Hexahedral Mesh Research Articles

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.

Modeling and hexahedral meshing of cerebral arterial networks from centerlines.

Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires extracting precise models of arteries from low-resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it encodes both the geometric and topological information and facilitates manual editing. In this work, we propose an automatic method to generate a structured hexahedral mesh suitable for CFD directly from centerlines. We addressed both the modeling and meshing tasks. We proposed a vessel model based on penalized splines to overcome the limitations inherent to the centerline representation, such as noise and sparsity. The bifurcations are reconstructed using a parametric model based on the anatomy that we extended to planar n-furcations. Finally, we developed a method to produce a volume mesh with structured, hexahedral, and flow-oriented cells from the proposed vascular network model. The proposed method offers better robustness to the common defects of centerlines and increases the mesh quality compared to state-of-the-art methods. As it relies on centerlines alone, it can be applied to edit the vascular model effortlessly to study the impact of vascular geometry and topology on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92% of the vessels and 83% of the bifurcations were meshed without defects needing manual intervention, despite the challenging aspect of the input data. The source code is released publicly.

Numerical simulation and experimental verification of fatigue crack propagation in high-strength bolts based on fracture mechanics.

To investigate the fatigue crack propagation behavior of high-strength bolts for high-speed train brake discs, the fatigue crack propagation of high-strength bolts with initial defects under various load ratios was numerically simulated and experimentally verified based on fracture mechanics in this paper. Firstly, the fracture mechanics model of a three-dimensional hexahedral mesh with initial root defects was established using ABAQUS-FRANC3D interactive technology. Then the stress intensity factor (SIF) of the crack front was calculated by the stress superposition of the crack surface to simulate the coupling effect of preload and axial cyclic load. Based on it, fatigue crack propagation was simulated. Finally, the corresponding fatigue experiments on prefabricated crack bolts were carried out. The results show that mode I cracks dominate in the process of crack propagation. The stable crack propagation zones of the fractured high-strength bolts all show a semi-elliptical cross-section. The SIF of the crack front decreases with the increase of the load ratio, thus making the crack propagation life increase with the increase of the load ratio. The experimental outcomes are in great agreement with the simulation results, which verify that the numerical simulation method can effectively and accurately evaluate the fatigue life of high-strength bolts with initial defects and provides an effective means for predicting the fatigue crack propagation life of the same type high-strength bolts in engineering applications.

Hexahedral Mesh Quality Improvement with Geometric Constraints

Hexahedral Mesh Quality Improvement with Geometric Constraints

Crack propagation analysis and fatigue life assessment of high-strength bolts based on fracture mechanics

To investigate the effect of initial cracks on the fatigue performance of high-strength bolts for high-speed train brake discs, the fatigue crack propagation behavior of high-strength bolts under the coupling action of preload and dynamic fatigue load was investigated experimentally and numerically based on the theory of linear elastic fracture mechanics. Firstly, fatigue tests of high-strength bolts with initial crack defects were carried out, and then a three-dimensional accurate numerical model with the hexahedral mesh for a bolt-nut was established by MATLAB, and the fatigue crack propagation behaviors were investigated using ABAQUS-FRANC3D interactive technology. In this paper, the effects of the initial crack state, the bolt preload, the axial excitation load, and the friction coefficient of the screw pair on crack propagation life were emphatically studied, and the simulated crack propagation trajectory and crack propagation life agreed well with the experimental results. The findings indicated that 0°-oriented cracks beginning at the maximum principal stress were predicted to have the shortest fatigue life. The crack propagation life was sensitive to the initial crack size, the coefficient of initial crack geometry, and the bolt preload, but not to the friction coefficient of the screw pair. Furthermore, when evaluating the effect of fatigue load on crack propagation, the load ratio, the mean load, and the load range should all be considered.

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.

