Mesh Generation Research Articles

A parameter robust reconstruction nonconforming virtual element method for the incompressible poroelasticity model

A reconstruction nonconforming virtual element method for the incompressible poroelasticity model is developed and analyzed. We investigate to determine the divergence-free displacement in incompressible poroelasticity model on polygons. The presented method mainly involves the parameter robust for μ also can be considered as the real pressure robustness for the virtual element. Using the H(div) space on the polygons to build the reconstruction operator, the method can be applied on general polygonal meshes, satisfy pressure robustness and overcome Poisson locking in incompressible model. The results are corroborated by theoretical derivations as well as numerical results.

Implementation of IDEAL algorithm based on Delaunay triangular mesh for 2D-compressible flows

PurposeTo present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.Design/methodology/approachProgramming completely in C++.FindingsFive compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.Originality/valueThe detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator models from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than 50% reduction in the resource usage required to achieve the same level of accuracy as uniform and user-constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

An efficient finite element mesh generation methodology based on μCT images of multi-layer woven composites

High-fidelity models are essential for accurate finite element (FE) simulations of composite material behavior. This paper proposes an efficient meshing methodology based on micro-Computed Tomography (μCT) images. U-Net convolutional neural network was used for image segmentation. Connected yarns were then separated using an improved procedure based on watershed algorithm and geometric transformations. The proposed Constrained Delaunay-Advancing Front Technique (CD-AFT) surface reconstruction algorithm extracts point cloud of yarns from segmented images and outputs high-quality and smooth orientable manifold watertight triangulated surface. Intersecting meshes of yarns are separated through node position detection and Laplacian moving. Experimental results show that proposed methodology is capable of accomplishing mesh generation for different mesh sizes. Compared with commercial software, it has obvious advantages in mesh quality and size control. Since the proposed method operates independently of commercial software and manual operation, it facilitates the automated generation of numerous high-fidelity models from μCT images for FE simulations.

Application of hilbert transform for power quality indicators monitoring in general purpose grids

During the operation of power grids, abnormal modes occur that lead to a decrease or increase in the grid voltage beyond permissible values, the appearance of high-frequency noise components and grid signal fading’s, which fading’s the power quality and can lead to the failure of electrical equipment. This requires constant monitoring of power quality indicators. The methods of measuring power quality indicators have been examined and analyzed in the article, their advantages and limitations have been considered, and the inefficiency of using the Fourier transform for estimating of power quality indicators in time domain has been justified. The application of Hilbert transform has been suggested for monitoring the indicators of power quality in general-purpose grids, which include measuring the duration and magnitude of voltage dips, the duration of voltage fading, localization and determination of the duration of high-frequency noise interference in the power grid, determination of phase shift during voltage dip. A simulation of the process of determining the indicators of power quality in time domain and the time intervals during which these indicators exceed the established limits has been performed, which confirmed the effectiveness of using the Hilbert transform in the systems of their monitoring. Keywords: general purpose power grid, power quality indicators, Hilbert transform.

Stretched Meshing in a 2D Computational Domain with Elbow Edges for CFD Applications

Mesh generation is critical for obtaining accurate and detailed solutions to mesh-based numerical problems, particularly when capturing specific information within a designated area of the domain. While structured meshes offer consistency, their uniform resolution limits their ability to achieve this. Mesh stretching offers a solution by introducing non-uniform element sizes based on an analytical relationship while preserving the original mesh structure. The objective of this study is to create a hybrid mesh model that leverages the strengths of both structured and stretched meshes. A 2D rectangle with elbow edges serves as the domain. To address the requirements of CFD applications, the domain is refined by increasing element density near the boundaries and corners. Skewness, aspect ratio, and element quality are then assessed to determine the overall mesh quality. The results demonstrate that stretching the structured mesh produced a mesh with quality that meets CFD domain standards.

