Mesh Generation Research Articles

A high‐order pure streamfunction method in general curvilinear coordinates for unsteady incompressible viscous flow with complex geometry

AbstractIn this paper, a high‐order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier‐Stokes equations. By constructing the fourth‐order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth‐order mixed derivative terms, and applying a Crank‐Nicolson scheme for the second‐order temporal discretization, we extend the unsteady high‐order pure streamfunction algorithm to flow problems with more general non‐conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von‐Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non‐conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.

Life cycle-based multi-objective model for optimal gaseous fuel generation and portfolio allocation in gas grids: A strategic decarbonization

Biomethane and hydrogen are acknowledged as transformative opportunities for decarbonizing the conventional gas grid. Essential to this transformation is the modeling of the gaseous fuel supply chain, particularly with hydrogen and biomethane, offering crucial insights for decision-makers. This study introduces a life cycle thinking-based multi-objective optimization model for the integrated design of biomethane and hydrogen gaseous fuel supply chain networks. The model determines optimal resource allocation for the production of the two fuels, integrating them into the conventional gas network. Moreover, it allocates conventional natural gas, biomethane, and hydrogen optimally across building, industry, and transport sectors, considering the life cycle environmental and economic performance of fuel integration paths. Objective functions include minimization of life cycle emissions and levelized cost of energy while maximizing revenue from fuel sales. Integrating life cycle assessment and cost analysis tools, the optimization model quantifies emissions and life cycle costs for biomethane and hydrogen paths. Results identify Pareto-optimal fuel production paths and portfolios, revealing that integrating the alternative fuels into the current gas grid can significantly reduce emissions (up to 250 tonCO2eq/year) and generate substantial carbon tax savings (up to $16,250/year). This model is useful for gaseous fuel industry stakeholders, offering a comprehensive view of supply chain costs and detailed insights into emission benefits when integrating alternative fuels into existing gas networks.

A novel family of Q1-finite volume element schemes on quadrilateral meshes

A novel family of isoparametric bilinear finite volume element schemes are constructed and analyzed to solve the anisotropic diffusion problems on general convex quadrilateral meshes. These new schemes are obtained by employing a special quadrature rule to approximate the line integrals in classical Q1-finite volume element method. The new quadrature rule is a linear combination of trapezoidal and midpoint rules, and the weights depend on a parameter ωK. The novelty of this work is that, for any fully anisotropic diffusion tensor, we provide some specific ωK to ensure the coercivity result of the proposed schemes on arbitrary parallelogram, quasi-parallelogram, trapezoidal and some general convex quadrilateral meshes. More interesting is that, the parameter ωK can only involves the anisotropic diffusion tensor and the geometry of quadrilateral cell. An optimal H1 error estimate is also proved on quasi-parallelogram meshes. Finally, the theoretical findings are validated by several numerical examples.

High-fidelity numerical simulation of longitudinal thermoacoustic instability in a high-pressure subscale rocket combustor

A detailed analysis of thermoacoustic combustion instability in a subscale rocket combustor at high pressure is reported in this paper using the high-fidelity large-eddy simulation (LES). Self-sustained longitudinal combustion instability is observed in the experiments for this combustor configuration. The computational setup follows the past experimental study of a rig called the Continuously Variable Resonance Combustor (CVRC). In this combustor, both stable combustion and unstable combustion dynamics have been observed by varying the oxidizer injector length. A combustor configuration with an oxidizer injector length of 12 cm is chosen for this study based on the experimental evidence of longitudinal combustion instability. An autonomous meshing using the modified cut-cell Cartesian grid generation approach, coupled with on-the-fly Adaptive Mesh Refinement (AMR) is employed in this study. Chemical reactions during turbulent combustion in this configuration are modeled by solving the species transport equations with a detailed chemistry solver using a kinetic mechanism with 21 species and 84 steps. Similar to the findings of the experiments, we observe a self-sustained combustion instability in the present study, which is characterized by a limit cycle behavior of the acoustic fluctuations. The spectral analysis of these acoustic fluctuations shows good agreement with experimental data for the frequency of the three dominant modes. We further analyze the features of time-averaged and instantaneous reacting flow to study the effects of combustion instability on the flame holding dynamics, vortex shedding, mixing, and combustion regime due to flame movement along the longitudinal direction of the combustor during a limit cycle. These phenomena are effectively captured through the integration of AMR with complex chemistry in the present study. A particular focus of the study is on understanding the role of minor species (OH, HO2, and CH2O) in the physical and state-space in sustaining the flame during the combustion instability. Additionally, the physical mechanisms responsible for the production and dissipation of enstrophy are examined to demonstrate that their contribution can create significant fluctuations in the reacting flow field, which can assist in sustaining the combustion instability.