Topology modification based rezoning strategies for the arbitrary Lagrangian-Eulerian method on unstructured hexahedral meshes

Topology modification based rezoning strategies for the arbitrary Lagrangian-Eulerian method on unstructured hexahedral meshes

Determination of cryogenic temperature loads for finite-element model of LNG bunkering ship under LNG release accident

Abstract The rising demand for liquefied natural gas (LNG)-fueled ships requires the LNG bunkering facility that partially uses a ship-to-ship operation. The bunkering process of LNG fuel may have a greater risk due to LNG volatility. The cryogenic temperature of LNG poses a threat to the personnel and structural embrittlement to ships. Therefore, cryogenic spill protection optimization was introduced concerning the structural strength analysis using finite element (FE) by utilizing cryogenic temperature loads provided by the computational fluid dynamics (CFD) model of an LNG release. This study aims to build a platform for transferring the temperature load profile from CFD to FE software accurately. The CFD model usually uses a structured Cartesian grid, and the FE method adopts an unstructured tetrahedral or hexahedral mesh. As a result, both configurations store results at different positions, and it is not preferred for the load profile to be transferred directly. The error will be greater due to the variance of positions. Random Forest, a machine learning method, has been employed that uses a regression technique to deal with a continuous variable. An accurate load profile for the FE model can be obtained by adopting decision tree learning in Random Forest. The procedure for determining the temperature load profile is presented in this article.

CutFEM forward modeling for EEG source analysis.

Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction effects in the human head, represented by a partial differential equation which can be solved using the finite element method (FEM). FEM offers flexibility when modeling anisotropic tissue conductivities but requires a volumetric discretization, a mesh, of the head domain. Structured hexahedral meshes are easy to create in an automatic fashion, while tetrahedral meshes are better suited to model curved geometries. Tetrahedral meshes, thus, offer better accuracy but are more difficult to create. We introduce CutFEM for EEG forward simulations to integrate the strengths of hexahedra and tetrahedra. It belongs to the family of unfitted finite element methods, decoupling mesh and geometry representation. Following a description of the method, we will employ CutFEM in both controlled spherical scenarios and the reconstruction of somatosensory-evoked potentials. CutFEM outperforms competing FEM approaches with regard to numerical accuracy, memory consumption, and computational speed while being able to mesh arbitrarily touching compartments. CutFEM balances numerical accuracy, computational efficiency, and a smooth approximation of complex geometries that has previously not been available in FEM-based EEG forward modeling.

HexBox: Interactive Box Modeling of Hexahedral Meshes

AbstractWe introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box‐model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non‐conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally‐provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid‐based meshing, such as mixing of 3‐refinement, 2‐refinement, and face‐refinement, and using templated topological bridges to enforce on‐the‐fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques.

Research on Cuttings Carrying Principle of New Aluminum Alloy Drill Pipe and Numerical Simulation Analysis

In order to improve the cuttings transport ability and well hole purification effect of horizontal shale gas wells in the Sichuan and Chongqing area, a new type of aluminum alloy drill pipe is put forward, and the floatability is validated by theoretical analysis and actual parameter calculation. According to the cuttings migration mechanism, the cuttings cleaning simulation model of the new aluminum alloy drill pipe and the traditional steel drill pipe was established by Fluent, and the hexahedral mesh is used to divide the model. Thus, the mesh independence and convergence of the two models are verified. Then, the simulation model is verified by comparing the calculation results of the two simulation models with the experimental data of the indoor cuttings migration device. Finally, the rock-cleaning ability of the two drill pipes is analyzed under the conditions of changing the cuttings particle size, well inclination angle, displacement, and mechanical speed. Compared with the traditional steel drill pipe, the new aluminum alloy drill pipe can improve the borehole purification capacity by 13% on average. This research result is of great significance in reducing the quality of cuttings in the annulus and improving the borehole purification effect.

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.

CFD Simulation of Pressure, Temperature and Rotational Speed Influence on the Cavitation in Centrifugal Pump Impeller

The impeller is a critical rotating part of a centrifugal pump where the energy transfer to the fluid takes place. The complex nature of the fluid flow inside the impeller can give rise to cavitation which is highly undesirable. Design and operating conditions in the impeller influence the extent of cavitation. The effect of the outlet pressure, temperature and rotational speed of the impeller was studied using ANSYS CFX Computation Fluid Dynamics (CFD) software. The impeller geometry was meshed with high-quality hexahedral meshes and the y + values around the blade surface are less than 2. The k - omega turbulence model was used along with the ZGB model of cavitation. The effects of the variable parameters on the cavitation volume and the head developed were extensively studied. The numerical trends are similar to those presented in the literature. By carefully controlling the outlet pressure, the effects of increased temperature can be mitigated. Thus, it is possible to operate a centrifugal pump at higher working fluid temperatures by operating the pressure above 275 kPa.

