Mesh Generation Method Research Articles

A data-free Kolmogorov–Arnold Network-based method for structured mesh generation

Mesh generation is a critical but time-consuming process for stable and accurate numerical simulations. Although multi-layer perceptron-based meshing methods can be effective, they suffer from slow training convergence and heavy reliance on prior datasets. To overcome these problems, we propose the Kolmogorov–Arnold Network-based meshing network, an efficient data-free method for structured mesh generation. The proposed method takes the meshing task as an optimization problem and embeds meshing-related differential equations into the loss function of Kolmogorov–Arnold Networks. It employs two parts to generate meshes efficiently. The Kolmogorov–Arnold Network part introduces learnable activation functions on the edges of the network, which enables the network to learn meshing rules between parametric and computational domains. The physics-informed learning part provides meshing-related information to guide the network training. Finally, the proposed method can produce high-quality structured meshes with a user-defined number of quadrilateral or hexahedral cells through feed-forward prediction. Experiments on different geometries show that the proposed method achieves up to three orders of magnitude improvement in meshing efficiency compared to traditional methods. It also outperforms state-of-the-art multi-layer perceptron-based methods, yielding high-quality meshes in both two-dimensional and three-dimensional cases without prepared data.

An automatic hybrid mesh generation method for combustion fluid dynamics simulations

PurposeAutomatic mesh generation is still a challenge problem for combustion fluid dynamics simulations because of the high-quality requirement and complexity of geometries. This paper aims to find an efficient automatic analysis model creation and mesh generation method to save the time for pre-processing in numerical simulations.Design/methodology/approachBased on the previous work, we explore effective model processing and mesh generation methods from practical engineering applications. Considering the automation and high quality requirement, we construct an automatic mesh generation procedure for combustion fluid dynamics problems.FindingsThe numerical results show that the procedure we proposed in this paper can automatically generate high quality mesh for combustion fluid dynamics simulations. The strategy of fluid model construction is time-saving and with high-precision. The mesh generation method in our procedure is automatic and efficient.Practical implicationsThe procedure proposed in this paper is applicable to the practical engineering application model, such as aircraft simulation, aeroengine simulation and so on. The procedure has been integrated into an numerical simulation software.Originality/valueThe method proposed in this paper has very practical application value. It can be used in the practical application and saves a lot of manual processing time for numerical stimulation specialists.

3D Reconstruction of Geometries for Urban Areas Supported by Computer Vision or Procedural Generations

This work presents a numerical mesh generation method for 3D urban scenes that could be easily converted into any 3D format, different from most implementations which are limited to specific environments in their applicability. The building models have shaped roofs and faces with static colors, combining the buildings with a ground grid. The building generation uses geographic positions and shape names, which can be extracted from OpenStreetMap. Additional steps, like a computer vision method, can be integrated into the generation optionally to improve the quality of the model, although this is highly time-consuming. Its function is to classify unknown roof shapes from satellite images with adequate resolution. The generation can also use custom geographic information. This aspect was tested using information created by procedural processes. The method was validated by results generated for many realistic scenarios with multiple building entities, comparing the results between using computer vision and not. The generated models were attempted to be rendered under Graphics Library Transmission Format and Unity Engine. In future work, a polygon-covering algorithm needs to be completed to process the building footprints more effectively, and a solution is required for the missing height values in OpenStreetMap.

Slot coating of time-dependent structured materials: Effects of thixotropy on the flow dynamics and operating limits

Some of the most common liquid-like formulations rooted in the coating industry consist of rheologically complex structured materials such as inks, paints, and slurries. Yet, the impact of time-dependent structuring effects due to thixotropy on thin film coating applications remains elusive and still unclear. Here, we present a computational study of the effects of thixotropy on slot coating of time-dependent structured materials. By coupling a recent fluidity-based constitutive model for thixotropic materials with a well-established finite element/elliptic mesh generation method for free surface flows, we assess the role of thixotropy by comparing the predictions from the thixotropic model with those from a simple Generalized Newtonian Fluid model that uses the same flow curve for the material steady-state equilibrium viscosity. We find that thixotropy can indeed have a major impact on slot coating applications, potentially bringing strong implications not only to the flow dynamics but also to the operating limits of the process. In conclusion, the results and discussions we present in this study underscore the importance of accounting for thixotropy to genuinely model and fundamentally understand the behavior of time-dependent structured materials with complex rheology in processing flows like those ubiquitous across the broad fields of coating science and engineering.

