Automatic Mesh Generation Research Articles

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.

Numerical computation of cut off wave number in polygonal wave guide by eight node finite element mesh generation approach

This study proposes a two-dimensional, eight-noded automated mesh generator for precise and efficient finite element analysis (FEA) in microwave applications. The suggested method for solving the Helmholtz problem employs an optimal domain discretization procedure. MAPLE-13 software's advanced automatic mesh generator was developed specifically for this work. To demonstrate the effectiveness of the approach, three distinct waveguide structures are analyzed, with the results compared to the best available analytical or numerical solutions. The findings indicate that the proposed method yields highly accurate and efficient finite element results, particularly for waveguide structures containing singularities. In microwave applications, this method can significantly enhance energy transmission efficiency.

Optimization of a Hydrogen-Fueled Parametric Strut Injector Using an Automated Workflow Computational Fluid Dynamics Method

Abstract A strut injector for burning hydrogen has been optimized using an automated workflow system. In order to choose the optimal set of injectors to cover the design space, an optimized design of experiments (DOE) method was used to automatically choose the parameters that best spanned the design space. One hundred candidate designs were chosen, and a script was used to generate a series of stereolithography (STL) files for each design. The STL files were then uploaded to a supercomputer for computational fluid dynamics analysis. For each of the 100 designs, a four step process was followed to generate the required data, and this included an automated mesh generation step, a field initialization step, a mesh adaptation step, and finally an large eddy simulation all within the yales2 numerical framework. In order to reduce the time required for postprocessing and the amount of data required, the simulations relied heavily on an on-the-fly postprocessing methodology, which reduced the complex time-unsteady flow fields to a small number of quantified outputs of interest that measured the suitability of each design such as the pressure drop across the injector and the efficiency of the mixing process. At the conclusion of these simulations, automated scripts translated these outputs into a smaller set of parameters that could be used to compare each design and allow subsequent optimization and surrogate modeling. Several surrogate modeling methods were attempted with mixed results; however, a simple classification methodology quickly identified the parameters of interest.

Finite element mesh transition for local–global modeling of composite structures

This study presents an automatic mesh generation algorithm designed to address computational challenges in simulating small-scale defects within large composite structures. The algorithm seamlessly transitions from a coarse mesh, corresponding to the global structure, to a highly refined mesh in targeted local regions of interest. The transition element number and shape can be adjusted by the specified parameters. Tailored to complement this method for non-homogeneous composite models, which include multiple materials such as cohesive layers representing interlayer properties, a volume fraction calculator is integrated to automatically assign the mixture material property in each transition element. Entire processes are fully automated using a MATLAB script, eliminating the need to open the FEA software interface. The validation studies of the reconstructed two-dimensional models, assembled with the wrinkle-defect model, demonstrate their feasibility. The performance of the model is examined in terms of strain and displacement at the connecting boundaries, load–displacement curve, and interlayer failure prediction. The mesh transition model achieves agreeable results compared to a fully fine mesh model, and a 92% reduction in computational time in stress analysis, showing the efficiency of the mesh transition for local–global modeling of composite structures.

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.

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.

Microstructure generation and full-field multi-scale analyses for short fiber reinforced thermoplastics: Application to PA66GF composites

Short Fiber Reinforced Thermoplastics (SFRTs) like PA66GF composites are highly heterogeneous materials with a rather complex microstructure such that the characterization and the prediction of their mechanical behavior remain quite challenging. So far, most of the research efforts have employed phenomenological and mean-field multi-scale models to deal with SFRTs. The present contribution rather focuses on a full-field multi-scale approach that incorporates advanced techniques in terms of microstructural representation and material modeling, allowing a deep insight of the dominating deformation mechanisms occurring in PA66GF composites. The proposed approach is based on an automatic periodic mesh generation algorithm for matrix-inclusion Representative Volume Elements (RVE) with randomly positioned fibers that follow a given Orientation Distribution Function (ODF). At the microscopic scale, while the fibers are assumed to be elastic, the behavior of the thermoplastic matrix is described by a phenomenological multi-mechanism constitutive model accounting for viscoelasticity, viscoplasticity and ductile damage. It results an advanced multi-scale model that enables to visualize the local deformation and degradation mechanisms occurring at the microscopic scale while simultaneously analyzing their influence on the macroscopic response of the composite upon monotonic, persistent and cyclic loading. The potential of the proposed approach is further evaluated by comparing the predicted responses against experimental data.