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell merging algorithm for smooth interfaces to automatically generate the induced mesh for piecewise smooth interfaces. An hp a posteriori error estimate is derived for a new unfitted finite element method whose finite element functions are conforming in each subdomain. Numerical examples illustrate the competitive performance of the method.

Adaptive random-grid and progressive color secret sharing with CNN super-resolution on a many-core system

This study introduces an innovative method combining Convolutional Neural Networks (CNN) with random grid generation for enhanced visual secret sharing. Our approach supports color images, reduces processing time, and offers non-pixel expansion and flexible share combinations. Utilizing GPU computation, it significantly improves practicality and efficiency by operating in a feed-forward manner, avoiding complex optimization. Experimental results demonstrate superior metrics: maximum PSNR of 32 dB, 99% NCC correlation with benchmarks, 2.9% NAE, and SSIM of 98%. We achieve substantial speedups– 493 × for 256 × 256 and 3145 × for 1024 × 1024 images–compared to sequential models. The scheme exhibits robustness against attacks, evidenced by CMY component and share histogram similarities, and scalability shown in combinatorial explosion visualization. These findings underscore the efficacy and efficiency of our approach, advancing secure image sharing applications significantly.

Achieving zero-bill for the grid-connected PV systems in Saudi Arabia governmental schools: a techno-economic analysis

Governmental schools are characterized as ideal places for installing grid-connected PV systems due to the availability of large spaces on their roofs. Schools are also characterized by their good annual load profile, in which most of the loads occur during the day, and there are no loads on nights or weekends or during summer and vacations. Moreover, in the winter, the loads drop dramatically due to the lack of air conditioning. This special annual load profile provides a relative property to government schools with regard to exporting the energy generated during off days to the general electricity grid. The main objective of this research is to attempt to design a grid-connected PV system that can balance imported and exported energy to the grid to achieve an annual zero bill based on the energy exchange tariff in Saudi Arabia. Three different schools in Buraidah City were selected for investigation. The annual energy consumption was estimated from energy bills for 3 years and compared with actual installed loads. The performance analysis was done by applying three widely used indicators: yield factor, capacity factor, and performance ratio. Also, the economic analysis was done using the life cycle analysis methodology based on the local market prices to find the levelized cost of energy (LCOE) and the payback time. The results of economic and performance analysis revealed the professionality of installing grid-connected PV systems in government schools.

Development of agent-based mesh generator for flow analysis using deep reinforcement learning

Development of agent-based mesh generator for flow analysis using deep reinforcement learning

