Mesh Generation Research Articles

A numerical framework for simulating progressive failure in composite laminates under high-cycle fatigue loading

In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [±45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.

Robust 3D Object Mesh Generation Based on NeRF with Image Brightness Equalization for Various Lighting Environments

Robust 3D Object Mesh Generation Based on NeRF with Image Brightness Equalization for Various Lighting Environments

Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing

We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.

3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing

We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).

Meshes with Spherical Faces

Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory. We therefore systematically describe so called sphere meshes with spherical faces and circular arcs as edges where the Möbius transformation group acts on all of its elements. Driven by aspects important for manufacturing, we provide the means to cluster spherical panels by their radii. We investigate the generation of sphere meshes which allow for a geometric support structure and characterize all such meshes with triangular combinatorics in terms of non-Euclidean geometries. We generate sphere meshes with hexagonal combinatorics by intersecting tangential spheres of a reference surface and let them evolve - guided by the surface curvature - to visually convex hexagons, even in negatively curved areas. Furthermore, we extend meshes with circular faces of all combinatorics to sphere meshes by filling its circles with suitable spherical caps and provide a remeshing scheme to obtain quadrilateral sphere meshes with support structure from given sphere congruences. By broadening polyhedral meshes to sphere meshes we exploit the additional degrees of freedom to minimize intersection angles of neighboring spheres enabling the use of spherical panels that provide a softer perception of the overall surface.

Developable Quad Meshes and Contact Element Nets

The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from special parametrizations to discrete-isometric mappings. However, so far a local criterion expressing developability of general quad meshes has been lacking. In this paper, we propose a new and efficient discrete developability criterion that is applied to quad meshes equipped with vertex weights, and which is motivated by a well-known characterization in differential geometry, namely a rank-deficient second fundamental form. We assign contact elements to the faces of meshes and ruling vectors to the edges, which in combination yield a developability condition per face. Using standard optimization procedures, we are able to perform interactive design and developable lofting. The meshes we employ are combinatorially regular quad meshes with isolated singularities but are otherwise not required to follow any special curves on a developable surface. They are thus easily embedded into a design workflow involving standard operations like remeshing, trimming, and merging operations. An important feature is that we can directly derive a watertight, rational bi-quadratic spline surface from our meshes. Remarkably, it occurs as the limit of weighted Doo-Sabin subdivision, which acts in an interpolatory manner on contact elements.

A node moving-based structural topology optimization method in the body-fitted mesh

The work presents a node-moving algorithm for topology optimization (NMTO) in the arbitrarily shaped design domain. Also, we further enhanced a body-fitted mesh generation algorithm to express smooth boundaries more efficiently. In each optimization iteration, a narrowband offset from the structural profile is established, based on which a signed-distance function is constructed to determine the node-moving direction. At the same time, the magnitude of node velocity is derived from the shape derivative of the objective function - the sum of mean compliance and mean curvature. After the signed-distance function is updated based on the new position of the nodes within the narrowband with the abovementioned velocity, boundaries implicitly represented by its zero-level contour are obtained naturally. Such a forward Euler updating scheme is much more efficient than the well-known upwind algorithm for the body-fitted mesh as it avoids the interpolation of triangular nodes to the rectangular nodes and a small time step. Compared with other methods, benchmark numerical examples demonstrate that the proposed method can produce elegant structures with smoother boundaries and better objective functions for optimization problems seeking maximal stiffness or displacement at a prescribed node. In addition, the proposed approach prevents, to a large extent, useless void parts from being included in the time-consuming finite element analysis.

Analysis of Defects and Harmonic Grid Generation in Domains with Angles and Cutouts

Analysis of Defects and Harmonic Grid Generation in Domains with Angles and Cutouts

Analysis of Defects and Harmonic Grid Generation in Domains with Angles and Cutouts

A survey of works concerning difficulties associated with harmonic grid generation in plane domains with angles and cutouts is given, and some new results are presented. It is well known that harmonic grids produced by standard methods in domains with cutouts or reentrant angles (i.e., interior angles greater than π) may contain defects, such as self-overlappings or exit beyond the domain boundary. It is established that, near the vertex of a reentrant angle, these defects follow from the asymptotics constructed for the underlying harmonic mapping, according to which the grid line leaving the angle vertex is tangent to one of the angle sides at the vertex (an effect referred to as “adhesion”), except for a special case. A survey of results is given for domains z of three types with angles or cutouts (L-shaped, horseshoe, and a domain with a rectangular cutout), for which standard methods for harmonic grid generation encounter difficulties. Applying the multipole method to such domains yields a harmonic mapping for them with high accuracy: the a posteriori error estimate of the mapping in the C(z) norm is 10–7 in the case of using 120 approximative functions.

