Mesh Size Research Articles

Higher order method based on the coupling of local discontinuous Galerkin method with multistep implicit-explicit time-marching for the micropolar Navier–Stokes equations

In this paper, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal multistep implicit-explicit (IMEX) evolution for the micropolar Navier–Stokes equations (MNSE) is adopted to construct an efficient fully discrete method. First, the multistep IMEX-LDG methods are constructed up to the third order, which have small computational scale and facilitate implementation to higher orders. Second, the unconditional stability of the fully discrete method on Cartesian grids is derived theoretically, meaning that the temporal step size τ is upper bounded by a positive constant independent of the spatial mesh size h. Last, numerical results for nonlinear MNSE with different boundary conditions are presented, confirming the theoretical validity and effectiveness of the method.

Temporal second-order two-grid finite element method for semilinear time-fractional Rayleigh-Stokes equations

In this paper, we have developed a temporal second-order two-grid FEM to solve the semilinear time-fractional Rayleigh-Stokes equations. The proposed two-grid FEM uses the L2-1σ scheme and second order scheme to approximate the Caputo fractional derivative and the time first-order derivative in temporal direction and the standard FEM in spatial direction. The L2-norm and H1-norm stability and error estimates for the standard finite element solution and the two-grid solution are derived. The results shown that as long as the mesh sizes satisfy H=h12 and H=hr2r+2 respectively, the two-grid algorithm can achieve asymptotically optimal approximation. Furthermore, the non-uniform L2-1σ scheme was applied for temporal discretization to handle the weak singularity of the solution. Finally, the theoretical findings were confirmed by numerical results, and the effectiveness of the two-grid algorithm was demonstrated.

Nanoscale roughness to mitigate polydimethylsiloxane (PDMS) sticking in liquid crystal display (LCD) vat photopolymerization (VPP): Separation force reduction without losing resolution

Liquid crystal display (LCD) vat photopolymerization (VPP) is gaining attention among polymer-based additive manufacturing (AM) processes due to its high accuracy, superior surface finish, and cost-efficiency. However, one of the main challenges is the high layer separation force, which is heavily influenced by the flexibility of the interface. Sticking between polydimethylsiloxane (PDMS) and the LCD panel reduces flexibility, shifting the separation behavior from Johnson-Kendall-Roberts (JKR) to Derjaguin-Muller-Toporov (DMT)-like behavior. This study presents a novel approach to mitigate PDMS sticking by introducing nanoscale surface roughness. Sandblasted sheet metals with varying sand mesh sizes were used as molds to create interfaces with different roughness levels. The findings reveal that a surface roughness of 0.262 µm significantly reduces PDMS sticking, making the interface more flexible. The optimized flexible interface (SP 2000) interface reduced the separation force 50-fold compared to unmodified PDMS while maintaining high print resolution. Case studies involving rigid and flexible photopolymer resins further emphasize the effectiveness of the SP 2000 interface in addressing PDMS sticking issues. This research highlights the critical role of interface flexibility and presents a promising solution for improving LCD VPP performance.

Two novel linearized energy-conserving finite element schemes for nonlinear regularized long wave equation

In this paper, two linearized second-order energy-conserving schemes for the nonlinear regularized long wave (RLW) equation are introduced, the unconditional superclose and superconvergence results are presented by using the conforming finite element method (FEM). Initially, through a skillful decomposition of the nonlinear term, two linearized second-order fully discrete schemes are developed. Compared to the previous nonlinear approaches, these schemes significantly reduce the number of iterations and improve computational efficiency; moreover, they conserve energy, and ensure the boundedness of the numerical solution in the H1-norm directly, which represents an advancement over the L∞-norm boundedness reported in prior studies. Secondly, based on the boundedness of the FE solution, the Ritz projection operator and high-precision results of the linear triangular element, the error estimates for superclose and superconvergence are derived without any restrictions on the ratio between time step size Δt and spatial mesh size h. Finally, four numerical examples are provided to confirm the accuracy of the theoretical analysis and the effectiveness of the method.

