Unstructured and semi-structured hexahedral mesh generation methods

Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version

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

High-quality conforming hexahedral meshes of patient-specific abdominal aortic aneurysms including their intraluminal thrombi

In order to perform finite element (FE) analyses of patient-specific abdominal aortic aneurysms, geometries derived from medical images must be meshed with suitable elements. We propose a semi-automatic method for generating conforming hexahedral meshes directly from contours segmented from medical images. Magnetic resonance images are generated using a protocol developed to give the abdominal aorta high contrast against the surrounding soft tissue. These data allow us to distinguish between the different structures of interest. We build novel quadrilateral meshes for each surface of the sectioned geometry and generate conforming hexahedral meshes by combining the quadrilateral meshes. The three-layered morphology of both the arterial wall and thrombus is incorporated using parameters determined from experiments. We demonstrate the quality of our patient-specific meshes using the element Scaled Jacobian. The method efficiently generates high-quality elements suitable for FE analysis, even in the bifurcation region of the aorta into the iliac arteries. For example, hexahedral meshes of up to 125,000 elements are generated in less than 130 s, with 94.8 % of elements well suited for FE analysis. We provide novel input for simulations by independently meshing both the arterial wall and intraluminal thrombus of the aneurysm, and their respective layered morphologies

HexBox: Interactive Box Modeling of Hexahedral Meshes

We 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

Unstructured hexahedral mesh generation of complex vascular trees using a multi-block grid-based approach

The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid-structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed

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

HexaLab.net: An online viewer for hexahedral meshes

© 2018 Elsevier Ltd We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. Our system offers also immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hexmesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community