Assessment of the solar energy–agriculture–water nexus in the expanding solar energy industry of India: An initiative for sustainable resource management

The rapid expansion of solar energy in India poses challenges in the context of cropland encroachment and water-resource scarcity. To help address these challenges, we used open access satellite observations and GIS technologies over Earth Engine platform to devise the Solar Panel Index (SPI) for efficient detection of solar farms, achieving a Land use/Land cover classification accuracy of 89 %. We have used cropland, water availability, power grid and land surface temperature data-sets for generation of land suitability map. Sentinel-2 data-sets along with SPI were used to develop solar farm locations and their estimated installed capacity within the study area. The outcomes from the study depicted that over 40 % of all solar farms in the country are located on agricultural land, with the highest seen in Karnataka (73.55 %) followed by Tamil Nadu (68.81 %). Furthermore, high installed capacity coincides with low groundwater depths, exacerbating local water strain. Madhya Pradesh was found to have almost no power plant located within 5 km of surface water bodies. Our findings emphasize the significance of the solar-agriculture-water (SAW) nexus for sustainable development. Using high-resolution Land Suitability Map (LSM) as a decision-making criteria for allocating land for power generation reveals that Rajasthan holds the highest potential for solar energy installation. Our integrated approach considering the interplay between solar-energy production, agriculture, and water-resource management contributes to the sustainable growth of the solar-energy sector and regional development.

Cell-centered Lagrangian Lax-Wendroff HLL hybrid scheme in 3D

This paper describes a cell-centered Lax-Wendroff type scheme with artificial dissipation for Lagrangian fluid dynamics on general unstructured 3D meshes. The method is an extension of a similar 2D approach to 3D. The dissipative terms are inspired by the finite volume HLL flux formulation and are used as artificial viscosity in the momentum equation and as artificial energy flux in the energy equation. Special treatment is formulated for contact discontinuities and mesh-aligned interfaces. The proposed second order method provides reasonable results for typical 3D hydrodynamic tests, such as Noh, Sedov, Kidder and spherical Sod problems.

Wake characteristics of a balloon wind turbine and aerodynamic analysis of its balloon using a large eddy simulation and actuator disk model

Abstract. In the realm of novel technologies for generating electricity from renewable resources, an emerging category of wind energy converters called airborne wind energy systems (AWESs) has gained prominence. These pioneering systems employ tethered wings or aircraft that operate at higher atmospheric layers, enabling them to harness wind speeds surpassing conventional wind turbines' capabilities. The balloon wind turbine is one type of AWESs that utilizes the buoyancy effect to elevate the turbine to altitudes typically ranging from 400 to 1000 m. In this paper, the wake characteristics and aerodynamics of a balloon wind turbine were numerically investigated for different wind scenarios. Large eddy simulation, along with the actuator disk model, was employed to predict the wake behavior of the turbine. To improve the accuracy of the simulation results, a structured grid was generated and refined by using an algorithm to resolve about 80 % of the local turbulent kinetic energy in the wake. Results contributed to designing an optimized layout of wind farms and stability analysis of such systems. The capabilities of the hybrid large eddy simulation and actuator disk model (LES–ADM) when using the mesh generation algorithm were evaluated against the experimental data on a smaller wind turbine. The assessment revealed a good agreement between numerical and experimental results. While a weakened rotor wake was observed at the distance of 22.5 diameters downstream of the balloon turbine, the balloon wake disappeared at about 0.6 of that distance in all the wind scenarios. Vortices generated by the rotor and balloon started to merge at the tilt angle of 10∘, which intensified the turbulence intensity at 10 diameters downstream of the turbine for the wind speeds of 7 and 10 m s−1. By increasing the tilt angle, the lift force on the wings experienced a sharper increase with respect to that of the whole balloon, which signified a controlling system requirement for balancing such an extra lift force.