Template mapping method for plane quadrilateral mesh generation with controllable density transitions

Template mapping method for plane quadrilateral mesh generation with controllable density transitions

Space–time isogeometric analysis of tire aerodynamics with complex tread pattern, road contact, and tire deformation

AbstractThe space–time (ST) computational method “ST-SI-TC-IGA” and recently-introduced complex-geometry isogeometric analysis (IGA) mesh generation methods have enabled high-fidelity computational analysis of tire aerodynamics with near-actual tire geometry, road contact, tire deformation, and aerodynamic influence of the car body. The tire geometries used in the computations so far included the longitudinal and transverse grooves. Here, we bring the tire geometry much closer to an actual tire geometry by using a complex, asymmetric tread pattern. The complexity of the tread pattern required an updated version of the NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, which was introduced recently and is robust even in mesh generation for complex shapes with distorted boundaries. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). They all play a key role. The ST-TC, uniquely offered by the ST framework, enables moving-mesh computation even with the topology change created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire.The computational analysis we present is the first of its kind and shows the effectiveness of the ST-SI-TC-IGA and NSVGMG in tire aerodynamic analysis with complex tread pattern, road contact, and tire deformation.

A nonconforming surface mesh generation method by binary tree

Computer-aided engineering (CAE) has emerged as an indispensable tool for facilitating engineering practices and driving industrial innovation. However, the insufficient quality and efficiency of discretizing complex computer-aided design (CAD) models significantly impede the advancement of CAE calculation accuracy and automation. The presence of “dirty” geometry leads to the fact that it is almost impossible to generate a traditional conforming mesh without geometry repair. In most instances, automating geometry repair proves to be even more challenging than meshing. To cope with intricate CAD model with “dirty” geometry, a novel binary tree surface subdivision method (BSSM) is proposed for automatically generated conforming and nonconforming meshes directly on CAD models. In contrast to the conventional conforming mesh, the nonconforming mesh allows for hanging nodes, thereby eliminating the limitations of the mesh conformance. This facilitates rapid transitions in mesh size for automatic mesh generation when dealing with “dirty” geometry. A series of numerical models employing BSSM are presented in this study. Results reveal that BSSM can automatically, efficiently and reliably generate high level quality mesh for arbitrary structures.

A general-purpose IGA mesh generation method: NURBS Surface-to-Volume Guided Mesh Generation

AbstractThe NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) is a general-purpose mesh generation method, introduced to increase the scope of isogeometric analysis in computing complex-geometry problems. In the NSVGMG, NURBS patch surface meshes serve as guides in generating the patch volume meshes. The interior control points are determined independent of each other, with only a small subset of the surface control points playing a role in determining each interior point. In the updated version of the NSVGMG we are introducing in this article, in the process of determining the location of an interior point in a parametric direction, more weight is given to the closer guides, with the closeness measured along the guides in the other parametric directions. Tests with 2D and 3D shapes show the effectiveness of the NSVGMG in generating good quality meshes, and the robustness of the updated NSVGMG even in mesh generation for complex shapes with distorted boundaries.

Investigation of sheath structure in surface flashover induced by high-power microwave

Flashover is a major limiting factor for the transmission and miniaturization of high-power microwave (HPM) devices. We conducted a study to investigate the developmental process of surface flashover on HPM dielectric windows through particle-in-cell-Monte Carlo collision simulations. A one-dimensional spatial distribution and three-dimensional velocity distribution model is established, encompassing the entire process of surface flashover, which includes electrode field emission, single-surface multipactor, outgassing, and gas breakdown. The nonuniform mesh generation method is employed to enhance the simulation accuracy. The growth rates of electron and ion densities increase as gas pressure rises. Additionally, the discharge transitions gradually from multipactor to gas ionization dominance. Notably, a space-charge-limited (SCL)-like sheath occasionally forms during an rf cycle near the surface under intermediate background pressure (∼0.05 Torr). The SCL-like sheath cannot exist stably. Instead, it periodically disappears and appears as the rf electric field changes. The underlying physics are explained by the variations of the rf electric field, which lead to the variations in the surface charge density, thereby affecting the normal electric field. The normal electric field interacts with the spatial distribution of charged particles, ultimately leading to the formation of the SCL-like sheath. This work may facilitate a comprehensive understanding of the developmental processes of surface flashover.

