis models, respectively. The proposed method had better adaptability to the complex model. The generated mesh was uniform and contained smooth transitions. The mesh generation result was similar to the original geometric model, which made the assembly model fit more accurately. This was significant for the convergence of the finite-element analysis program.

An agglomeration strategy for accelerating RBF-based mesh deformation

RBF-based mesh deformation methods have been recognized during the past years as an essential tool for numerical simulations involving mesh deformation. Nevertheless, they call for excessive memory and computation time requirements, especially for large-scale problems. A remedy to this shortcoming appears to be the selection of a reduced number of surface mesh nodes, to be used as RBF-centers, resulting in decreased dimensions of the system of equations. In this study a methodology for the reduction of the RBF-centers is developed, based on the agglomeration of boundary nodes' control areas. This technique has been adopted from the multigrid methods frequently employed in numerical simulation of fluid flow, heat transfer, etc. The fusion strategy is performed on a topology-preserving framework, while it resembles the advancing front technique, as it begins from regions with surface discontinuities extending successively to the interior. The proposed algorithm was evaluated against benchmark test cases, concerning deformation of the wing of a transonic commercial aircraft and the blade of a wind turbine, revealing its potential for radically improved computational performance of the grid deformation procedure. Moreover, the obtained results confirm its capability to preserve grid quality, despite the notable reduction of RBF-centers.

Fast algorithms for intersection of non-matching grids using Plücker coordinates

The XFEM and Mortar methods can be used in combination with non-matching or non-conforming grids to deal with problems on complex geometries. However the information about the mesh intersection must be provided. We present algorithms for intersections between 1d and 2d unstructured multi component simplicial meshes and their intersections with a background unstructured 3d mesh. A common algorithm based on the advancing front technique is used for the efficient selection of candidate pairs among simplicial elements. Bounding interval hierarchy (BIH) of axes aligned bounding boxes (AABB) of elements is used to initialize the front tracking algorithm. The family of element intersection algorithms is built upon a line–triangle intersection algorithm based on the Plücker coordinates. These algorithms combined with the advancing front technique can reuse the results of calculations performed on the neighboring elements and reduce the number of arithmetic operations. Barycentric coordinates on each of the intersecting elements are provided for every intersection point. Benchmarks of the element intersection algorithms are presented and three variants of the global intersection algorithm are compared on the meshes raising from hydrogeological applications.

Generating Free-Form Grid Truss Structures from 3D Scanned Point Clouds

Reconstruction, according to physical shape, is a novel way to generate free-form grid truss structures. 3D scanning is an effective means of acquiring physical form information and it generates dense point clouds on surfaces of objects. However, generating grid truss structures from point clouds is still a challenge. Based on the advancing front technique (AFT) which is widely used in Finite Element Method (FEM), a scheme for generating grid truss structures from 3D scanned point clouds is proposed in this paper. Based on the characteristics of point cloud data, the search box is adopted to reduce the search space in grid generating. A front advancing procedure suit for point clouds is established. Delaunay method and Laplacian method are used to improve the quality of the generated grids, and an adjustment strategy that locates grid nodes at appointed places is proposed. Several examples of generating grid truss structures from 3D scanned point clouds of seashells are carried out to verify the proposed scheme. Physical models of the grid truss structures generated in the examples are manufactured by 3D print, which solidifies the feasibility of the scheme.

Advances in co-volume mesh generation and mesh optimisation techniques

This paper introduces developments in modified techniques for the generation of unstructured, non-uniform, dual orthogonal meshes which are suitable for use with co-volume solution schemes. Two new mesh generation techniques, a modified advancing front technique and an octree-Delaunay algorithm, are coupled with a mesh optimisation algorithm. When using a Delaunay–Voronoi dual, to construct mutually orthogonal meshes for co-volume schemes, it is essential to minimise the number of Delaunay elements which do not contain their Voronoi vertex. These new techniques provide an improvement over previous approaches, as they produce meshes in which the number of elements that do not contain their Voronoi vertex is reduced. In particular, it is found that the optimisation algorithm, which could be applied to any mesh cosmetics problem, is very effective, regardless of the quality of the initial mesh. This is illustrated by applying the proposed approach to a number of complex industrial aerospace geometries.

Parallel generation of meshes with cracks using binary spatial decomposition

This work describes a technique to generate tetrahedral meshes with cracks using parallel computers with distributed memory. This technique can be used for models without cracks as well. It employs a binary partitioning structure that uses axis-aligned planes to decompose the domain. Those decomposing planes are determined based on a refined octree that is built to estimate the amount of work necessary to generate the whole mesh, so that the amount of work in each subdomain is approximately the same. A serial advancing front technique is used in each subdomain concurrently, in such a way that the generated tetrahedra do not cross the decomposing planes. After local synchronizations, meshes are generated interfacing the subdomains. The results show that the prediction of the number of elements in each subdomain is accurate, leading to a well-balanced algorithm and to a good speed-up. Also, the meshes generated in parallel have very good quality, similar to the that of a serially generated mesh.