Estimating the Strength and Deformation Properties of the End Milling Process Using Numerical Analysis Methods

In the study, the end mill made of titanium material and having a unique design with a 4-flute was simulated during the milling of the workpiece with a geometry of a rectangular prism made of aluminum material. Ansys Explicit Dynamics was used in the study. Modeling and simulation of the milling process were made with finite element analysis for the estimation of the strength properties. The end mill is chosen as a titanium alloy, while the milled workpiece is aluminum. All parameters were kept constant and only the depth of cut was examined in three scenarios 3, 6, and 9 mm. The simulations were carried out by taking the spindle speed of 4000 RPM and the feeding rate of 3350 mm/s. One of the conveniences provided by Explicit Dynamics is that it can be solved in very small time intervals, and for this reason, the time step in the analysis is solved by taking 0.001 seconds. While hexahedral mesh is applied to the tool, a tetrahedral mesh is applied to the workpiece. The generated mesh has 8,012 nodes and 17,052 mesh elements. Average deformations for both tool and workpiece are 36.92, 38.10, and 38.29 mm, respectively. Strain also shows a similar trend to the total deformation and the average values for all three scenarios were found to be 2.84 x 10-3, 4.43 x 10-3 and 3.99 x 10-3 mm/mm. Also, the stress values were obtained as 78.23, 76.83, and 77.99 MPa.

A 3D face interpolated discretisation method for simulating anisotropic diffusive processes on meshes coming from wood morphology

In this paper, a new 3D numerical discretisation method for solving the anisotropic, steady-state diffusion problem is developed and analysed. The scheme is constructed on hexahedral meshes using the geometrical properties of the cells. Indeed, each cell provides a local basis formed using the centres of its lateral faces. The discrete cell gradient approximation is then obtained by using three discrete directional derivatives resolved in terms of this basis, and by invoking the consistent relationships between opposite faces of the same cell. The face degrees of freedom are interpolated to reduce the complexity of the numerical scheme, resulting in the main unknowns being entirely nodal based. The scheme is unconditionally coercive and admits a unique solution. Various numerical experiments are performed to highlight the accuracy and the robustness of the method with respect to the mesh and anisotropy. An important outcome is that second order convergence is observed for all problems considered, even for highly deformed meshes. After this validation process, the method is applied to the prediction of the effective thermal conductivity of wood from its real 3D morphology. The property is estimated in the radial tangential and longitudinal directions. The solver is robust, efficient and yields to similar results compared to recent contributions.

Exploration of 3D motorcycle complexes from hexahedral meshes

Shape decompositions that are guided by a motorcycle graph endow topological properties that are relevant for many engineering applications, such as T-spline fitting, shape compression and structured mesh generation. While for the surface case this is a widely studied and well-established construction, the concept of motorcycle graph was lifted to volumes only recently (Brückler et al., 2021). Due to this recent introduction, the generation of volumetric motorcycle graphs that fulfill application dependent criteria, such as minimal number of blocks or high approximation capabilities, is still an open problem. In this article we study and compare two alternative approaches to the computation of volume shape decompositions guided by a motorcycle graph. The proposed methodologies are designed to optimize alternative application-dependent quality criteria and, overall, perform better than prior art in most of the cases.

CARD18: In vitro and in silico Characterization of Aggregation and Embolization of Thrombi on Ventricular Assist Device Cannula

