Fine Mesh Research Articles

Optimising hydrofoils using automated multi-fidelity surrogate models

ABSTRACT Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship, thus decreasing resistance. To attain efficient hydrofoils, the geometries can be obtained from an automated optimisation process. However, hydrofoil simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil. Simulation-based optimisation can therefore be very expensive. To speed up the fully automated hydrofoil optimisation procedure, we propose a multi-fidelity framework which takes advantage of both an efficient low-fidelity potential flow solver dedicated to hydrofoils and a high-fidelity RANS solver enhanced with adaptive grid refinement and dedicated foil-aligned overset meshes, to attain high accuracy with a limited computational budget. Both solvers are shown to be reliable for automatic simulation, and remarkable correlation between potential-flow and RANS results is obtained. Two different multi-fidelity frameworks are compared for a realistic hydrofoil: only RANS based and potential-RANS based. According to the optimisation results, the drag is able to be reduced by 17% and 8% in these frameworks, within a realistic time frame. Thus, industrial optimisation of hydrofoils appears possible. Finally, critical areas of future improvement regarding the robustness and efficiency of the optimisation procedure are discussed in this study.

Study on cross effect of mesh and turbulence model on separated flow prediction using a tandem cylinder case

Abstract Low dissipative separated flow prediction is still a great challenge in aeronautics engineering. An open-source CFD code named SU2 is employed to study the cross effect of mesh as well as turbulence model on the numerical resolution of separated flow for a tandem cylinder case. Firstly, a nonlinear variation of the numerical resolution for the separated flow is found by comparing the mean surface pressure distribution, mean streamwise velocity profile, the instantaneous vorticity magnitude as well as the aerodynamic forces on the rear cylinder. The resolution of separated flow from the medium mesh is the best compared to those getting from the coarse and fine mesh. Secondly, the reason causing the nonlinear variation of flow resolution is analyzed considering the influence of spatial discretization error and turbulent viscosity locally. A finer mesh would lead to a low spatial discretization error and then a high turbulent viscosity and then causes nonlinear variation of flow resolution. Finally, the existence of a “density boundary” of the mesh is proposed which could balance the spatial precision as well as turbulent viscosity and achieve the prediction of separated flow with a good resolution employing the RANS method.

Numerical research of functionally graded magneto-electro-elastic structures under thermal environment via the thermo-mechanical-electro-magnetic enriched finite element method

Abstract In this work, the functionally graded magneto-electro-elastic (FG-MEE) structures were used to study mechanical performance under a thermal environment using the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM). Through enhancing the traditional solution space of the finite element method (FEM), additional degrees of freedom are introduced without modifying the mesh structure. Therefore, as a class of higher-order finite element methods, field variables with high gradients can be captured without a relatively finer mesh. The accuracy of TMEM-EFEM is improved by using interpolation covers. The feasibility of TMEM-EFEM is proven by numerical examples. The proposed TMEM-EFEM is proven to be accurate under the relatively coarse mesh. Through numerical examples, the high accuracy of TMEM-EFEM is demonstrated. Therefore, TMEM-EFEM can be a good alternative for the statics study of FG-MEE structures.

An improved efficient adaptive method for large-scale multi-explosives explosion simulations

Shock wave caused by a sudden release of high-energy, such as explosion and blast, usually affects a significant range of areas. The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise results is inefficient in terms of computational resource. This is particularly evident when large-scale fluid field simulations are conducted with significant differences in computational domain size. In this work, a variable-domain-size adaptive mesh enlargement (vAME) method is developed based on the proposed adaptive mesh enlargement (AME) method for modeling multi-explosives explosion problems. The vAME method reduces the division of numerous empty areas or unnecessary computational domains by adaptively suspending enlargement operation in one or two directions, rather than in all directions as in AME method. A series of numerical tests via AME and vAME with varying nonintegral enlargement ratios and different mesh numbers are simulated to verify the efficiency and order of accuracy. An estimate of speedup ratio is analyzed for further efficiency comparison. Several large-scale near-ground explosion experiments with single/multiple explosives are performed to analyze the shock wave superposition formed by the incident wave, reflected wave, and Mach wave. Additionally, the vAME method is employed to validate the accuracy, as well as to investigate the performance of the fluid field and shock wave propagation, considering explosive quantities ranging from 1 to 5 while maintaining a constant total mass. The results show a satisfactory correlation between the overpressure versus time curves for experiments and numerical simulations. The vAME method yields a competitive efficiency, increasing the computational speed to 3.0 and approximately 120,000 times in comparison to AME and the fully fine mesh method, respectively. It indicates that the vAME method reduces the computational cost with minimal impact on the results for such large-scale high-energy release problems with significant differences in computational domain size.