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.

Mathematical and numerical analysis of reduced order interface conditions and augmented finite elements for mixed dimensional problems

In this paper, we are interested in the mathematical properties of methods based on a fictitious domain approach combined with reduced-order interface coupling conditions, which have been recently introduced to simulate 3D-1D fluid-structure or structure-structure coupled problems. To give insights on the approximation properties of these methods, we investigate them in a simplified setting by considering the Poisson problem in a two-dimensional domain with non-homogeneous Dirichlet boundary conditions on small inclusions. The approximated reduced problem is obtained using a fictitious domain approach combined with a projection on a Fourier finite-dimensional space of the Lagrange multiplier associated to the Dirichlet boundary constraints, obtaining in this way a Poisson problem with defective interface conditions. After analyzing the existence of a solution of the reduced problem, we prove its convergence towards the original full problem, when the size of the holes tends towards zero, with a rate which depends on the number of modes of the finite-dimensional space. In particular, our estimates highlight the fact that to obtain a good convergence on the Lagrange multiplier, one needs to consider more modes than the first Fourier mode (constant mode). This is a key issue when one wants to deal with real coupled problems, such as fluid-structure problems for instance. Next, the numerical discretization of the reduced problem using the finite element method is analyzed in the case where the computational mesh does not fit the small inclusion interface. As is standard for these types of problem, the convergence of the solution is not optimal due to the lack of regularity of the solution. Moreover, convergence exhibits a well-known locking effect when the mesh size and the inclusion size are of the same order of magnitude. This locking effect is more apparent when increasing the number of modes and affects the Lagrange multiplier convergence rate more heavily. To resolve these issues, we propose and analyze a stabilized method and an enriched method for which additional basis functions are added without changing the approximation space of the Lagrange multiplier. Finally, the properties of numerical strategies are illustrated by numerical experiments.

Mechanical Properties of Novel Hybrid Bamboo Fibre/Aluminium Mesh Reinforced Polymer Composite

Bamboo fibres are one of the sustainable lignocellulosic resources explored for polymer composites in recent years. Research has shown that bamboo fibres have the potential to be used in a variety of critical applications. Nevertheless, bamboo fibres are susceptible to thermal and hygroscopic loads, and their mechanical properties are limited by the unequal interfacial strength and varying fibre dimensions. Implementing hybrid procedures or incorporating alternative materials, such as aluminium metal, is strongly advised to address this issue. Thus, this study investigates the tensile and flexural performances of the hybrid bamboo fibre/aluminium expanded mesh-reinforced polymer composites. The composites were fabricated using epoxy resin reinforced with bamboo fibre, and an aluminium expanded mesh sheet was constructed using a vacuum infusion process utilising various stacking sequences and mesh sizes. The test findings indicated that the composite material exhibited tensile stress values ranging from 27 to 34 MPa and a corresponding tensile strain value between 1.1% and 1.6%. The flexural strength and strain values were measured within the range of 44 Mpa to 59 Mpa and 2.2% to 3.2%, respectively. ANOVA analysis showed that both stacking sequences and mesh size significantly affected the tensile performances of the composites, while only stacking sequences affected the flexural performance significantly. Overall, a hybrid composite of bamboo fibre and aluminium mesh is well-suited as a substitute material in industries requiring exceptional mechanical properties.