Comparison of different agglomeration multigrid schemes for compressible and incompressible flow simulations

Different parallel agglomeration multigrid schemes have been developed aiming to improve the computational performance of a compressible and an incompressible academic Computational Fluid Dynamics (CFD) codes, named Galatea and Galatea-I, respectively. Flow prediction is succeeded via the implementation of Reynolds-Averaged Navier–Stokes (RANS) equations combined with appropriate turbulence models on three-dimensional unstructured tetrahedral or hybrid meshes. The sequence of required coarser grids, composed of irregular polyhedral elements, is generated either with the isotropic or directional (full- or semi-coarsening) fusion of neighbouring control volumes on a topology-preserving framework; it resembles the advancing-front technique as it begins from solid wall surfaces and extends successively to the interior domain. The multigrid accelerated approximation of flow and turbulence equations is achieved via the V-cycle implementation of either the Full Approximation Scheme (FAS) or its coupled version with Full Multigrid (FMG) method. Multigrid approaches with different agglomeration and solution strategies have been extensively tested against three- and quasi-three-dimensional test cases, all of them demonstrating their potential for considerably improved efficiency. Their contributions to the reduction of simulations' computation time are analysed, while additionally the differences due to the type of the flow (compressible or incompressible) are thoroughly discussed.

A mesh generation procedure to simulate bimaterials

It is difficult to develop an algorithm which is able to generate the appropriate mesh around the interfaces in bimaterials. In this study, a corresponding algorithm is proposed for this class of unified structures made from different materials with arbitrary shapes. The non-uniform mesh is generated adaptively based on advancing front technique available in Abaqus software. Implementing several preliminary analyses, the output of each step prepared data source for the next step of mesh generation. After examining several criteria, the mean elemental stress derivative is selected as a suitable criterion to evaluate the performance of current mesh. The convergence indicates non-isometric final mesh with appropriate and optimum distribution. In general, automatic mesh generators determine the mesh density only based on the geometry of the model; however, the developed algorithm modifies mesh after sensing the stress intensity due to various reasons including loading condition and any change in material and geometry. In addition, the proposed algorithm converges to accurate result fast enough if considering the numbers of remeshing steps. An adaptive mesh generator code can be programmed based on the developed procedure to automatically generate mesh if implementing in Abaqus as a subroutine.

Unsteady wall shear stress analysis from image-based computational fluid dynamic aneurysm models under Newtonian and Casson rheological models.

The aim of this work was to determine whether or not Newtonian rheology assumption in image-based patient-specific computational fluid dynamics (CFD) cerebrovascular models harboring cerebral aneurysms may affect the hemodynamics characteristics, which have been previously associated with aneurysm progression and rupture. Ten patients with cerebral aneurysms with lobulations were considered. CFD models were reconstructed from 3DRA and 4DCTA images by means of region growing, deformable models, and an advancing front technique. Patient-specific FEM blood flow simulations were performed under Newtonian and Casson rheological models. Wall shear stress (WSS) maps were created and distributions were compared at the end diastole. Regions of lower WSS (lobulation) and higher WSS (neck) were identified. WSS changes in time were analyzed. Maximum, minimum and time-averaged values were calculated and statistically compared. WSS characterization remained unchanged. At high WSS regions, Casson rheology systematically produced higher WSS minimum, maximum and time-averaged values. However, those differences were not statistically significant. At low WSS regions, when averaging over all cases, the Casson model produced higher stresses, although in some cases the Newtonian model did. However, those differences were not significant either. There is no evidence that Newtonian model overestimates WSS. Differences are not statistically significant.

The Research on Tetrahedral Mesh Optimization Algorithm of the Double Channel Pump

The quality of mesh generation is very important for the computational simulation of the double channel pump. According to the special characteristics of the double channel pump, there exist a g reat amount of poor-quality elements, most of which are so called Sliver elements, generated by the tetrahedral mesh generation algorithms of Advancing Front Technique (AFT) and Delaunay Triangulation. By studying the type, distribution and reason of the badly sha ped elements, a method to eliminate these Sliver elements was proposed. Then this method was combined with advanced optimization-based smoothing, Laplacian smoothing and swapping optimization to optimize the tetrahedral mesh. The computer language C++ is applied to develop the algorithms. Computational experiments of a double channel pump shown that the worst elements can be removed and the whole quality can be improved noticeably. After comparing the result of numerical simulation with that of the experiment, it is believed that the tetrahedral mesh optimization algorithm can satisfy the computational simulation of the double channel pump.

Hemodynamic differences in intracranial anerusysm blebs due to blood rheology

Computational blood flow simulations over patient-specific image-based three dimensional domains under personalized flow conditions have been extensively used to investigate associations between flow characteristics and aneurysm initiation, progress and rupture. Although it is widely accepted that the wall shear stress is associated to those processes, there is still no agreement about what stress characteristics are responsible for triggering those biomechanical processes. Although the incorporation of the blood rheology in large arterial systems containing aneurysms resulted in similar hemodynamic characterizations for most aneurysms, large aneurysms, especially those containing blebs, are expected to have flow rates in the range where Newtonian and non-Newtonian models largely differ. However, there is no consent among authors about the impact of blood rheology on the intraaneurysmal wall shear stress magnitude. In this work we used high resolution models reconstructed from rotational angiography images to perform unsteady finite element blood flow simulations to investigate the differences in WSS distribution and alignment for Newtonian and non-Newtonian rheologies. Unstructured finite element meshes were generated using an advancing front technique. Personalized flow conditions were imposed at the inlets of the models. The Casson model was incorporated as a velocity-dependent apparent viscosity and the results were compared to those using the Newtonian rheology. Associations between the localization of regions with large differences in wall shear stress magnitude and orientation, and the regions of differentiated wall shear stress magnitude were studied in a cohort of patients.