Mesh-controllable multi-level-of-detail text-to-3D generation

Text-to-3D generation is a challenging but significant task and has gained widespread attention. Its capability to rapidly generate 3D digital assets holds huge potential application value in fields such as film, video games, and virtual reality. However, current methods often face several drawbacks, including long generation times, difficulties with the multi-face Janus problem, and issues like chaotic topology and redundant structures during mesh extraction. Additionally, the lack of control over the generated results limits their utility in downstream applications. To address these problems, we propose a novel text-to-3D framework capable of generating meshes with high fidelity and controllability. Our approach can efficiently produce meshes and textures that match the text description and the desired level of detail (LOD) by specifying input text and LOD preferences. This framework consists of two stages. In the coarse stage, 3D Gaussians are employed to accelerate generation speed, and weighted positive and negative prompts from various observation perspectives are used to address the multi-face Janus problem in the generated results. In the refinement stage, mesh vertices and faces are iteratively refined to enhance surface quality and output meshes and textures that meet specified LOD requirements. Compared to the state-of-the-art text-to-3D methods, extensive experiments demonstrate that the proposed method performs better in solving the multi-face Janus problem, enabling the rapid generation of 3D meshes with enhanced prompt adherence. Furthermore, the proposed framework can generate meshes with enhanced topology, offering controllable vertices and faces with textures featuring UV adaptation to achieve multi-level-of-detail(LODs) outputs. Specifically, the proposed method can preserve the output’s relevance to input texts during simplification, making it better suited for mesh editing and rendering efficiency. User studies also indicate that our framework receives higher evaluations compared to other methods.

Smart home load scheduling system with solar photovoltaic generation and demand response in the smart grid

This study introduces a smart home load scheduling system that aims to address concerns related to energy conservation and environmental preservation. A comprehensive demand response (DR) model is proposed, which includes an energy consumption scheduler (ECS) designed to optimize the operation of smart appliances. The ECS utilizes various optimization algorithms, including particle swarm optimization (PSO), genetic optimization algorithm (GOA), wind-driven optimization (WDO), and the hybrid genetic wind-driven optimization (HGWDO) algorithm. These algorithms work together to schedule smart home appliance operations effectively under real-time price-based demand response (RTPDR). The efficient integration of renewable energy into smart grids (SGs) is challenging due to its time-varying and intermittent nature. To address this, batteries were used in this study to mitigate the fluctuations in renewable generation. The simulation results validate the effectiveness of our proposed approach in optimally addressing the smart home load scheduling problem with photovoltaic generation and DR. The system achieves the minimization of utility bills, pollutant emissions, and the peak-to-average demand ratio (PADR) compared to existing models. Through this study, we provide a practical and effective solution to enhance the efficiency of smart home energy management, contributing to sustainable practices and reducing environmental impact.

Integration of Distributed Generations and electric vehicles in the distribution system

Power quality challenges are a major problem these days because of the significant increase in load demand and the existence of various reasons for disruptions in the distribution system. A voltage sag or a decrease in the magnitude of the line voltage can be brought on by rapid fluctuations in load or distribution system issues. Enhancing the grid current profile, reducing grid voltage sag, and improving other performances can all be achieved through the combination of electric vehicles with distribution generation systems. In this paper, the integration of Distributed Generation with Electric Vehicles in the distribution system has been done to enhance system performances such as true power loss index, imaginary power loss index, voltage deviation index, short circuit current index, cost function, and environmental impact reduction index for 16 bus distribution system in constant impedance, constant current, and constant power load models, or ZIP load models through proper location, sizing, coordinated controlling, and types of Distributed Generation and Electric Vehicle pairs for both charging and discharging modes by adopting Hybrid Genetic Algorithm - Monte Carlo Simulation optimization methodologies. This study's primary goal is to determine the optimal distribution generation and electric vehicle pairing to improve the aforementioned parameters, which will assist researchers in their future planning. Researchers, industry professionals, scientists, and individuals working with Distributed Generation and Electric vehicles in the smart grid will find this statement to be of great use.

Gridder-HO: Rapid and efficient parallel software for high-order curvilinear mesh generation