A neural network approach for unstructured mesh quality evaluation

PurposeThe quality of the unstructured mesh has a considerable impact on the stability and accuracy of aerodynamic simulation in computational fluid dynamics (CFD). Typically, engineers spend a significant portion of their time on mesh quality evaluation to ensure a valid, high-quality mesh. The extensive manual interaction and a priori knowledge required to undertake an accurate and timely evaluation process have become a bottleneck in the idealized efficient CFD workflow. This paper aims to introduce a neural network-based quality evaluation approach for unstructured meshes to enable higher efficiency and the level of automation.Design/methodology/approachThe paper investigates the capability of deep neural networks for the quality evaluation of unstructured meshes. For training the network, we build a training dataset for mesh quality learning algorithms. The dataset contains a rich variety of unstructured aircraft meshes with different mesh sizes, densities, cell distribution, growth ratios and cell numbers to ensure its diversity and availability. We also design a neural network, AircraftNet, to learn the effect of mesh quality on the convergent properties of the numerical solutions. The proposed network directly manipulates raw point data in mesh source files rather than passing it to an intermediate data representation. During training, AircraftNet extracts non-linear quality features from high-dimensional data spaces and then automatically predicts the overall quality of the input unstructured mesh.FindingsThe paper provides a series of experimental results on GPUs. It shows that AircraftNet is able to effectively analyze the quality-related features like mesh density and distribution from the extracted features and achieve high prediction accuracy on the proposed dataset with even a small number of training runs.Research limitations/implicationsBecause of the limited training dataset, the research results may lack generalizability. Therefore, researchers are encouraged to test the proposed propositions further.Originality/valueThe paper publishes a benchmarking dataset for mesh quality learning algorithms and designs a novel neural network approach for unstructured mesh quality evaluation.

Hydrogel interfaced glass nanopore for high-resolution sizing of short DNA fragments

Solid-state nanopores, known for their label-free detection and operational simplicity, face challenges in accurately sizing the short nucleic acids due to fast translocation and a lack of enzyme-based control mechanisms as compared to their biological counterparts with sizing resolutions still limited to ≥100 bp. Here, we present a facile polyethylene glycol-dimethacrylate (PEG-DMA) hydrogel interfaced glass nanopore (HIGN) system by inserting glass nanopore into the hydrogel to achieve sub-100 base pair (bp) resolution in short DNA sizing analysis. We systematically investigated the effects of hydrogel mesh size, spatial configurations of glass nanopores about the hydrogel, applied bias voltage, and analyte concentration on the transport dynamics of 200 bp double-stranded DNA (dsDNA). A 7.5 w/v% PEG-DMA hydrogel induced ∼11x increase in the mean dwell times compared with bare solution nanopore system. The insertion locations and depths of the glass nanopore into the hydrogel resulted in 7.16% and 5.28% coefficients of variation (CV) for mean normalized event frequencies. This enhancement of dwell times and invariability in translocation characteristics enables precise sizing of dsDNA fragments under 400 bp using HIGN, with an achieved size resolution of 50 bp with observable mean normalized peak amplitude (ΔI/Io) of ∼0.005. Furthermore, we have demonstrated the capability of HIGN to perform multiplex detection of influenza A virus (IAV) and severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) through reverse transcriptase-polymerase chain reaction (RT-PCR). These results demonstrated the potential of HIGN as a versatile tool in nucleic acid analysis and multiplexed label-free molecular diagnostics.

Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes II: Unsteady flows

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to alleviate the restrictions on the time step for unsteady simulations. In order to improve the efficiency and keep the high-order accuracy, a two-stage third-order implicit time-accurate discretization is proposed. In each stage, an artificial steady solution is obtained for the implicit system with the pseudo-time iteration. In the iteration, the classical implicit methods are adopted to solve the nonlinear system, including the lower-upper symmetric Gauss-Seidel (LUSGS) and generalized minimum residual (GMRES) methods. To achieve the spatial accuracy, the HGKSs with both non-compact and compact reconstructions are constructed. For the non-compact scheme, the weighted essentially non-oscillatory (WENO) reconstruction is used. For the compact one, the Hermite WENO (HWENO) reconstruction is adopted due to the updates of both cell-averaged flow variables and their derivatives. The expected third-order temporal accuracy is achieved with the two-stage temporal discretization. For the smooth flow, only a single artificial iteration is needed. For uniform meshes, the efficiency of the current implicit method improves significantly in comparison with the explicit one. For the flow with discontinuities, compared with the well-known Crank-Nicholson method, the spurious oscillations in the current schemes are well suppressed. The increase of the artificial iteration steps introduces extra reconstructions associating with a reduction of the computational efficiency. Overall, the current implicit method leads to an improvement in efficiency over the explicit one in the cases with a large variation of mesh size. Meanwhile, for the cases with strong discontinuities on a uniform mesh, the efficiency of the current method is comparable with that of the explicit scheme.

