Mesh Generation Research Articles

Wave Propagation for Structural Health Monitoring (WaveProSHM): open software with GUI

Guided wave–based SHM methods have been explored extensively in recent decades. The wave propagation modelling including piezoelectric transducers and various damage types helps understand intricacies of guided wave behavior and for designing a robust SHM system. However, modelling aspects are still challenging. Moreover, commercially available software for the modelling of guided waves often lacks appropriate high-order elements and code optimization for fast GPU computations. This research aimed to develop and disseminate to the SHM community the open software based on highly efficient vectorised code of the time domain spectral element method which can be run on GPU. The developed code is written in MATLAB with Graphical User Interface (GUI) and communicates with GMSH – open source finite element mesh generator. It can model signals of propagating guided waves in structures which are excited and registered by an array of piezoelectric transducers. The capabilities of the software are shown in an example of a large-scale problem of interacting guided waves with delamination.

Mesh morphing-based pre-processing and numerical simulation of blockage accident in lead–bismuth fast reactor fuel assembly

This paper presents a CFD modeling approach for a 19-rod bundle fuel assembly with spiral semi-cylindrical ribs, which potentially can be used for liquid metal cooled fast reactor, as well as a numerical simulation of flow and thermal behavior under partially blocked conditions. The ribs on fuel rod surface are integrally formed with the cladding to enhance heat transfer while preventing detachment. However, the complex channel geometry presents challenges for grid generation, as using a large number of tetrahedral or polyhedral elements would consume significant computational resources. Therefore, this paper proposes a mesh morphing-based pre-processing method to establish a structured hexahedral mesh for such complex geometry. Using this approach, the 19-rods assembly is analyzed, and the result has been verified by conventional mesh scheme as well as experiment.

Topology and parameter optimization of IPM motor considering mechanical strength by stress and connection constraints

PurposeThe purpose of this study is to apply the topology and parameter optimization (TPO) to interior permanent magnet (IPM) motors to obtain the optimized shape with higher torque, lower ripple and sufficient mechanical strength.Design/methodology/approachThe constraints regarding the maximum stress, connectivity and mesh quality were considered to achieve not only high electrical performance but also high mechanical strength. To enhance the accuracy of the finite element analysis of the elastic analysis, this paper used body-fitted mesh adaptation technique to avoid the stress concentration.FindingsThe proposed method in this study resulted in feasible shapes with sufficiently high strength compared to previous studies. It is also shown that TPO yielded IPM motors with higher torque compared to topology optimization (TO) with fixed parameters.Practical implicationsDifferent from the existing studies on topology optimization of IPM motors, the mechanical strength is even considered by evaluating the stress values. Therefore, in the practical phase, geometries can be designed that are less likely to be damaged due to deformation, even in the high-speed rotation range.Originality/valueThis paper performed TO and parameter optimization (PO) simultaneously, considering not only the electrical performance but also the mechanical strength. Furthermore, the mechanical strength was evaluated more precisely by devising the elastic analysis conditions and mesh generation.

Elastic response of trabecular bone under compression calculated using the firm and floppy boundary lattice element method

Micro-Finite Element analysis (μFEA) has become widely used in biomechanical research as a reliable tool for the prediction of bone mechanical properties within its microstructure such as apparent elastic modulus and strength. However, this method requires substantial computational resources and processing time. Here, we propose a computationally efficient alternative to FEA that can provide an accurate estimation of bone trabecular mechanical properties in a fast and quantitative way. A lattice element method (LEM) framework based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) open-source software package is employed to calculate the elastic response of trabecular bone cores. A novel procedure to handle pore-material boundaries is presented, referred to as the Firm and Floppy Boundary LEM (FFB-LEM). Our FFB-LEM calculations are compared to voxel- and geometry-based FEA benchmarks incorporating bovine and human trabecular bone cores imaged by micro Computed Tomography (μCT). Using 14 computer cores, the apparent elastic modulus calculation of a trabecular bone core from a μCT-based input with FFB-LEM required about 15 min, including conversion of the μCT data into a LAMMPS input file. In contrast, the FEA calculations on the same system including the mesh generation, required approximately 30 and 50 min for voxel- and geometry-based FEA, respectively. There were no statistically significant differences between FFB-LEM and voxel- or geometry-based FEA apparent elastic moduli (+24.3% or +7.41%, and +0.630% or -5.29% differences for bovine and human samples, respectively).