An Assessment of Solar Micro-Grid System in the Islands of Bangladesh for Sustainable Energy Access

The isolated islands in the northern Bay of Bengal face difficulties accessing electricity from the central grid and use fossil fuel-based generators, which causes health risks, environmental damage, and high expenses. So, this study aims to replace these fossil fuel-based power sources with Solar Photovoltaic (SPV) microgrids to provide continuous power to remote islands and contribute to reducing emissions. A specific location on the island of Manpura is selected for the SPV plant installation, considering land availability and vulnerability to erosion. Solar power density and other technical parameters such as Direct Normal Irradiation, Global Horizontal Irradiation, Diffuse Horizontal Irradiation, Global Tilted Irradiation, the optimum tilt angle of Photovoltaic (PV) modules, air temperature, and terrain elevation are analyzed using some prominent online analytical tools named “Global Solar Atlas (GSA)”, “Photovoltaic Geographical Information System (PVGIS)” etc. Based on these datasets, a 10kW ground-mounted PV system using monocrystalline silicon solar panels is designed for off-grid operation. The developed system can generate 14.808 MWh of energy per year. This design’s environmental and social impacts are critically analyzed considering the Sustainable Development Goals (SDGs). Compared with conventional energy sources, the results show that the 10kW microgrid SPV system can reduce CO2 emissions by 284 tons. Financial analysis shows the recovery period of the investment based on electricity production at around 8.8 years, making solar PV microgrids a viable option for remote areas like Manpura Island.

Challenges in high-fidelity thermal–hydraulic simulation of SFR cores: Insights and PACA-S4FR solutions

Numerical simulations in studying thermal–hydraulic behavior in sodium-cooled fast reactors (SFR) have gained attention for their safety and cost advantages. While low-fidelity numerical simulations commonly used in industry have the advantage of lower computational costs, they face challenges in accurately representing intricate flow phenomena. On the other hand, high-fidelity numerical simulations offer excellent characterization of turbulence but demand significant computational resources. The emergence of exascale supercomputers has provided opportunities and challenges for large-scale high-fidelity numerical simulations. In this paper, firstly, we review the research progress of thermal–hydraulic numerical simulations of SFR cores using both low-fidelity and high-fidelity methods. Secondly, we estimate the computational and storage requirements for high-fidelity numerical simulations of SFR core based on calculations performed on China Experimental Fast Reactor (CEFR). Subsequently, we analyze the challenges of conducting high-fidelity thermal–hydraulic simulations of the entire SFR core, including large-scale mesh generation, appropriate numerical discretization methods, efficient simulation acceleration techniques, coupled simulations, and the complexities of validation and verification processes. Finally, we present the research progress of PACA-S4FR, a high-fidelity thermal–hydraulic simulation software in the China Virtual Reactor (CVR1.0) project, along with the ongoing efforts to address challenges in high-fidelity simulations. This paper contributes to advancing the comprehension of SFR core thermal hydraulics, potentially aiding in safety and performance enhancements in SFR.

Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes

Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes

Pullout capacity of horizontal circular plates embedded in sand using the method of stress characteristics

The pullout capacity of horizontal anchor plates plays a crucial role in ensuring the stability and performance of various structures subjected to uplift or lateral loading. This paper presents an investigation into the pullout capacity of horizontal anchor plates using the method of stress characteristics. The method offers a simplified analytical approach that allows for quick estimations and insights into the stress distribution and failure mechanism of anchor plates. The study focuses on circular anchor plates with varying embedment ratios, considering different soil friction angles. Through computational analyses and the generation of characteristic grids, the behavior and stress distribution of anchor plates are examined. The results are compared with several experimental data from the literature to validate the applicability of the method. The findings provide valuable insights into the influence of embedment ratios and soil friction angles on the pullout capacity of horizontal anchor plates. This research contributes to the understanding of anchor plate behavior and offers a practical tool for assessing their performance in geotechnical engineering applications.