Computing the matrix exponential with the double exponential formula

Abstract This article considers the computation of the matrix exponential e A {{\rm{e}}}^{A} with numerical quadrature. Although several quadrature-based algorithms have been proposed, they focus on (near) Hermitian matrices. In order to deal with non-Hermitian matrices, we use another integral representation including an oscillatory term and consider applying the double exponential (DE) formula specialized to Fourier integrals. The DE formula transforms the given integral into another integral whose interval is infinite, and therefore, it is necessary to truncate the infinite interval. In this article, to utilize the DE formula, we analyze the truncation error and propose two algorithms. The first one approximates e A {{\rm{e}}}^{A} with the fixed mesh size, which is a parameter in the DE formula affecting the accuracy. The second one computes e A {{\rm{e}}}^{A} based on the first one with automatic selection of the mesh size depending on the given error tolerance.

Development of Low-Resistance Coastal Stow Net Using Numerical Analysis and Model Experiments

In coastal stow net fishing, the heavy weight of a typical anchor (750–1000 kg) can increase the risk of capsizing the boat and crew member injury during hoisting operations. Thus, to prevent these accidents, a reduction in the anchor weight is required. One strategy to achieve this is to reduce the resistance force of the fishing gear used, which would allow lighter anchors to be employed. This requires the accurate estimation of the resistance force for various gear designs. Therefore, the resistance force and shape during the operation of two representative types of coastal stow nets currently employed in the Korean coastal stow net fishing industry were investigated using simulations and modeling experiments. The modeled fishing gear was divided into four sections according to the mesh size. Based on the results, the twine thickness was reduced in order to target areas of the gear where the greatest resistance was observed, while the front part of the gear was redesigned to prevent the front of the net from being pushed back into a suboptimal shape. The proposed low-resistance fishing gear has the potential to improve occupational safety in the coastal stow net fishing industry.

Evidence to inform spatiotemporal management of a western Pacific Ocean tuna purse seine fishery.

Fisheries can profoundly impact co-occurring species exposed to incidental capture. Spatiotemporal fisheries management holds substantial potential to balance socioeconomic benefits with ecological costs to threatened bycatch species. This study estimated the effect of the spatial and temporal distribution of effort by a western Pacific Ocean tuna purse seine fishery on catch rates of target and at-risk species by fitting spatially explicit generalized additive multilevel regression models within a Bayesian inference framework to observer data. Mean field prediction surfaces defined catch rate hotspots for tunas, silky sharks, rays, and whale sharks, informing the design of candidate area-based management strategies. Due to limited sample sizes, odontocete and marine turtle catch rate geospatial patterns were summarized using simple 2D hexagonal binning. Effort could be focused in two areas within core fishing grounds to reduce overlap with hotspots for silky sharks, rays, and whale sharks without affecting target catch. Effort could be shifted outside of core fishing areas to zones with higher target tuna catch rates to reduce overlap with hotspots for at-risk species. Sparse and small marine turtle and whale shark hotspots occurred across the fishing grounds. Results did not identify opportunities for temporally dynamic spatial management to balance target and at-risk catch rates. Research on the economic and operational viability of alternative spatial management strategies is a priority. A small subset of sets had disproportionately large odontocete captures. Real-time fleet communication, move-on rules, and avoiding sets on dolphin schools might reduce odontocete catch rates. Managing set association type and mesh size present additional opportunities to balance catch rates of at-risk and target species. Employing output controls that effectively constrain the fishery would alter the spatial management strategy to focus fishing within zones with the lowest ratio of at-risk bycatch to target tuna catch. Findings inform the design of alternative spatial management strategies to avoid catch rate hotspots of at-risk species without compromising the catch of principal market species.