The advancement in high-order computational methods is reshaping the landscape of mesh generation in Computational Fluid Dynamics (CFD), steering the focus towards curvilinear mesh techniques to meet the escalating accuracy demands. Gridder-HO, the software designed to generate high-order curvilinear mesh efficiently and rapidly, has been developed. Gridder-HO supports the elevation of meshes to P2 (quadratic-order) or P3 (cubic-order). It features a layered architecture and utilizes the concurrent hash table and the Alternating Digital Tree (ADT) data structure, supporting thread-level parallelism to convert straight-edge mesh into high-order curvilinear mesh seamlessly. Gridder-HO utilizes the projection method based on a thread pool to precisely preserve geometry, and employs a novel localized RBF method with ADT for volume node interpolation to untangle the mesh, which aims to achieve a satisfactory balance between efficiency and accuracy. Validated through CFD simulations using the GPU-accelerated Python Flux Reconstruction (PyFR) solver, the practicality of Gridder-HO is demonstrated across various Reynolds numbers in typical cases such as sphere, cylinder, and SD7003 airfoil. These results confirm the high-order curvilinear meshes generated by Gridder-HO meet the high-order requirements of emerging computational methods. Moreover, Gridder-HO exemplifies its effectiveness in generating large-scale, high-order curvilinear meshes for the DLR-F6 transport aircraft configuration standard test cases. It elevates a mesh with 5 million elements to P2 in 3 min 39 sec at 68% parallel efficiency on 16 threads, and another with 14 million elements to P3 in 52 min 39 sec at 60% efficiency, illustrating its efficiency and potential in satisfying the demands of complex geometries in engineering applications.

Method for computer tomography voxel-based finite element analysis and validation with digital image correlation system

Understanding the mechanical behavior of heterogeneous materials is becoming increasingly crucial across various fields, including aerospace engineering, composite materials development, geology, and biomechanics. While substantial literature exists on this topic, conventional methods often rely on commercial software packages. This study presents a framework for computed tomography (CT) scan-based finite element (FE) analysis of such materials using open-source software in most of the workflow.Our work focuses on three key aspects:1.Mesh generation that incorporates spatially varying mechanical properties and well-defined boundary conditions.2.Validation of the FE results through comparison with digital image correlation (DIC) system measurements.3.Open-source software utilization throughout the entire process, making it more accessible and cost-effective.This work aims to demonstrate the effectiveness of this framework for analyzing heterogeneous materials in various fields, offering a more accessible and affordable approach.

A lightweight interactive approach for unstructured surface mesh generation

PurposeThe paper aims to propose a generation approach for unstructured surface mesh to speed up mesh generation.Design/methodology/approachThe paper proposes a lightweight interactive generation approach for unstructured surface mesh and presents several key technologies to support this approach.FindingsThe experimental results show that the proposed approach is feasible for unstructured meshes and it can accelerate the mesh generation process.Research limitations/implicationsMore geometric defects should be covered, and more convenient and efficient interactive means need to be provided.Practical implicationsThe proposed approach and key technologies are implemented in NNW-GridStar.UG, which is the unstructured version of the mesh generation software of National Numerical Windtunnel (NNW).Originality/valueThis paper proposes a lightweight interactive approach for unstructured surface mesh generation, which can speed up mesh generation.

What's the Situation With Intelligent Mesh Generation: A Survey and Perspectives.

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG.

Research on photovoltaic grid-connected inverters with source filtering function

Abstract To suppress the current harmonics caused by the nonlinear load connected to the grid when the photovoltaic system is connected to the grid for power generation, this paper adopts a composite control strategy based on the PI-RC controller to realize the synthesis of the command current signal in different modes. According to the different command current signals, the system can work in three modes: photovoltaic grid-connected harmonic compensation control, photovoltaic grid-connected control, and harmonic compensation unified control. Under the composite control strategy, the system realizes the active output of the photovoltaic grid-connected system with the function of source filtering, compensates for the harmonics caused by nonlinear loads, successfully reduces the harmonic distortion rate of grid current, and then realizes the function expansion of photovoltaic grid-connected inverter. Finally, the feasibility and rationality of the unified control strategy designed in this study are verified by simulation experiments.