An efficient unstructured quadrilateral-dominated surface mesh generation method for arbitrary geometry with tiny features or crack defects in DiBFM

An efficient unstructured quadrilateral-dominated surface mesh generation algorithm is presented to generate high-quality surface elements for arbitrary geometry with tiny features or crack defects. For complex entities with proximity features, a novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. The algorithm also works for regions with proximity features, as well as for arbitrary geometry with one or multiple cracks. The procedure incorporates aspects of well-known meshing techniques, but includes some original and efficient processes. The refinement field is constructed according to mesh size, boundary curvature, surface curvature and other geometry features. In order to effectively generate the core mesh, a fast intersection algorithm between topological elements and the solid boundary is established, which improves the efficiency of intersection calculation. The geometry-based techniques are employed for boundary matching of the core mesh. The method has been successfully employed in conjunction with the dual interpolation boundary face method (DiBFM). Several realistic geometries with cracks or proximity features are applied to demonstrate the accuracy and validity of the proposed approach.

Feature-preserving quadrilateral mesh Boolean operation with cross-field guided layout blending

Compared to triangular meshes, high-quality quadrilateral meshes offer significant advantages in the field of simulation. However, generating high-quality quadrilateral meshes has always been a challenging task. By synthesizing high-quality quadrilateral meshes based on existing ones through Boolean operations such as mesh intersection, union, and difference, the automation level of quadrilateral mesh modeling can be improved. This significantly reduces modeling time. We propose a feature-preserving quadrilateral mesh Boolean operation method that can generate high-quality all-quadrilateral meshes through Boolean operations while preserving the geometric features and shape of the original mesh. Our method, guided by cross-field techniques, aligns mesh faces with geometric features of the model and maximally preserves the original mesh's geometric shape and layout. Compared to traditional quadrilateral mesh generation methods, our approach demonstrates higher efficiency, offering a substantial improvement to the pipeline of mesh-based modeling tools.

A Structured Mesh Generation Based on Improved Ray-Tracing Method for Finite Difference Time Domain Simulation

A structured mesh generation method based on an improved ray-tracing technique is proposed for finite time difference domain (FDTD) simulation in this paper. This method converts the triangular faces provided by the STL file into the structured mesh required by the FDTD method. The size of the generated structured mesh is determined by the size of the triangular element, so it is non-uniform and can adapt to the shape of the target. In addition, this method proposes an improved ray-tracing technique to avoid the singularities of the object, so it has much better accuracy than the conventional method. Two representative electromagnetic objects, an Su-30 aircraft and a complex bow-tie antenna, representing a typical electrically large model and fine structure, respectively, are used to validate the accuracy of the mesh generation method. The results show that the presented method has high accuracy, regardless of whether it is used for large targets or fine structures such as a small hole, strip, thin layer, etc.

Slot coating of viscoplastic materials: A computational study of the effects of viscoplasticity on the flow dynamics and low-flow limit

Yield-stress materials such as structurally complex formulations of paints, slurries, and waxes have been long ubiquitous in the coating industry, though the practice of coating engineering remains largely empirical as the fundamental role of viscoplasticity due to the yield stress of the coating material in most coating applications is still unclear. Here, we couple a recent harmonic mean viscosity regularization for the Bingham model with a well-established finite element/elliptic mesh generation method for free surface flows to present a detailed computational study of slot coating applications of viscoplastic materials. By neglecting inertia and focusing on the downstream section of a slot coater, we introduce suitable dimensionless parameters to discuss a comprehensive set of results that unravels a striking impact of viscoplasticity on the flow dynamics and low-flow limit. We show that viscoplastic effects have major implications to the velocity field and recirculation pattern in the coating bead as well as to the development length and free surface in the film formation region. Most importantly, we find that viscoplastic effects markedly widen the operating window of the process, delaying the onset of the low-flow limit and thereby suggesting that structurally complex yield-stress materials may be used to coat thinner films and/or at higher speeds than predicted by the standards far established for simple Newtonian liquids.