Introducing new wheat milling passages to manage the ultra-fine flours of primary streams: Roles of granulation in starchy content

The size distribution of ultra-fine flours (UFF) is crucial for determining the physicochemical properties of the final wheat milling product. To optimize the milling process, new passages with a stack of fine mesh sieves are used. The UFF extracted from both break and reduction passages exhibits a wide range of functionality and physicochemical characteristics, were incorporated into five reconstituted flour blends. By splitting of UFF fraction isolated from primary passages, the quality of baked bread can be modified manually without using any enzymes or chemical improvers. Substituting the default milling stream with 60% of primary UFF increases the availability of starch for gelatinization by shifting the peak temperature to a higher number. This creates stronger starch-gluten network exhibiting increased elasticity. Raised viscoelasticity and hence water absorption value result in higher loaf volume. The infrared spectroscopy analysis revealed a specific peak at 1659 cm−1, associated with water absorption in the amorphous region of starches, which was recorded as the highest intensity for UFF reduction samples. These results were in agreement with imposing a higher starch damage. Furthermore, structural amorphization was also observed based on a broader shallow XRD curve for samples incorporated with UFF of reduction passages due to higher grinding strength generated through the smooth rolls. The lowest polydispersity index content was calculated for break UFF samples and more uniformity in particle size distribution was found. This finding highlighted the effective role of corrugated rolls for producing the certain range of flour granulation.

Benchmark Simulation of Laminar Reactive Micromixing Using Lattice Boltzmann Methods

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multicomponent flows are considered. Despite the laminar streaming regime (e.g., Re = 186), there exist secondary flow microstructures. For this setup, accurate predictions of those structures are possible with a large-eddy simulation on a fine mesh resolving till the Batchelor microscales. Utilizing the open-source lattice Boltzmann method (LBM) framework, OpenLB, a benchmark simulation of the reacting micromixer, is re-established with new, more precise computation results. In this context, a Schmidt-number-based stabilization method for LBM-discretized reactive advection–diffusion equations by laminar secondary flow structures is used. A convergence study is performed, which is also a novelty. All computations have been performed on the high-performance computing cluster HoreKa using up to 160 NVIDIA A100 graphics processing units.

Exploring Effects of Nutrient Availability, Species Composition, Stand Age, and Mesofaunal Exclusion on Leaf Litter Decomposition in Northern Hardwood Forests

In northern hardwood forests, litter decomposition might be affected by nutrient availability, species composition, stand age, or access by decomposers. We investigated these factors at the Bartlett Experimental Forest in New Hampshire. Leaf litter of early and late successional species was collected from four stands that had full factorial nitrogen and phosphorus additions to the soil and were deployed in bags of two mesh sizes (63 µm and 2 mm) in two young and two mature stands. Litter bags were collected three times over the next 2 years, and mass loss was described as an exponential function of time represented by a thermal sum. Litter from young stands had higher initial N and P concentrations and decomposed more quickly than litter from mature stands (p = 0.005), regardless of where it was deployed. Litter decomposed more quickly in fine mesh bags that excluded mesofauna (p < 0.001), which might be explained by the greater rigidity of the large mesh material making poor contact with the soil. Neither nutrient addition (p = 0.94 for N, p = 0.26 for P) nor the age of the stand in which bags were deployed (p = 0.36) had a detectable effect on rates of litter decomposition.

Cyclic shift short-distance attention for defect detection of fine etching mesh

Abstract Based on the deficiency of the existing Swin Transformer in the detection of surface defects in metal etched grids, i.e. the isolation of information transmission between different windows, and the limitations of image matrix size and network structure,which make it not suitable for long sequence data processing and dense prediction scenarios, a defect detection method for metal etching nets based on Cyclic shift Long Short Distance Attention (C-LSDA) is proposed. In the proposed method, cross-scale features are used to capture long and short distance relationships,and enhance the feature transfer between windows. Tracking position bias (TPB) is also used to improve relative position bias (RPB), in order to help the model to better understand the spatial relationships in the input data. In addition, the image is downsampled at various scales, so that the proposed method can be suitable for long sequence data processing and dense prediction scenarios. In order to improve the detection accuracy of small targets. a multi-feature fusion pyramid network (MFFPN) for feature fusion is also proposed. The experimental results show that the proposed method is significantly superior to the traditional CNN recognition method and the transformer recognition method. The proposed methodhas good identification accuracy and low computational cost.