Uncertainty qualification in seismic analysis of concrete dams based on model order reduction accelerated stochastic SBFEM

A pioneering framework for uncertainty quantification in seismic analysis of concrete dams rooted in the stochastic scaled boundary finite element method (SSBFEM) is proposed. For seismic analysis of dams, octree decomposition is used for mesh generation. SSBFEM is developed to predict the structural responses with randomly distributed material properties. The script in this paper can integrate octree mesh and SSBFEM into ABAQUS user element (UEL). Implementing octree SSBFEM on commercial software provides accurate and convenient full order models for uncertainty quantification. Monte Carlo simulation (MCs) is deployed to calculate the statistical characteristics of structural responses under random variables. Additionally, singular value decomposition (SVD) and radial basis function (RBF) are leveraged to refine traditional MCs. The solution space of MCs is decomposed into lower-order subspaces. Any structural responses can be rapidly evaluated from linear combinations of subspaces. Particularly, the method has been successfully applied to seismic analysis of concrete dams with different random material properties. Finally, several illustrative examples are provided to validate the accuracy and efficacy of the algorithm.

Unconditionally optimal error estimates of linearized Crank-Nicolson virtual element methods for quasilinear parabolic problems on general polygonal meshes

In this paper, we construct, analyze, and numerically validate a linearized Crank-Nicolson virtual element method (VEM) for solving quasilinear parabolic problems on general polygonal meshes. In particular, we consider the more general nonlinear term a(x, u), which does not require Lipschitz continuity or uniform ellipticity conditions. To ensure that the fully discrete solution remains bounded in L∞-norm, we construct two novel elliptic projections and apply a new error splitting technique. With the help of the boundedness of numerical solution and delicate analysis of the nonlinear term, we derive the optimal error estimates for any k-order VEMs without any time-step restrictions. Numerical experiments on various polygonal meshes validate the accuracy of theoretical analysis and the unconditional convergence of the proposed scheme.

Dissipative Non-Slip MHD Nanofluid Flow with Variable Viscousity and Thermal Conductivity in the Presence of Arrhenius Chemical Reaction

This research investigates the intricate dynamics of dissipative non-slip magnetohydrodynamic (MHD) nanofluid flow, characterized by variable viscosity and thermal conductivity, under the influence of an Arrhenius chemical reaction. The inclusion of the Arrhenius chemical reaction adds complexity through heat generation or absorption, impacting temperature and concentration gradients. The study is motivated by the extensive applications of nanofluids in engineering and industrial processes, where precise control of heat and mass transfer is critical. We develop a comprehensive mathematical model that incorporates the variable properties of the nanofluid, the effects of the Lorentz force due to the applied magnetic field, and the temperature-dependent reaction rates dictated by the Arrhenius equation. The formulated governing equations were non-dimensionalised to identify the flow governing parameters. Finite Element Method (FEM), grid generation, solution algorithms, and post-processing to analyse velocity, temperature, and concentration distributions were used to obtain the numerical methods to solve fluid flow problems based on the Navier-Stokes equations, involving concepts of discretization. pdsolve subpackage in Maple 2023 was used to numerically solve PDEs with specific initial and boundary conditions, incorporating the plot and display commands for graphical analysis, and the results are presented and discussed. The findings reveal that the interplay between parameters like Hartmann number, Darcy parameter, and heat generation or absorption profoundly influences flow behaviour and thermal characteristics. The reactivity parameter is crucial, dictating the rate of chemical reactions and affecting system dynamics. This research enhances understanding of the interdependencies among fluid properties, chemical reactions, and external parameters in nanofluid flows.

Efficient and consistent adaptive mesh generation for geophysical models: A case study over the Gulf of Thailand

Geophysical domains typically exhibit intricate, irregular boundaries characterized by fractal-like geometries, while underlying physical processes operate across a broad spectrum of spatial scales. The challenge lies in generating spatial discretization of these domains that conform to their geographical constraints, utilizing anisotropic, fully adaptive meshes. This problem is compounded by the vast range of scales and a notably heterogeneous parameter space. Current methodologies often rely on ad hoc, model-specific, or application-dependent approaches, which lack comprehensive descriptions. Consequently, the development of new spatial domains is labor-intensive, prone to errors, challenging to replicate, and difficult to maintain consistency due to substantial human involvement. This predicament poses obstacles to the reproducibility of simulations and the establishment of provenance in data handling and model initialization, and it hinders rigorous model intercomparisons. Furthermore, the likelihood of discrepancies in model initialization and forcing parameters increases when employing flexible adaptive meshes. This paper introduces a systematic approach to the automated generation of adaptive meshes for geophysical models. This method is efficient in its generation process and readily reproducible, offering robust and consistent adherence to the source data. The proposed approach facilitates research in complex multi-scale geophysical domains, which would be challenging using existing methods. A simulation of monthly mean currents was carried out as a case study in the Gulf of Thailand. Results revealed that the simulated current circulations agreed with the observation. Examples of its application in various ongoing geophysical modeling endeavors illustrate its effectiveness.