An Enhanced Progressive Damage Model for Laminated Fiber-Reinforced Composites Using the 3D Hashin Failure Criterion: A Multi-Level Analysis and Validation.

This paper presents a progressive damage model (PDM) based on the 3D Hashin failure criterion within the ABAQUS/ExplicitTM 2021 framework via a VUMAT subroutine, enhancing the characterization of the mechanical performance and damage evolution in the elastic and softening stages of composite materials via the accurate calculation of damage variables and accommodation of non-monotonic loading conditions. In the subsequent multi-level verification, it is found that the model accurately simulates the primary failure modes at the element level and diminishes the influence of element size, ensuring a reliable behavior representation under non-monotonic loading. At the laminate level, it also accurately forecasts the elastic behavior and damage evolution in open-hole lamina and laminates, demonstrating the final crack band at ultimate failure. This paper also emphasizes the importance of correct characteristic length selection and how to minimize mesh size impact by selecting appropriate values. Compared to ABAQUS's built-in 2D model, the 3D VUMAT subroutine shows superior accuracy and effectiveness, proving its value in characterizing the mechanical behavior and damage mechanisms of fiber-reinforced polymer (FRP) materials. The enhanced 3D PDM accurately characterizes the softening processes in composite materials under simple or complex stress states during monotonic or non-monotonic loading, effectively minimizes the mesh dependency, and reasonably captures failure crack bands, making it suitable for future simulations and resolutions of numerical issues in composite material models under complex, three-dimensional stress states.

A coupled scaled boundary finite element and phase-field algorithm for seismic loading

Seismic-induced damage, integral to the safety evaluations of major engineering projects, persists as a key focus of research worldwide. Based on the Scaled Boundary Finite Element Method (SBFEM) and the Phase-Field Method (PFM), a coupled algorithm tailored for reciprocal loading was introduced in this paper, integrating strategies including "closure constraints," "numerical threshold strategy," and "subdomain block integration." Adopting object-oriented principles, a universal coupling solution framework has been built and seamlessly embedded within GEODYNA, a self-developed finite element software system. The accuracy was validated through rigorous benchmark tests. The entire process of crack initiation, propagation, and dynamic opening-closing cycles in the Koyna concrete gravity dam was reproduced. Furthermore, the effect of mesh size and computational timestep on the structural seismic response, crack localization, and the extent of damage in the dam were explored. The outcomes demonstrated that the SBFEM-PFM coupling algorithm performs effectively and meets the engineering precision criteria for seismic evaluations and reinforcement analyses of crucial structures.

Experimental studies and calculation of crack propagation at the nil ductility temperature of shipbuilding steel

Resistance to crack propagation in low-alloyed steels is verified by the experimental evaluation of ductile-to-brittle transition temperatures. Though, correlations of test results obtained according to used methods with the minimum design temperature of marine structures should be substantiated. The paper suggests a fracture mechanics based formula for the required nil ductility temperature (NDT). An original FEM simulation method with uniform mesh size is applied.

Quantitative Macromolecular Modeling Assay of Biopolymer-Based Hydrogels

The rubber elasticity theory has been lengthily applied to several polymeric hydrogel substances and upgraded from idealistic models to consider imperfections in the polymer network. The theory relies solely on hyperelastic material models in order to provide a description of the elastic polymer network. While this is also applicable to polymer gels, such hydrogels are rather characterized by their water content and visco-elastic mechanical properties. In this work, we applied rubber elasticity constitutive models through hyperelastic parameter identification of hydrogels based on their stress–strain response to compression. We further performed swelling experiments and determined the intrinsic properties, i.e., density, of the specimens and their components. Additionally, we estimated their equilibrium swelling and employed it in the swelling-equilibrium theory in order to determine the polymer–solvent interaction parameter of each hydrogel with regard to cross-linking. Our results show that the average mesh size obtained from the rubber elasticity theory can be regarded as a concentration-dependent characteristic length of the hydrogel’s network and couples the non-linear elastic response to the specimens’ inherent visco-elasticity through hysteresis as a quantifier of energy dissipation under large deformation.