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 automatic mesh generator for coupled 1D–2D hydrodynamic models

Abstract. Two-dimensional (2D), depth-averaged shallow water equation (SWE) models are routinely used to simulate flooding in coastal areas – areas that often include vast networks of channels and flood-control topographic features and/or structures, such as barrier islands and levees. Adequately resolving these features within the confines of a 2D model can be computationally expensive, which has led to coupling 2D simulation tools to less expensive one-dimensional (1D) models. Under certain 1D–2D coupling approaches, this introduces internal constraints that must be considered in the generation of the 2D computational mesh used. In this paper, we further develop an existing automatic unstructured mesh generation tool for SWE models, ADMESH+, to sequentially (i) identify 1D constraints from the raw input data used in the mesh generation process, namely the digital elevation model (DEM) and land–water delineation data; (ii) distribute grid points along these internal constraints, according to feature curvature and user-prescribed minimum grid spacing; and (iii) integrate these internal constraints into the 2D mesh size function and mesh generation processes. The developed techniques, which include a novel approach for determining the so-called medial axis of a polygon, are described in detail and demonstrated on three test cases, including two inland watersheds with vast networks of channels and a complex estuarine system on the Texas, USA, coast.

An effective higher order finite element computation method for analyzing the eddy current losses in induction motors using subparametric transformations

An enhanced sub-parametric finite element method is presented for analyzing the eddy current losses in induction motors using higher order sub-parametric transformations. The purpose of this study is to construct a very efficient, simple, and exact higher order sub-parametric approach employing a 2D automated mesh generator implemented in JuliaFEM. Alternating current motors are employed in a wide range of industrial and household applications on a frequent basis such as in fans, water heaters, ovens, pumps and many more. High efficiency of the motors is one of the most desirable parameters of these motors. Eddy current losses are predominant in these motors which are responsible for a decline in the efficiency. Consequently, the use of eddy current analysis is vital in evaluating the behaviour of electric devices under various loads. This paper proposes a novel finite element method approach to minimize the 2D eddy current phenomenon by taking the diffusion equation into account. Eddy currents are the primary source of torque in various types of equipment, such as induction motors. In other cases, it is important to analyse the eddy currents to estimate the losses, reactance, and resistance.

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

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

Open-source complex-geometry 3D fluid dynamics for applications with unpredictable heterogeneous dynamic high-performance-computing loads

We discuss the software implementation of a finite element method, intended for the simulation of complex-geometry 3D flows, using hardware resources effectively, including problems with a priori unknown, heterogeneous, and dynamic parallel computational load. Our fundamental choices of data structures, algorithm, and software design specifically target engineering resolution and accuracy requirements. Some of these choices are: unstructured grids (to explicitly resolve complex 3D geometries), tetrahedra-only computational elements (to enable automatic mesh generation), edge-based finite element scheme (to reduce indirect addressing for increased performance), distributed-memory parallel computing paradigm (to enable large problems), and Charm++ (https://charmplusplus.org) as the runtime system (to effectively use computing resources even in the presence of hardware heterogeneities and dynamic application requirements). We discuss aspects of the implementation that enable exercising unique features of the runtime system, e.g., the single Charm++ programming abstraction, overdecomposition, asynchronous execution, latency-hiding parallel communication and computation, task-parallelism, and dynamic load balancing via object migratability. Multiple test problems are used to verify and validate the numerical solutions and computational performance and scalability to high-performance computing environments are discussed. For maximum transparency and reproducibility, and to encourage future research, development, and use, the full source code, together with regression tests and documentation, is publicly available at https://xyst.cc.

An efficient Cartesian mesh generation strategy for complex geometries

Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems.