An optimized CIP-FEM to reduce the pollution errors for the Helmholtz equation on a general unstructured mesh

The continuous interior penalty finite element method (CIP-FEM) has shown promise in reducing pollution errors when numerically simulating the Helmholtz equation with high wave numbers. However, its reliance on structured meshes largely limits its applicability. To address this limitation, this paper presents a novel approach to CIP-FEM on general unstructured meshes. The interior penalty parameters of the CIP-FEM are determined in an offline phase through minimizing the residual obtained by substituting the plane waves into the CIP finite element equation. To enhance accuracy, a quasi-Newton algorithm is employed to correct the penalty parameters and minimize errors of the CIP finite element approximations to the plane waves. The calculated interior penalty parameters can be saved, enabling the online solutions of CIP-FEM to be obtained by reusing these parameters for arbitrary sources during practical computations. Numerical experiments are presented to demonstrate the significant reduction of pollution errors for both linear and higher-order CIP-FEMs on unstructured meshes. Furthermore, the proposed algorithm successfully simulates high-frequency acoustic fields in a three-dimensional vehicle cabin with greatly reduced errors within certain fixed computational time, demonstrating its practical effectiveness in real-world scenarios.

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.

Modelling and analysis of nuclear reactor system coupled with a liquid metal battery

AbstractTraditionally, nuclear power plants in the U.S. provide baseload power to the power grid because they have less flexibility for ramping their output power than natural gas peaking plants. However, achieving climate goals to reduce the consumption of fossil‐based natural gas places pressure on nuclear power plants and other power generators to ramp up their power output to balance grid generation with demand. This paper presents the modelling and performance analysis of a nuclear reactor system (NRS) coupled to a liquid‐metal battery (LMB) to improve its dynamic response and enable its black start capability. The NRS and LMB thermal behaviour are modelled in Dymola, while the electrical dynamics of the LMB and power grid are modelled in RTDS‐RSCAD. Both simulation platforms are coupled and share their thermal and electrical data using a Transmission Control Protocol/Internet Protocol (TCP/IP) communication protocol. The dynamic performance of the NRS‐LMB integration is tested on the IEEE 9 bus, which demonstrates its ability to respond and provide frequency and voltage regulation. The black start capability of the NRS‐LMB is also evaluated by simulating a grid outage and using the LMB to supply the auxiliary loads required to bring the NRS back online as soon as possible. The results show that coupling an NRS to an LMB improves the system dynamic performance and enables it to black start after being disconnected from the grid for several days.

Numerical simulations of bio-inspired approaches to enhance underwater swimming efficiency

The present study discusses the numerical simulation results of swimming similar to manta rays. The complex three-dimensional kinematics of manta rays were implemented to unravel the intricacies of its propulsion mechanisms by using the discrete vortex method (DVM). The DVM replaces the requirement for a structured grid across the computational domain with a collection of vortex elements. This method simplifies grid generation, especially for intricate geometries, resulting in time and effort savings in meshing complex shapes. By modeling the pectoral fins with discrete panels and utilizing vortex rings to represent circulation and wake, the study accurately computes the pressure distribution, circulation distribution, lift coefficient, and thrust coefficient of the manta ray. This study focuses on the modulation of aerodynamic performance by altering the span length and the length change ratio during the downstroke and upstroke motion (SV). The manta ray's three-dimensional vortex configurations comprise a combination of vortex rings, vortex contrails, and horseshoe vortices. Analysis of the three-dimensional vortex structure indicates the presence of multiple vortex rings and horseshoe vortex rings at higher SV values, while adequate formation of horseshoe vortices is not observed at lower SV values. In terms of propulsive performance, both lift and thrust increase with SV, while the propulsive efficiency demonstrates its peak at SV = 1.75. The analysis reveals that at higher SV values, the net thrust generated primarily originates from the tip of the fins. Moreover, the study illustrates a significant enhancement in propulsive efficiency, particularly in association with optimal Strouhal numbers ranging between 0.3 and 0.4. The key findings of this study may be used in efficient design of agile autonomous underwater vehicles for marine exploration and surveillance applications.