Optimizing dielectric constants of epoxy composites infused with Palmyra palm and nano fillers using response surface methodology

The study focuses on Palm fruit Fibers (PF) extracted from the palmyra palm tree (Borassus flabellifer) treated with 5 % alkali solution (NaOH). This treatment eliminates impurities from the fiber surface and enhances bonding with the epoxy matrix. Epoxy composites, reinforced with PF/nanofillers (h-BN, Al2O3 and MWCNT), are developed by using the box Behnken method (BBD) and dielectric constant is investigated under high-frequency and electrical field conditions. Dielectric constants (K) of the nanocomposites are determined using various capacitor terminal setups. The electrical properties of the Epoxy/PF nanocomposite, based on fiber content (Wt. %), fiber mesh size (μm) and nanofillers are evaluated using response surface methodology (RSM). Models, predicting nanocomposite dielectric constants, are established, fitting experimental values closely with R2 nearing 1 and residuals adhering to a normal probability plot. The optimized dielectric constant of 1.05 is achieved at 3 wt% palm fiber content, 150 μm fiber mesh size and 1 wt% nano h-BN.

Numerical Modeling of Tsunamis Generated by Subaerial, Partially Submerged, and Submarine Landslides

Using the existing two-dimensional experimental data and Open-source Fields Operation and Manipulation (OpenFOAM) software, this study performs a comprehensive comparative analysis of three types of landslide-generated tsunamis (subaerial, partially submerged, and submarine). The primary objective was to assess whether numerical simulations can accurately reproduce the experimental results of each type and to compare the predictive equations of the tsunami amplitudes derived from experimental and simulated data. The mesh size and dynamic viscosity parameters were initially optimized for a specific partially submerged landslide tsunami scenario and then applied across a broader range of experimental scenarios. Most of the simulated wave amplitudes remained within the 50% error margin, although significant discrepancies were observed between landslide types. When focusing on the crest amplitude of the first wave, the simulations of subaerial landslides least deviated from the experimental data, with a mean absolute percentage error of approximately 20%, versus approximately 40% for the partially submerged and submarine landslides. The predictive equations derived from the simulations closely matched those from the experimental data, confirming that OpenFOAM can effectively capture complex landslide–tsunami dynamics. Nonetheless, variations in the coefficients related to slope angles highlight the need for further calibration to enhance the simulation fidelity.

Algorithms and data structures for Cs-smooth RMB-splines of degree 2s + 1

The simple mesh refinement algorithm of Groiss et al. (2023) generates T-meshes admitting Reachable Minimally supported (RM) B-splines that possess the property of local linear independence and form a non-negative partition of unity. The construction was first presented for the bilinear case and has later been extended to Cs-smooth splines of degree p=2s+1. The present paper is devoted to algorithms and data structures for RMB-splines. We prove that the memory consumption of the data structures for representing a T-mesh and the associated RMB-splines is linear with respect to the mesh size, and we describe the details of the underlying refinement algorithm. Moreover, we introduce a novel evaluation algorithm for RMB-spline surfaces, which is based solely on repeated convex combinations of the control points, thereby generalizing de Boor's algorithm for tensor-product splines. Numerical experiments are included to demonstrate the advantageous behavior of the proposed data structures and algorithms with respect to their efficiency. We observe that the total computational time (which includes also error estimation and spline coefficient computation) scales roughly linearly with the number of degrees of freedom for the meshes considered.