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

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

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

Suppressing spurious oscillations is crucial for designing reliable high-order numerical schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated over the past several decades. This paper proposes a novel, robust, and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method on general meshes, motivated by the damping technique (see J. Lu, Y. Liu, and C. W. Shu [SIAM J. Numer. Anal. 59 (2021), pp. 1299–1324]). The OEDG method incorporates an oscillation-eliminating (OE) procedure after each Runge–Kutta stage, and it is devised by alternately evolving the conventional semidiscrete discontinuous Galerkin (DG) scheme and a damping equation. A novel damping operator is carefully designed to possess both scale-invariant and evolution-invariant properties. We rigorously prove the optimal error estimates of the fully discrete OEDG method for smooth solutions of linear scalar conservation laws. This might be the first generic fully discrete error estimate for nonlinear DG schemes with an automatic oscillation control mechanism. The OEDG method exhibits many notable advantages. It effectively eliminates spurious oscillations for challenging problems spanning various scales and wave speeds, without necessitating problem-specific parameters for all the tested cases. It also obviates the need for characteristic decomposition in hyperbolic systems. Furthermore, it retains the key properties of the conventional DG method, such as local conservation, optimal convergence rates, and superconvergence. Moreover, the OEDG method maintains stability under the normal Courant–Friedrichs–Lewy (CFL) condition, even in the presence of strong shocks associated with highly stiff damping terms. The OE procedure is nonintrusive, facilitating seamless integration into existing DG codes as an independent module. Its implementation is straightforward and efficient, involving only simple multiplications of modal coefficients by scalars. The OEDG approach provides new insights into the damping mechanism for oscillation control. It reveals the role of the damping operator as a modal filter, establishing close relations between the damping technique and spectral viscosity techniques. Extensive numerical results validate the theoretical analysis and confirm the effectiveness and advantages of the OEDG method.

Solar powered membrane bioreactor (MBR) treating wastewater for reuse at a hospital in Kampala, Uganda – Results of pilot-scale trials

A robust and cost-effective pilot solar-powered membrane bioreactor (MBR) with downstream granular activated carbon (GAC) filter hospital wastewater treatment was developed for the Lubaga hospital in Kampala, Uganda. The MBR-GAC pilot included a 25 m2 ultrafiltration (UF) module, a 100 kg GAC filter, 20 photovoltaic panels totaling 7 kWp and a 3.55 kWh supercapacitor energy storage unit to produce non-potable and reusable water for toilet flushing, cleaning and irrigation. The pilot operated with 43% clean energy autonomy with grid and diesel generator backup for power outages of more than 1 hour. The MBR pilot produced an average flux of 10–15 L m–2 h–1 with 50% total organic carbon (TOC) removal. The nitrification, denitrification and filtration tanks were separated to achieve a nitrification of 80% and denitrification of 20%. The removal of typical hospital pharmaceutical residues that could not be reduced by the MBR increased to approximately 90% after the downstream GAC filter was upgraded. The removal efficiency of the GAC decreased to approximately 25% at 4,290 bed volume (BV). The significant increase of 75% in the removal efficiency of diclofenac in the MBR was attributed to the acclimation of the activated sludge. The quality of the treated wastewater from the pilot plant was sufficient for reuse by irrigation of the hospital garden, toilet flushing and cleaning. Finally, the study discussed ways to optimize the design and operation of the plant. The pilot is scalable to be replicated elsewhere and adapted in an efficient and cost-effective manner in sub-Saharan countries in Africa.

Velocity model-based adapted meshes using optimal transport

In geophysical numerical models using the finite-element method or its variant, the spectral-element method, to solve seismic wave equations, a mesh is employed to discretize the domain. Generating or adapting a mesh to complex geological properties is a challenging task. To tackle this challenge, we develop an r-adaptivity method to generate or adapt a two-dimensional mesh to a seismic velocity field. Our scheme relies on the optimal transport theory to perform vertices relocation, which generates good-shaped meshes and prevents tangled elements. The mesh adaptation can delineate different regions of interest, like sharp interfaces, salt bodies, and discontinuities. The algorithm has a few user-defined parameters that control the mesh density. With typical seismic velocity examples (e.g., Camembert, SEAM Phase, Marmousi-2), mesh adaptation capability is illustrated within meshes with triangular and quadrilateral elements, commonly employed in seismic codes. Besides its potential use in mesh generation, the method developed can be embedded in seismic inversion workflows like multiscale full waveform inversion to adapt the mesh to the field being inverted without incurring the I/O cost of re-meshing and load rebalancing in parallel computations. The method can be extended to three-dimensional meshes.