Debunking common myths in coastal circulation modeling

Despite tremendous progress in algorithm development, computational efficiency and transition into operations over the past two decades, coastal modeling still lacks scientific rigor due to proliferation of many ‘gray’ areas related to various modeling choices made by modelers. In this paper, we propose some guiding principles for the modeling community to improve performance, and we also debunk commonly held myths that make the coastal modeling lack rigor. Using our own experience in developing seamless cross-scale unstructured-grid based models for the past two decades, we describe in unprecedented detail the end-to-end modeling process (i.e., from digital elevation models (DEMs) to mesh generation to post analysis), and demonstrate that defensible modeling is within reach for any end user by following three guiding principles: (1) Bathymetry is a first order forcing in coastal domains and thus should be respected in all aspects of modeling; (2) Oceanographic processes are driven across multiple spatial scales and so models should enable appropriate resolution as needed; and (3) Model assessment should focus on physical processes. Through qualitative and quantitative model assessments, we demonstrate the fundamental role played by bathymetry/topography as embedded in DEMs in making the results defensible, which is unfortunately glossed over in many modeling studies. Focusing on process-based assessment simplifies the calibration process. A major conclusion of this work is that model developers and operators should maximize the scientific rigor for in silico oceanography by avoiding some common pitfalls that rely on error compensation at the expense of representation of physical system processes. We present some best practice procedures for defensive and trustworthy numerical modeling.

Analysis of power quality and additional loss in distribution network with distributed generation

As the penetration of distributed generation in the power grid, the power quality issues in the active distribution network are becoming increasingly diversified, hence followed with complex changes of the additional loss. The article investigates the additional loss caused by disorder power flow and power quality disturbances in the active distribution network. Firstly, the active distribution network model is established based on typical parameters. The impact of the access of distributed generation on power quality issues, including three-phase imbalance, harmonic distortion and voltage deviation and rise, is analyzed. Then, the influence of different power quality disturbances on additional loss with distributed generation is quantitatively explored. By introducing the concept of harmonic three-phase imbalance, the article analyzes the variation characteristics of network loss under the disturbances of composite power quality issues, and introduces the concept of a loss reduction interval, whose size is related to the average current. Finally, the validity of the analysis is verified through simulation. This article provides a new approach for loss analysis in distribution network containing distributed generation, which is beneficial for identifying and minimizing network loss in distribution networks.

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.

Hybrid meshless-FEM method for 3-D magnetotelluric modelling using non-conformal discretization

SUMMARY We propose a novel method for 3-D magnetotelluric (MT) forward modelling based on hybrid meshless and finite-element (FE) methods. This method divides the earth model into a central computational region and an expansion one. For the central region, we adopt scatter points to discretize the model, which can flexibly and accurately characterize the complex structures without generating unstructured mesh. The meshless method using compact support radial basis function is applied to simulate this area's electromagnetic field. While in the expansion region, to avoid the heavy time consumption and numerical error of the meshless method caused by non-uniform nodes, we adopt a node-based finite-element method with regular hexahedral mesh for stability. Finally, the two discretized systems are coupled at the interface nodes according to the continuity conditions of vector and scalar potentials. Considering that the normal electric field is discontinuous at the interface with resistivity discontinuity, while the shape functions for the meshless method are continuous, we further adopt the visibility criterion in constructing the support region. Numerical experiments on typical models show that using the same degree of freedom, the hybrid meshless-finite element method (FEM) algorithm has higher accuracy than the node-based FEM and meshless method. In addition, the electric field discontinuity at interfaces is well preserved, which proves the effectiveness of the visibility criterion method. In general, compared to the conventional grid-based method, this new approach does not need the complex mesh generation for complex structures and can achieve high accuracy, thus it has the potential to become a powerful 3-D MT forward modelling technique.

A Delaunay refinement algorithm for the particle finite element method applied to free surface flows

AbstractThis article proposes two contributions to the calculation of free‐surface flows using the particle finite element method (PFEM). The PFEM is based upon a Lagrangian approach: a set of particles defines the fluid and each particle is associated with a velocity vector. Then, unlike a pure Lagrangian method, all the particles are connected by a triangular mesh. The difficulty lies in locating the free surface from this mesh. It is a matter of deciding which of the elements in the mesh are part of the fluid domain, and to define a boundary—the free surface. Then, the incompressible Navier–Stokes equations are solved on the fluid domain and the particle position is updated using the velocity vector from the finite element solver. Our first contribution is to propose an approach to adapt the mesh with theoretical guarantees of quality: the mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh. The approach we use here is based on a Delaunay refinement strategy, allowing to insert and remove nodes while gradually improving mesh quality. We show that what is proposed allows to create stable and smooth free surface geometries. One characteristic of the PFEM is that only one fluid domain is modeled, even if its shape and topology change. It is nevertheless necessary to apply conditions on the domain boundaries. When a boundary is a free surface, the flow on the other side is not modeled, it is represented by an external pressure. On the external free surface boundary, atmospheric pressure can be imposed. Nevertheless, there may be internal free surfaces: the fluid can fully encapsulate cavities to form bubbles. The pressure required to maintain the volume of those bubbles is a priori unknown. For example, the atmospheric pressure would not be sufficient to prevent the bubbles from deflating and eventually disappearing. Our second contribution is to propose a multi‐point constraint approach to enforce global incompressibility of those empty bubbles. We show that this approach allows to accurately model bubbly flows that involve two fluids with large density differences, for instance water and air, while only modeling the heavier fluid.