Advancing Front Surface Mapping

AbstractWe present Advancing Front Mapping (AFM), a novel algorithm for the computation of injective maps to simple planar domains. AFM is inspired by the advancing front meshing paradigm, which is here revisited to operate on two embeddings at once, becoming a tool for compatible mesh generation. AFM extends the capabilities of existing robust approaches, supporting a broader set of embeddings (star‐shaped polygons) with a direct approach, without resorting to intermediate constructions. Our method only relies on two topological operators (split and flip) and on the computation of segment intersections, thus permitting to compute a valid embedding without solving any numerical problem. AFM is therefore easy to implement, debug and deploy. This article is mainly focused on the presentation of the compatible advancing front idea and on the demonstration that the algorithm provably converges to an injective map. We also complement our theoretical analysis with an extensive practical validation, executing more than one billion advancing front moves on 36K mapping tasks.

Developing meshing workflows in Gmsh v4.11 for the geologic uncertainty assessment of high-temperature aquifer thermal energy storage

Abstract. Evaluating uncertainties of geological features on fluid temperature and pressure changes in a reservoir plays a crucial role in the safe and sustainable operation of high-temperature aquifer thermal energy storage (HT-ATES). This study introduces a new automated surface fitting function in the Python API (application programming interface) of Gmsh (v4.11) to simulate the impacts of structural barriers and variations of the reservoir geometries on thermohydraulic behaviour in heat storage applications. These structural features cannot always be detected by geophysical exploration but can be present due to geological complexities. A Python workflow is developed to implement an automated mesh generation routine for various geological scenarios. This way, complex geological models and their inherent uncertainties are transferred into reservoir simulations. The developed meshing workflow is applied to two case studies: (1) Greater Geneva Basin with the Upper Jurassic (“Malm”) limestone reservoir and (2) the 5° eastward-tilted DeepStor sandstone reservoir in the Upper Rhine Graben with a uniform thickness of 10 m. In the Greater Geneva Basin example, the top and bottom surfaces of the reservoir are randomly varied by ± 10 and ± 15 m, generating a total variation of up to 25 % from the initially assumed 100 m reservoir thickness. The injected heat plume in this limestone reservoir is independent of the reservoir geometry variation, indicating the limited propagation of the induced thermal signal. In the DeepStor reservoir, a vertical sub-seismic fault juxtaposing the permeable sandstone layers against low permeable clay-marl units is added to the base case model. The fault is located in distances varying from 4 to 118 m to the well to quantify the possible thermohydraulic response within the model. The variation in the distance between the fault and the well resulted in an insignificant change in the thermal recovery (∼ 1.5 %) but up to a ∼ 10.0 % pressure increase for the (shortest) distance of 4 m from the injection well. Modelling the pressure and temperature distribution in the 5° tilted reservoir, with a well placed in the centre of the model, reveals that heat tends to accumulate in the updip direction, while pressure increases in the downdip direction.

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.

A Novel Cell-Based Adaptive Cartesian Grid Approach for Complex Flow Simulations

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR’s efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations.

Application of 1D model for overland flow simulations on 2D complex domains

High computational demand limits the applications of two-dimensional (2D) shallow water equation models for high resolution overland flow simulations, while one-dimensional (1D) models can achieve higher computing efficiency. This study applied a 1D hydrodynamic model to surrogate 2D models for overland flow simulations on complex 2D domains. With one dimension reduced, the surrogate model simulation would have acceptable accuracy with much higher computing efficiency. The surrogating is fulfilled through mimicking 2D models in mesh generations, so that the 1D channel network is generated in such a way that it geometrically covers the whole domain without overlapping and intersection, and hydrologically follows the steepest slopes. Several benchmark cases on 2D domains in both laboratory and field scales with complex geometry, where no 1D models have been ever applied, are used to compare the 1D and 2D model simulations. The comparisons demonstrate that the 1D model does have potentials to efficiently simulate overland flow on 2D complex domains with accuracy comparable to 2D models.

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.