Design and Analysis of a Peak Time Estimation Framework for Vehicle Occurrences at Solar Photovoltaic and Grid-Based Battery-Swappable Charging Stations

Due to global environmental impacts, the electric vehicle (EV) adoption rate is increasing. However, unlike conventional petrol vehicles, EVs take a considerable time to charge. EVs on the road with different battery charging statuses and driving demographics may cause uncertain peak time arrivals at charging stations. Battery-swappable charging stations are a quick and easier way to replace uncharged batteries with charged ones. However, charging due to uncertain EV arrival causes higher charging profiles posing load to the grid, management of charged and discharged batteries, and peak time charging tariffs. These challenges hinder the wide operation of battery-swappable charging stations. Nevertheless, a pre-assessment of peak hours using EV demographics can reduce congestion. In recent literature surveys for battery-swappable charging stations, spot congestion has not been given much attention, which has a direct influence on the sizing and operation of battery-swappable charging stations. This research study is focused on estimating peak time events using a novel integrated techno-economic assessment framework. A fuzzy-based parametric assessment tool is developed that identifies the factors that influence higher congestion events. Based on the peak event assessment, grid, and solar PV-based generation is optimized using mixed integer linear programming. In the final step, an environment analysis of a swappable charging station is performed. Furthermore, the results achieved using the proposed framework for battery-swappable charging stations (BSCSs) were compared with fast-charging (FC) stations. FC can economically perform well if integrated with solar PV systems; however, the capital cost is 80% greater than the BSCSs designed under the proposed framework. The operational cost of BSCSs is 39% higher than FC stations as they use 29% higher grid units than FC stations due to night operations under congestion.

Intelligent mesh generation for crack simulation using graph neural networks

Mesh generation for crack simulation is often the rate-limiting step because of the rapid variations in crack shape. The classical meshing paradigm, place-nodes-and-link, relies on predefined rules and fails to generalize various crack shapes. We proposed a graph neural networks-based method for recovering the missing connection information in the crack meshes. The constrained Delaunay triangulation method created a representative training mesh dataset with different crack shapes. Comprehensive and systematic analyses compare the effectiveness and efficiency of five state-of-art GNNs under different graph representations. Our study shows that the trained GraphSAGE outperforms the state-of-art GNNs on the triangular meshing task efficiently and reveals GNNs' potential to restore the missing information between adjacency vertices or edges. This work pioneers the application of GNNs for intelligent mesh generation and paves the way for complex crack simulation.

Automatic micro-scale modelling and evaluation of effective properties of highly porous ceramic matrix materials using the scaled boundary finite element method

This paper presents an approach to the numerical estimation of effective properties of highly porous materials based on the scaled boundary finite element method (SBFEM). The latter can be formulated on quadtree meshes with hanging nodes and thus facilitates the efficient mesh generation and analysis of a large number of randomly created samples. To generate the corresponding Representative Volume Elements (RVEs), an improved Random Sequential Addition (RSA) method with overlap is used. Moreover, an alternative image-based digital matrix method for generating random assemblies of circular particles of the same size is proposed. In addition, a modified smoothing algorithm to treat the staircase boundaries present in a quadtree mesh is developed in order to accurately and efficiently capture the sinter-neck features of overlapping circular particles. The proposed image-based mesh generation and analysis procedure is used to evaluate the relationship between microstructural parameters and effective Young’s modulus considering a large number of samples. In this context, a new dimensionless morphological parameter Nfc is proposed. The latter represents the morphology and connectivity of voids and is shown to be a useful indicator with respect to the effective elastic properties of highly porous ceramic matrix material.

Heat flux predictions for hypersonic flows with an overset near body solver on an adaptive block-structured Cartesian off-body grid

The manual volume mesh generation process for body-fitted CFD codes can be a time-intensive process, particularly for complex flight vehicles. The work shown here presents a hybrid body-fitted/Cartesian overset CFD solver capable of automatic volume mesh generation capabilities and accurate surface heating predictions. The solver uses a body-conformal near body solver for capturing boundary layer effects and an off-body Cartesian solver with adaptive mesh refinement for shock and wake tracking within the CHAMPS CFD code. The formulated near body Cartesian solver is the first of its kind to be applied within the context of low and high enthalpy, hypersonic viscous flows. The developed solver is validated on a Mach 9.47 Mars Science Lander and a Mach 6 Orion Crew Exploration Vehicle in a low-enthalpy flow at various non-zero angles of attack followed by a Mach 25.2 AS-202 capsule at a 17.8-degree angle of attack for Earth re-entry. Validation is shown based on grid convergence studies as well as good agreement to available numerical and experimental data in consideration of surface heating and surface pressure predictions.