Application of a finite element method variant in nonconvex domains to parabolic problems

In this paper we address one of the major difficulties which is the nonconvex behavior of the domains while finding the solution of the problems. The part of the domain where the nonsmoothness appears is where the challenge arises and the way that area is handled using different numerical methods reveals the effectiveness of these techniques. Here in this article, we study the semilinear parabolic problem in nonconvex polygonal domain. For the approximation of the solution we use the Composite Finite Element (CFE) method, which is a classification of the Finite Element Method. CFE discusses the two-scale discretization — the larger mesh also known as the coarse mesh with the size H and the smaller mesh, also known as the fine mesh with the size h. It helps in reducing the dimension of the domain space of consideration. The fine scale grid is used to resolve the nonconvexity of the boundary whereas the coarse scale grid is comprised of larger grids at an appropriate distance from the boundary. The degrees of freedom depends on the coarse grid. This is the precedence of CFE over other methods, i.e., it eases the task of reducing the domain complexity. In this article, we consider two approaches — the semi discrete analysis where only space discretization is carried out, and the fully discrete analysis where both the time and space discretization is done using both backward Euler and Crank–Nicolson method. We study the error analysis in the L∞(L2)-norm and in the L∞(H1)-norm for the semidiscrete case whereas for the fully discrete case, we study the error analysis in the L∞(L2)-norm. Also, we check for the optimal results. For the CFE technique in the L∞(L2)-norm, we derive the convergence having optimal order in time and almost optimal order in space even if the domain is nonconvex. We consider a T-shaped domain and another star shaped domain to carry out the theoretical findings. Thereafter, numerical computations are implemented to validate the theoretical results.

A novel post-processed finite element method and its convergence for partial differential equations

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable for most partial differential equations. For simplicity, we use the second-order elliptic problem as an example to show how the novel approach improves the accuracy of the finite element method. Numerical tests are also conducted to validate the main theoretical results.

Study on Fast Temporal Prediction Method of Flame Propagation Velocity in Methane Gas Deflagration Experiment Based on Neural Network

To address the challenges of high experimental costs, complexity, and time consumption associated with pre-mixed combustible gas deflagration experiments under semi-open space obstacle conditions, a rapid temporal prediction method for flame propagation velocity based on Ranger-GRU neural networks is proposed. The deflagration experiment data are employed as the training dataset for the neural network, with the coefficient of determination (R2) and mean squared error (MSE) used as evaluation metrics to assess the predictive performance of the network. First, 108 sets of pre-mixed methane gas deflagration experiments were conducted, varying obstacle parameters to investigate methane deflagration mechanisms under different conditions. The experimental results demonstrate that obstacle-to-ignition source distance, obstacle shape, obstacle length, obstacle quantity, and thick and fine wire mesh obstacles all significantly influence flame propagation velocity. Subsequently, the GRU neural network was trained, and different activation functions (Sigmoid, Relu, PReLU) and optimizers (Lookahead, RAdam, Adam, Ranger) were incorporated into the backpropagation updating process of the network. The training results show that the Ranger-GRU neural network based on the PReLU activation function achieves the highest mean R2 value of 0.96 and the lowest mean MSE value of 7.16759. Therefore, the Ranger-GRU neural network with PReLU activation function can be a viable rapid prediction method for flame propagation velocity in pre-mixed methane gas deflagration experiments under semi-open space obstacle conditions.

Deep Inverse Design of an Infrared Metasurface Diffuser

AbstractMachine learning (ML) algorithms have become invaluable tools for tackling design challenges associated with achieving unique scattering effects in artificial electromagnetic materials (AEMs). However, their effectiveness is reliant on substantial, well‐constructed training datasets. Building such datasets using traditional methods becomes impractical for increasingly complex and large‐scale geometric models. Achieving a specific diffuse scattering is one example and this often requires electrically large and diverse AEM arrays. Unfortunately, while numerical simulations offer high accuracy by utilizing fine meshing, their computational limitations render them incapable of handling such large structures and computing their scattering parameters efficiently. This work proposes a new approach to overcome these limitations by replacing conventional numerical simulations with a hybrid method that combines electromagnetic simulations with an analytical model, enabling the rapid and accurate generation of datasets for electrically large metamaterial arrays. Utilizing this approach, an optimized metasurface geometry for the mid‐infrared range is successfully identified and tested that exhibits desirable diffuse scattering effects. This innovative method paves the way for significantly faster design and optimization of metamaterials, while also unlocking the potential for a new generation of large‐scale, high‐quality ML datasets for AEM problems.