Background: The unacceptably high stroke rate of HeartMate III VAD without signs of pump thrombosis is hypothesized to be the result of the thrombi originating on the inflow cannula, ingesting and ejecting emboli from the VAD. Therefore, inflow cannula thrombosis has been an emerging focus. The inflow cannula of contemporary VADs, which incorporate both polished and rough regions serve as useful benchmarks to study the effects of roughness and shear on thrombogenesis. An in-vitro study was conducted to emulate the micro-hemodynamic condition on a sintered inflow cannula, and to observe the deposition and detachment patterns. With a computational fluid dynamic tool, this study aimed to provide insight into the optimization of inflow cannula and potentially reducing adverse neurological events due to upstream thrombus. Methods: A parallel plate channel was designed for this study which incorporates periodic teeth (approximately 75-micron Ra) that mimic the sintered surface treatment of a left ventricular inflow cannula. Anti-coagulated whole human blood (3.2% sodium citrate), collected from 17 healthy donors, was perfused through the microchannel by a syringe pump at calibrated flow rates to achieve shear rates of 1000, 2500, and 7500s-1 (Reynolds numbers 3.06 - 22.88). Deposition of fluorescently labeled platelets was visualized using inverted epifluorescence microscopy. Mean fluorescence intensity, deposition probability, and embolization pattern were collected. Numerical simulations of a previously validated thrombosis model were performed using OpenFOAM. A hexahedral dominant mesh was used with the transition to prism elements near the refinement region at the boundary. Results: The average fluorescence intensity map (Fig.1) depicts the time-course deposition within the serrated micro-channel for three perfusion rates studied. Sustained growth of platelets adhesion was seen in all shear conditions. Increasing the shear rate results in less adhesion and more bulk embolization, which was captured by real-time video. Variance in deposition location was also found associated with an increasing shear rate, confirmed by CFD simulation. At the lowest shear rate, platelets aggregated onto the tips of the teeth and were trapped within the valleys between teeth. At 7500 s-1, less deposition was found on the tips, and emboli were observed washing off from the tips. Conclusion: This in vitro and in silico thrombus formation study is the first to focus on emulating clinical-related surface roughness and supraphysiological shear of a VAD inflow cannula. The simulation reproduced the experimental observation of the shear-dependent spatial distribution of platelet deposition. The findings in the variance of adherent thrombus and mean intensity of platelet deposition may suggest that a supraphysiological flow induces embolization around the cannula’s rough surface, which raises concerns about hemocompatibility of inflow cannula without signs of adherent thrombus.Figure 1. (A) Experiment set-up to emulate the micro-hemodynamic condition on a sintered inflow cannula. (B) Mean fluorescent intensity of platelet deposition for three shear rates studied. N=5. (C) The results of thrombosis CFD simulation at the corresponding shear rates confirm the in vitro observation.

Computation for biomechanical analysis of aortic aneurysms: the importance of computational grid

Aortic wall stress is the most common variable of interest in abdominal aortic aneurysm (AAA) rupture risk assessment. Computation of such stress has been dominated by finite element analysis. However, the effects of finite element (FE) formulation, element quality, and methods of FE mesh construction on the efficiency, robustness, and accuracy of such computation have attracted little attention. In this study, we fill this knowledge gap by comparing the results of the calculated aortic wall stress for ten AAA patients using tetrahedral and hexahedral meshes when varying the FE formulation (displacement-based and hybrid), FE shape functions, spatial integration scheme, and number of elements through the wall thickness.

Higher-order block-structured hex meshing of tubular structures

Numerical simulations of the cardiovascular system are growing in popularity due to the increasing availability of computational power, and their proven contribution to the understanding of pathodynamics and validation of medical devices with in-silico trials as a potential future breakthrough. Such simulations are performed on volumetric meshes reconstructed from patient-specific imaging data. These meshes are most often unstructured, and result in a brutally large amount of elements, significantly increasing the computational complexity of the simulations, whilst potentially adversely affecting their accuracy. To reduce such complexity, we introduce a new approach for fully automatic generation of higher-order, structured hexahedral meshes of tubular structures, with a focus on healthy blood vessels. The structures are modeled as skeleton-based convolution surfaces. From the same skeleton, the topology is captured by a block-structure, and the geometry by a higher-order surface mesh. Grading may be induced to obtain tailored refinement, thus resolving, e.g., boundary layers. The volumetric meshing is then performed via transfinite mappings. The resulting meshes are of arbitrary order, their elements are of good quality, while the spatial resolution may be as coarse as needed, greatly reducing computing time. Their suitability for practical applications is showcased by a simulation of physiological blood flow modelled by a generalised Newtonian fluid in the human aorta.

A staggered projection scheme for viscoelastic flows

We develop a numerical scheme for the flow of viscoelastic fluids, including the Oldroyd-B and FENE-CR constitutive models. The space discretization is staggered, using either the Marker-And-Cell (MAC) scheme for structured nonuniform grids, or the Rannacher and Turek (RT) nonconforming low-order finite element approximation for general quadrangular or hexahedral meshes. The time discretization uses a fractional-step algorithm where the solution of the Navier–Stokes equations is first obtained by a projection method and then the transport-reaction equation for the conformation tensor is solved by a finite volume scheme. In order to obtain consistency, the space discretization of the divergence of the elastic part of the stress tensor in the momentum balance equation is derived using a weak form of the MAC scheme. For stability and accuracy purposes, the solution of the transport-reaction equation for the conformation tensor is split into pure convection steps, with a change of variable to the log-conformation tensor, and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the flow in the lid-driven cavity at Weissenberg numbers above one and the flow around a confined cylinder confirm the efficiency of the scheme.