Simulation and experimental study on contact pressure distribution of contact interface in single and double bolted connection structures

Bolted joints play an important role in aerospace, machinery manufacturing, weapons and other fields, and the contact pressure distribution at the connection interface seriously affects the service performance of the bolts. Contact pressure analysis is an essential basis and reference for structural design, calibration, inspection, and safety monitoring of bolted connection structures. Considering the preload force and frictional contact between the joint components, a block mapping hexahedron mesh generation and finite element modeling method for bolted connections is presented, and the finite element models of single and double bolted structures are constructed. Then, an experimental test platform for measuring contact pressure distribution is constructed. Comparison of finite element analysis results with experimental results for the contact pressure distribution in the single and double-bolted joints; the root mean squared error of contact pressure distribution is less than 5%, which verifies the effectiveness of the finite element models. After that, the models are used to study the contact pressure distribution in single-bolted joints and contact pressure coupling effect of double-bolted joints, and the normal stress distribution features within members and contact pressure distribution contour are revealed for single and double-bolted joint. Finally, the finite element models are adopted to investigate the effects of the clamping length, preload, material properties, hole clearance, and bolt size on contact pressure distribution in single-bolted joints. The coupling effect of contact pressure distribution in double-bolted joints under different preloads and geometric parameters are also examined.

An Implicit Adaptive FDTD Mesh Generation Techniquebased on Tetrahedrons

A novel implicit adaptive FDTD mesh generation method based on tetrahedrons is proposed in this paper. According to the vertex coordinates of tetrahedrons which make up an object, non-uniform grid lines are generated first. These grid lines are constrained by the structure of the object and follow three rules mentioned in the paper. The first rule is to find demarcation points of the object and drop grid lines on these points. The second rule is to make sure all mesh sizes are less than one-tenth of the wavelength by adding more grid lines. The last rule is to densify mesh at the fine structure of the object. Then by comparing the positional relationship between center points of Yee cells and tetrahedrons, the object can be discretized by Yee cells. Finally, numerical examples are given to verify the validity and accuracy of this novel method.

Boundary constrained quadrilateral mesh generation based on domain decomposition and templates

Compared to triangular or mixed meshes, pure quadrilateral meshes generally offer higher accuracy and computational efficiency in numerical simulations. Recently, the main obstacles in the generation of quadrilateral meshes have revolved around the identification of mesh singularities and the subsequent decomposition of the domain. In this study, a novel quadrilateral mesh generation method based on domain decomposition and templates is presented. The basic idea is to decompose the domain by separating the mesh singularities rather than identifying their precise locations. Surfaces composed of a set of surface patches are meshed independently. For each surface patch, the problem domain is divided into several simple polygonal subregions, including quadrangles, triangles, and pentagons, using constrained Delaunay triangulation (CDT) and recursive bisections. Subsequently, mesh templates with a limited number of singularities are employed to rapidly generate high-quality quadrilateral meshes over those subregions. By constraining the boundary discretization of each surface patch, mesh conformability is automatically achieved. An integer linear programming equation is presented to ensure that the total number of boundary nodes on each surface is an even value. Several experimental results are presented and discussed, demonstrating the reliability and efficiency of the proposed method.

Structured triangular mesh generation method for free-form gridshells based on conformal mapping and virtual interaction forces

With the rapid development of computer-aided design, manufacturing, and construction techniques, free-form single-layer reticulated shells (SLRSs) are increasingly applied in modern architectures. However, generating a uniform and smooth mesh directly on a three-dimensional free-form surface is challenging. This paper proposes a fast and automatic method to generate structured triangular mesh for free-form SLRSs. The difficulty is reduced by generating the mesh on the two-dimensional (2D) parametric plane obtained by conformal mapping. The virtual interaction forces (VIFs) combined with the area map are used to automatically adjust the distribution of the 2D structured base mesh to reduce distortions. Subsequently, mesh clipping and barycentric interpolation are used to map the planar mesh back to the original surface. Finally, the VIF-based mesh smoothing is conducted to improve the mesh uniformity and smoothness. Case studies show that the proposed method successfully generates high-quality structured triangular meshes on various types of free-form SLRSs. Moreover, this method can precisely control the overall size and direction of the mesh, providing architects and engineers with more choices of mesh patterns.