Validation and analysis of a coupled fluid-ablation framework for modeling low-temperature ablator

Ablation of certain highly volatile materials, such as camphor, naphthalene, and dry ice, can be achieved at relatively mild hypersonic conditions in unheated wind tunnels. This provides a convenient way to test fundamental aspects of the ablation process, develop measurement techniques, and validate numerical simulations. In this study, we develop a coupled framework between hypersonic flow and material response solvers and validate the numerical approach against recent experiments conducted by the von Karman Institute of Fluid Dynamics. The flow environment is modeled with an overset near body - Cartesian solver developed within CHAMPS. The solver is equipped with capabilities for automatic mesh generation, adaptive mesh refinement (AMR), and an interpolation algorithm for exchanging boundary conditions with external solvers. The material domain is modeled with a network of one-dimensional rays, incorporating a heat conduction solver, several types of surface ablation models, and a coupled system of surface balance equations required for coupling with the flow solver. The material environment in the simulation aims to closely match the experimental design of the ablating sample, which included a thin layer of camphor applied on top of a copper holder. By taking into account the cooling effect introduced by the back structure, we were able to achieve close agreement with the experimental data for the stagnation point recession and the overall shape change of the geometry. The obtained results are also compared to uncoupled equilibrium-based and steady-state (coupled) solutions, highlighting the importance of the coupled approach for modeling ablation problems. In addition, we explore the effects of different transport properties on the ablation rate of the material, highlighting a strong dependence on the diffusivity of the ablating species. Finally, using the flexibility of the developed algorithm, we explore the effect of the iterative scheme and coupling frequency between the solvers on the accuracy of the solution and the overall duration of the simulation.

Objective Functions for the Blade Shape Optimisation of a Cross-Flow Tidal Turbine under Constraints

Hydro-kinetic cross-flow tidal turbines (CFTT) are omni-directional and offer higher area-based power density compared to horizontal-axis tidal turbines, making them very attractive for tidal energy exploitation. However, the rotating motion around the vertical axis results in continuously varying angles of attack, causing alternating loads, which may lead to fatigue failure and structural damage. The OPTIDE Project addresses these challenges by implementing intracycle blade pitching to individually control the angle of attack, increasing the power coefficient CP and reducing structural loads. For this purpose a Darrieus turbine is designed with embedded actuators in each blade. Firstly a blade shape optimization will be conducted to fit the actuator at the quarter-chord position while ensuring sufficient thickness. The optimization procedure couples Computational Fluid Dynamics (CFD) with a Genetic Algorithm. The employed optimizer OPAL++ sets ten variables for each individual, which describe the hydrofoil shape, length and tip speed ratio (TSR). A smooth hydrofoil shape is generated from the variables, followed by an automatic mesh generation. Subsequently, numerical simulations of each individual at the desired TSR are conducted, while keeping the blade pitch angle constant. Simulation results provide the CP and stress acting on the turbine blades, which are the two optimization objectives (maximize CP while minimizing stress). This process is repeated during the optimization, aiming to determine the most suitable blade shape, that fits the actuator, and operating point (TSR) in a trade-off between CP and structural loads. This will lead to the increase of efficiency and a longer turbine lifetime.

Multi-fidelity and multi-objective aerodynamic short nacelle shape optimisation under different flight conditions