Parametric Modeling and Numerical Simulation of a Three-Dimensional Random Aggregate Model of Lime–Sand Piles Based on Python–Abaqus

A lime–sand pile is a three-phase particle composite material composed of a lime matrix, sand, and a loess aggregate at the meso level. Establishing a random aggregate model that can reflect the actual aggregate gradation, content, and morphology is the premise of numerical simulations of the meso-mechanics of lime–sand piles. In this paper, the secondary development of Abaqus 2022 is realized by writing Python 3.12 scripts, and a parameterized three-phase mixed lime–sand pile random meso-spherical aggregate model is obtained. A meso-modeling idea of lime–sand piles is creatively proposed, the integrated-generation algorithm of a spherical aggregate of different materials is written, and the material’s properties and mesh generation are given by the algorithm. Finally, a numerical simulation of temperature–expansion statics is carried out using an established mesoscopic model. Under different mixing ratios, the expansion force increases with an increase in the lime proportion. The increase in the expansion force is approximately 45% of that without an increased lime proportion. The simulated expansion forces are 8.81 kN, 12.61 kN, and 18.89 kN, respectively, which are similar to the experimental results for laboratory specimens, and the relative error is less than 3%. In the case of different height ratios, with increases in height, the change in the expansion force is very small, and the relative error between the simulated value and the experimental value is less than 2%, which further verifies the reliability of the mesoscopic random model of lime–sand piles. The model can be used to guide the practical application of engineering.

An improved polygon mesh generation and its application in SBFEM using NURBS boundary

An improved polygon mesh generation and its application in SBFEM using NURBS boundary

Integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with a coupled CFD solver

The occurrence of fluid flow near a wellhead is the major concern of the petroleum industry, as pressure drop, loss of formation, and other variables of interest are mostly affected in this region. The fluid flows from the hydrocarbon reservoir to the wellbore can be characterized as laminar to turbulent; thus, it is important to model this phenomenon with the integrated wellbore-reservoir model. Using 3D Navier–Stokes equations, an integrated wellbore-reservoir model is created in this study, and it incorporates the formation damage zone. For the porous-porous and porous-fluid interfaces, the General Grid Interface (GGI) approach is applied in conjunction with the conservative mass flux interface model. Model equations are solved using a velocity-pressure coupling solver that is pressure-based. For reliable and quick results, the system of equations is solved using an algebraic multigrid approach. The pressure diffusivity equation’s analytical solution under steady-state flow circumstances is used to validate the model. The integrated wellbore-reservoir model is applied to different reservoir scenarios, for example, different production rates, formation zones, and reservoir formation conditions. The results indicate that the present Computational Fluid Dynamics (CFD) model can be extended to simulate the real field scale model. integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with efficient computational techniques can lead the field of petroleum industries to advance current knowledge.

Joint Optimization of Internet of Things and Smart Grid for Energy Generation, Battery (Dis)charging, and Information Delivery

Joint Optimization of Internet of Things and Smart Grid for Energy Generation, Battery (Dis)charging, and Information Delivery

A Staggered Scheme for the Compressible Euler Equations on General 3D Meshes

A Staggered Scheme for the Compressible Euler Equations on General 3D Meshes

Deep neural network method to predict the dynamical system response under random excitation of combined Gaussian and Poisson white noises