Developing a novel structured mesh generation method based on deep neural networks

In this paper, we develop a novel structured mesh generation method, MeshNet. The core of the proposed method is the introduction of deep neural networks to learn high-quality meshing rules and generate desired meshes. To accomplish this, MeshNet employs a well-designed physics-informed neural network to approximate the potential transformation (mapping) between computational and physical domains. The training process is governed by differential equations, boundary conditions, and a priori data derived from coarse mesh generation, which has been disregarded in previous studies. The automatic subdivision of a given domain into quadrilateral elements is achieved through efficient feed-forward neural prediction. A series of experiments are conducted to investigate the robustness of the proposed method. The results across different cases demonstrate that MeshNet is fast and robust. It outperforms state-of-the-art neural network-based generators and produces meshes of comparable or higher quality compared to expensive traditional meshing methods. Furthermore, the proposed method enables fast varisized mesh generation without re-training. The simplicity and computational efficiency of MeshNet make it a novel meshing tool in the discretization part of simulation software.

Structure optimization of helium-cooled blanket for fusion reactor based on three-dimensional full-scale thermal-hydraulic analysis

Fusion energy is widely considered as the most promising method to solve the energy crisis, while the blanket is of vital importance in the fusion device due to its main function of thermal extraction and energy conversion. The high heat flux from plasma and the internal nuclear heat deposition are imposed on fusion blanket. Slice model or two-dimensional model is usually adopted for traditional design of fusion blanket, in which most side effects are neglected, introducing relatively large uncertainty for thermal removal capability of the blanket. In this study, the integral three-dimensional full-scale model is established based on the split-zone method for mesh generation. Based on the validated numerical method, the preliminary thermal-hydraulic analysis of the full-scale model shows that inadequate heat transfer and significant flow distribution difference are encountered for the initial blanket design, in which the full-scale effect is not considered. After that, the specific structure modifications are proposed for different blanket components to solve the abovementioned problems. The maximum temperature of first wall is reduced from 671°C to 639°C, which is under the material temperature limit of 650°C; the inverse V-shaped flow distribution in the cap is modified as more even flow in cap channels; the maximum temperature of the function zone in blanket is reduced from 999°C to 759°C, which is an important structure modification for the blanket. The integral three-dimensional full-scale thermal-hydraulic analysis is performed after the local structure modification. The results show that the function zone is cooled down obviously by the coolant in the side wall. Compared to the temperature limit of 900°C for lithium orthosilicate, there is a more rigorous limit for the beryllium material, since they share the common cooling capability layer by layer while the temperature limit for the latter is only 650°C. The three-dimensional full-scale thermal-hydraulic analysis in our research is valuable to evaluate the integral reliability of the fusion blanket.

Proposing a Method for Performance Evaluation of a Designed Two-Phase Vertical Separator and a Piston Pump Using Computational Fluid Dynamics

Summary Designing and testing effective separators is a time-consuming task that requires sophisticated laboratory equipment or expensive field tests. Computer-aided simulation could be a fast and affordable alternative if the method demonstrates effectiveness and reliability. This work implements a method to simulate a hybrid separator by considering variable outlet boundary conditions caused by a piston pump. This method consists of a novel mesh generation method and a two-phase unsteady-state computational fluid dynamics model that enables full-scale simulations and shows acceptable results that comply with experimental data. Furthermore, the simulation is repeated in several gas/liquid ratios and piston speeds, leading to a correlation to predict the separation efficiency of similar designs. As expected, the results revealed that the pressure drop would increase and separator efficiency would decrease by increasing the piston speed. The influence of the gas/liquid ratio on the pressure drop and separation efficiency was negligible.