A novel multilevel finite element method for a generalized nonlinear Schrödinger equation

In this article, we focus on an efficient multilevel finite element method to solve the time-dependent nonlinear Schrödinger equation which is one of the most important equations of mathematical physics. For the time derivative, we adopt implicit schemes including the backward Euler method and the Crank–Nicolson method. Based on these stable implicit schemes, the proposed method requires solving a nonlinear elliptic problem at each time step. For these nonlinear elliptic equations, a multilevel mesh sequence is constructed. At each mesh level, we first derive a rough approximation by correcting the approximation of the previous mesh level in a special correction subspace. The correction subspace is composed of a coarse finite element space and an additional approximate solution derived from the previous mesh level. Next, we only need to solve a linearized elliptic equation by inserting the rough approximation into the nonlinear term. Then, we derive an accurate approximate solution by performing the aforementioned solving process on the multilevel mesh sequence until we reach the final mesh level. Owing to the special construct of the correction subspace, we derive a multilevel finite element method to solve the nonlinear Schrödinger equation for the first time, and meanwhile we also derive an optimal error estimate with linear computational complexity. Additionally, unlike the existing multilevel methods for nonlinear problems, that typically require bounded second-order derivatives of the nonlinear terms, the nonlinear term in our study requires only one-order derivatives. Numerical results are provided to support our theoretical analysis and demonstrate the efficiency of the presented method.

Multi-Fidelity Learned Emulator for Waves and Porous Coastal Structures Interaction Modelling

A thorough understanding and treatment of wave-structure interaction (WSI) mechanics is essential for the rigorous engineering design of coastal protections. Conventional numerical analysis methods are accurate and generalize well, but are heavily dependent on the adopted mesh resolution and frequently incur substantial computational costs. To bypass these limitations, a meshless multi-fidelity residual neural network (MRNN) emulator is introduced in this study to infer the spatio-temporal responses arising from WSI. MRNN first employs a ‘low-fidelity’ simulator to learn basic WSI relationships by training on simulations obtained using a coarse numerical mesh. Subsequently, a ‘high-fidelity’ (HF) simulator is then employed to learn the mapping between numerical simulations performed using the coarse mesh and additional detailed fine meshes. The results indicate that MRNN is a highly robust emulator which requires significantly less HF data through its hierarchical framework compared to conventional single-fidelity data-driven strategies. By way of example, the MRNN emulator is applied to the cases of a porous dam break and breakwater. A broad spectrum of WSI responses, such as water through the porous dam medium, can be accurately captured using the MRNN emulator which is benchmarked against a conventional numerical modelling with a fine mesh. The computational efficiency of the MRNN is shown to be independent of the mesh resolution and complexity of the studied partial differential equations. It provides a generic and utilitarian emulator for any engineering problem of interest.

Free-Form Deformation as a non-invasive, discrete unfitted domain method: Application to the time-harmonic acoustic response of a saxophone

The Finite Element method, widely used for solving Partial Differential Equations, may result in suboptimal computational costs when computing smooth fields within complex geometries. In such situations, IsoGeometric Analysis often offers improved per degree-of-freedom accuracy but building analysis-suitable representation of complex shapes is generally not obvious. This paper introduces a non-invasive, spline-based fictitious domain method using Free-Form Deformation to efficiently solve the Helmholtz equation in complex domains, such as in musical instruments. By immersing a fine FE mesh into a simple B-spline box, the approximation subspace size is significantly reduced without compromising accuracy. Accompanied by specific conditioning treatment, the method not only proves to be efficient, but also robust and easy to implement in existing FE software. Applied to an alto saxophone, the method reduces the number of degrees of freedom by over two orders of magnitude and the computation time by more than one compared to standard FE methods with comparable accuracy when compared to experimental tests.