Nonlinear dynamical systems excited by combined Gaussian and Poisson white noises are widely found in the scientific field. However, the introduction of Poisson white noise results in the associated forward Kolmogorov equation becoming an integro-differential equation (IDE), which makes it difficult to solve the response of these dynamical systems. At present, traditional numerical IDE solvers are limited due to both the mesh generation and high computational costs. In this context, this paper integrates the multi-element Gauss–Legendre (GL) quadrature into the physics-informed neural networks (PINNs) algorithm to predict the response of systems excited by combined Gaussian and Poisson white noises. A residual-based adaptive distribution (RAD) sampling method, which replaces Latin hypercube sampling (LHS) method, is implemented to adjust the residual points to improve the accuracy and training efficiency of the proposed algorithm. The results demonstrate that the integration of the PINNs algorithm with RAD sampling method dramatically enhances the tolerance of noisy data and expedites the convergence of the PINNs algorithm compared with the LHS sampling method. It has the ability to achieve better performance in a shorter training time and reduces the demand for data during the training process. Additionally, the Monte Carlo (MC) simulation is carried out to demonstrate the effectiveness of the numerical results in this paper.

An adaptive mesh generation and higher-order difference approximation for the system of singularly perturbed reaction–diffusion problems

The paper presents a hybrid difference method to solve a coupled system of singularly perturbed reaction–diffusion problems over an adaptive mesh. The solution to the problem manifests a distinctive multi-scale nature, characterized by localized narrow regions where the solution undergoes exponential changes. The mesh-generating procedure relies upon equidistributing a non-negative monitor function. The method utilizes a suitable combination of the cubic and exponential spline difference schemes over a layer adaptive mesh. The proposed method is unconditionally stable and uniformly convergent. The convergence obtained is optimal, being free from logarithmic factors. Moreover, it is free from directional bias. Numerical experiments have been performed and presented for two model problems. The results obtained are in agreement with the theoretical estimates.

SCADA World: An Exploration of the Diversity in Power Grid Networks

Despite a growing interest in understanding the industrial control networks that monitor and control our critical infrastructures (such as the power grid), to date, SCADA networks have been analyzed in isolation from each other. They have been treated as monolithic networks without taking into consideration their differences. In this paper, we analyze real-world data from different parts of a power grid (generation, transmission, distribution, and end-consumer) and show that these industrial networks exhibit a variety of unique behaviors and configurations that have not been documented before. To the best of our knowledge, our study is the first to tackle the analysis of power grid networks at this level. Our results help us dispel several misconceptions proposed by previous work, and we also provide new insights into the differences and types of SCADA networks.

Implementation of the High-Performance Computing Summer Institute at Jackson State University

Between May 25, 2023 and June 21, 2023, we hosted the inaugural four-week High-Performance Computing Summer Institute at Jackson State University. This endeavor was made possible through the support of a three-year NSF CISE-MSI grant. The primary objective of this Summer Institute revolved around the engagement, education, and empowerment of minority and underrepresented students in the realm of High-Performance Computing (HPC) within the field of engineering. Nine undergraduate students with diverse background were recruited to participate in this program. Throughout the program, we immersed these students in a comprehensive curriculum that covered various critical facets of HPC. This curriculum encompassed hands-on instruction in Linux operating system command-line operations, C programming within the Linux environment, fundamental HPC concepts, parallel computing utilizing the Message Passing Interface (MPI) library, and GPU computing through OpenCL. Additionally, we delved into foundational aspects of fluid mechanics, geometric modeling, mesh generation, flow simulation via our in-house flow solvers, and the visualization of solutions. At the end of the program, every participant was tasked with delivering an oral presentation and submitting a written report encapsulating their acquired knowledge and experiences during the program. We are excited to share a detailed overview of our program's implementation with our audience. This includes insights into our utilization of ChatGPT to enhance C programming learning and our suggestion of the NSF ACCESS resources to gain access to HPC systems. We are proud to announce that the program has achieved remarkable success, as evidenced by the positive feedback we received from the participants.

A multislope MUSCL method for vectorial reconstructions

Variables interpolation is one of the key concepts of MUSCL schemes. Originally developed for one-dimensional frameworks, many improvements have been made over the last decades to extend these methods to general unstructured multi-dimensional meshes. It results that scalar interpolation in a finite volume cell-centered framework is already quite well understood. It is known that linear reconstructions have to be limited in order to prevent non-physical oscillations of the solutions while ensuring a spatial second-order accuracy for smooth solutions. This is done thanks to a limiting function which allows the reconstruction to satisfy a monotonicity property, which then ensure the stability of the scheme. Nevertheless, some difficulties arise when we try to extend this process to vectorial variables. Generally, vectorial reconstructions are done componentwise, but this process reveals to be frame-dependent and leads to a loss of precision due to false detection of extrema. In this paper, we present a new method dealing with vectorial reconstructions in a multislope MUSCL context.

Generating Synthetic Power Grids Using Exponential Random Graph Models

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids. Published by the American Physical Society 2024