AbstractThroughout the course of a flight mission, a range of aerodynamic conditions, including design-point conditions and off-design conditions, are encountered. As the bypass ratio increases and the fan-pressure ratio decreases to reduce the engine’s specific fuel consumption, the engine diameters increase, which results in an increase in the nacelle weight and overall drag. To reduce its weight and drag, a shorter nacelle with a length-to-diameter ratio $L/D = 0.35$ is investigated. In this study, an adaptive cokriging-based multi-objective optimisation method is applied to the design of a short aero-engine nacelle. Two nacelle performance metrics were employed as the objective functions for the optimisation routine. The cruise drag coefficient is evaluated under cruise conditions, whereas the intake pressure recovery is evaluated under takeoff conditions. The cokriging metamodel are refined using an effective infilling strategy, where high-fidelity samples are infilled via the modified Pareto fitness, and low-fidelity samples are infilled via the Pareto front. By combining parameterised geometry generation, automated mesh generation, numerical simulations, surrogate model construction, Pareto front exploration based on the non-dominated sorting genetic algorithm-II and sample infilling, an integrated multi-objective optimisation framework for short aero-engine nacelles is developed. Two-objective and three-objective test functions are used to validate the effectiveness of the proposed framework. After the optimisation process, a set of non-dominated nacelle designs is obtained with better aerodynamic performance than the original design, demonstrating the effectiveness of the optimisation framework. Compared with the kriging-based optimisation framework, the cokriging-based optimisation framework outperforms the single-fidelity method with a higher hypervolume value at the same number of iteration loops.

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation which quantifies the mesh resolution of the geometry of the interface. Numerical examples are presented to illustrate the competitive performance of the method.

An arbitrarily high-order finite element method on arbitrarily shaped domains with automatic mesh generation

An arbitrarily high-order finite element method on arbitrarily shaped domains with automatic mesh generation

ISpliter: an intelligent and automatic surface mesh generator using neural networks and splitting lines

In this paper, we present a novel surface mesh generation approach that splits B-rep geometry models into isotropic triangular meshes based on neural networks and splitting lines. In the first stage, a recursive method is designed to generate plentiful data to train the neural network model offline. In the second stage, the implemented mesh generator, ISpliter, maps each surface patch into the parameter plane, and then the trained neural network model is applied to select the optimal splitting line to divide the patch into subdomains continuously until they are all triangles. In the third stage, ISpliter remaps the 2D mesh back to the physical space and further optimizes it. Several typical cases are evaluated to compare the mesh quality generated by ISpliter and two baselines, Gmsh and NNW-GridStar. The results show that ISpliter can generate isotropic triangular meshes with high average quality, and the generated meshes are comparable to those generated by the other two software under the same configuration.

Toward the use of LES for industrial complex geometries. Part I: automatic mesh definition

With the constant increase of computational power for the past years, Computational Fluid Dynamics (CFD) has become an essential part of the design in complex industrial processes. In this context, among the scale resolving numerical methods, Large-Eddy Simulation (LES) has become a valuable tool for the simulation of complex unsteady flows. To generalise the industrial use of LES, two main limitations are identified. First, the generation of a proper mesh can be a difficult task, which often relies on user-experience. Secondly, the ‘time-to-solution’ associated with the LES approach can be prohibitive in an industrial context. In this work, these two challenges are addressed in two parts. In this Part I, an automatic procedure for mesh definition is proposed, whereas the Part II is devoted to numerical technique to reduce the LES ‘time-to-solution’. The main goal of these works is then to develop an accurate LES strategy at an optimised computational cost. Concerning the mesh definition, because LES is based on separation between resolved and modelled subgrid-scales, the quality of the computed solution is then directly linked to the quality of the mesh. However, the definition of an adequate mesh is still an issue when LES is used to predict the flow in an industrial complex geometry without a priori knowledge of the flow dynamics. This first part presents a user-independent approach for both the generation of an initial mesh and the convergence of the mesh in the LES framework. An automatic mesh convergence strategy is proposed to ensure LES accuracy. This strategy is built to guarantee a mesh-independent mean field kinetic energy budget. The mean field kinetic energy is indeed expected to be mesh independent since only turbulent scales should be unresolved in LES. The approach is validated on canonical cases, a turbulent round jet and a turbulent pipe flow. Finally, the PRECCINSTA swirl burner is considered as a representative case of complex geometry. First, an algorithm for the generation of an unstructured mesh from a STL file is proposed to generate a coarse initial mesh, before applying the mesh convergence procedure. The overall strategy including automatic first mesh generation and its automatic adaptation paves the way to use LES approach as a decision support tool for various applications, provided that the ‘time-to-solution’ is compatible with the applications constraint. A second paper, referred as Part II, is devoted to the reduction of this time.