Two-level Arrow–Hurwicz iteration methods for the steady bio-convection flows

To avoid solving a saddle-point system, in this paper, we study two-level Arrow–Hurwicz finite element methods for the steady bio-convection flows problem which is coupled by the steady Navier–Stokes equations and the steady advection–diffusion equation. Using the mini element to approximate the velocity, pressure, and the piecewise linear element to approximate the concentration, we use the linearized Arrow–Hurwicz iteration scheme to obtain the coarse mesh solution and use three different one-step Stokes/Oseen/Newton linearized scheme to obtain the fine mesh solution. The optimal error estimate O(h+H2+χm/2) of the velocity and concentration in the H1-norm and the pressure in the L2-norm are derived, where h and H are fine and coarse mesh sizes, respectively, and χm/2 denotes the iteration error with 0<χ<1. Numerical results are given to support the theoretical analysis and confirm the efficiency of the proposed two-level methods.

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.

Approximation of acoustic black holes with finite element mixed formulations and artificial neural network correction terms

Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized using a variational multiscale FEM. A non-linear ANN correction term is then designed to be added to the FEM algebraic matrix system and produce accurate solutions when solving elastodynamics on coarse meshes. As a case study we consider acoustic black holes (ABHs) on structural elements with high aspect ratios such as beams and plates. ABHs are traps for flexural waves based on reducing the structural thickness according to a power-law profile at the end of a beam, or within a two-dimensional circular indentation in a plate. For the ABH to function properly, the thickness at the termination/center must be very small, which demands very fine computational meshes. The proposed strategy combining the stabilized FEM with the ANN correction allows us to accurately simulate the response of ABHs on coarse meshes for values of the ABH order and residual thickness outside the training test, as well as for different excitation frequencies.

Tessellation and interactive visualization of four-dimensional spacetime geometries

This paper addresses two problems needed to support four-dimensional (3d+t) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface points of the geometry are embedded in a four-dimensional space as the geometry moves in time. The geometry is first tessellated at prescribed time steps and then these tessellations are connected in the parameter space of each geometry entity to form tetrahedra. In contrast to previous work, this approach allows the resolution of the geometry to be controlled at each time step. The only restriction on the algorithm is the requirement that no topological changes to the geometry are made (i.e. the hierarchical relations between all geometry entities are maintained) as the geometry moves in time. The validity of the final mesh topology is verified by ensuring the tetrahedralizations represent a closed 3-manifold. For some analytic problems, the 4d volume of the tetrahedralization is also verified. The second problem addressed in this paper is the design of a system to interactively visualize four-dimensional meshes when the 4d view changes, including tetrahedra (embedded in 4d) and pentatopes. Algorithms that either include or exclude a geometry shader are described, and the efficiency of each approach is then compared. Overall, the results suggest that visualizing tetrahedra (either those bounding the domain, or extracted from a pentatopal mesh) using a geometry shader achieves the highest frame rate, realizing interactive frame rates of at least 15 frames per second for meshes with about 50 million tetrahedra.

Assessment of the CTF subchannel code for modeling a large-break loss-of-coolant accident reflood transient

With increased industry interest in extending reactor operating cycles, the neams! (neams!) program has been investigating the behavior of high-burnup fuel during design basis accidents such as the lbloca! (lbloca!) with consideration for risk of ffrd! (ffrd!). As part of that activity, the neams! subchannel th! (th!) code, CTF, is being used for modeling of lbloca! and to determine the impact of subchannel resolution on results. Although CTF includes a wide range of models for lbloca! conditions, the code has not been used for this application while maintained at ornl! (ornl!) until now. Therefore, in this work, a preliminary assessment of several of these models was performed using openly available reflood experimental data from the feba! (feba!) tests. One coarse mesh and one fine mesh model were set up in CTF for high and low flooding rate tests performed in the unblocked feba! facility. A coarse TRACE model was set up to be as consistent as possible with the coarse CTF model to allow for code-to-code benchmarking. The assessment shows a tendency of the codes to over-predict pct! (pct!) near the top of the bundle and to quench early. Advanced spacer grid models were shown to improve upper bundle predictions in CTF. The resolved CTF model over-predicted pct! by a larger degree in the center channels in the low-flooding rate test, and it is believed that the radiative heat transfer model, which was not used in this study, may be needed to correct this over-prediction. Finally, this work demonstrates the importance of the droplet model in determining quench time and vapor temperature and pct! prediction, which necessitates a more in-depth validation of these models in the future.