Mesh Size Research Articles

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.

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.

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.

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.

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.

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.

Contrasting responses to aridity by different-sized decomposers cause similar decomposition rates across a precipitation gradient.

Litter decomposition is expected to be positively associated with precipitation despite evidence that decomposers of varying sizes have different moisture dependencies. We hypothesized that higher tolerance of macro-decomposers to aridity may counterbalance the effect of smaller decomposers, leading to similar decomposition rates across climatic gradients. We tested this hypothesis by placing plant litter baskets of different mesh sizes in seven sites along a sharp precipitation gradient, and by characterizing the macro-decomposer assemblages using pitfall trapping. We found that decomposers responded differently to precipitation levels based on their size. Microbial decomposition increased with precipitation in the winter while macro-decomposition peaked in arid sites during the summer. This led to similar overall decomposition rates across the gradient except in hyper-arid sites. Macro-decomposer richness, abundance, and biomass peaked in arid environments. Our findings highlight the importance of macro-decomposition in arid-lands, possibly resolving the dryland decomposition conundrum, and emphasizing the need to contemplate decomposer size when investigating zoogeochemical processes.

Contrasting responses to aridity by different-sized decomposers cause similar decomposition rates across a precipitation gradient

Litter decomposition is expected to be positively associated with precipitation despite evidence that decomposers of varying sizes have different moisture dependencies. We hypothesized that higher tolerance of macro-decomposers to aridity may counterbalance the effect of smaller decomposers, leading to similar decomposition rates across climatic gradients. We tested this hypothesis by placing plant litter baskets of different mesh sizes in seven sites along a sharp precipitation gradient, and by characterizing the macro-decomposer assemblages using pitfall trapping. We found that decomposers responded differently to precipitation levels based on their size. Microbial decomposition increased with precipitation in the winter while macro-decomposition peaked in arid sites during the summer. This led to similar overall decomposition rates across the gradient except in hyper-arid sites. Macro-decomposer richness, abundance, and biomass peaked in arid environments. Our findings highlight the importance of macro-decomposition in arid-lands, possibly resolving the dryland decomposition conundrum, and emphasizing the need to contemplate decomposer size when investigating zoogeochemical processes.

Chironomid Pupal Exuviae Technique in Ecological Research of Man-Made Water Bodies

Reservoirs serve functional purposes such as irrigation and power generation. However, concerns are raised due to the alterations of the connected riverine ecosystems. Chironomidae (Diptera), a diverse aquatic macroinvertebrate group, are vital to the functioning of ecosystems and serve as water quality indicators. Their holometabolous development includes the pupal stage after four larval stages. The chironomid pupal skin (exuvia) is used in environmental assessments, where the Chironomid Pupal Exuvial Technique (CPET) is a recognized standard. The CPET method is adaptable to different freshwater environments and here was applied in the study of 28 man-made lakes in the Pannonian Lowlands and Dinaric Western Balkan Ecoregion in Croatia to obtain information on chironomid diversity and analyze the potential influence of environmental factors on the chironomid community. The lake surface was skimmed with an exuvial hand net (mesh size of 300 µm) along the lake edge with a transect length of 10 m in the area of accumulated debris of organic and inorganic matter. Individual exuviae were mounted in a Berlese mounting medium and identified by morphological characteristics to the lowest taxonomic level. During the study, 5698 chironomid pupal skins were collected, and 141 taxa (including 97 species) belonging to five subfamilies were identified. The tribe Tanytarsini comprised 40% of the identified taxa, with Paratanytarsus spp. being the most abundant. In the Dinaric ecoregion, Paratanytarsus bituberculatus dominated, while Microchironomus tener and the genus Cricotopus were the dominant taxa in the Pannonian ecoregion. Community structure in the Pannonian ecoregion was influenced by total organic carbon (TOC) and orthophosphates (PO43−), indicating higher anthropogenic pressure compared to the Dinaric ecoregion, where water conductivity influenced Chironomidae assemblages. The research has provided valuable and useful information on the chironomid diversity in man-made and highly altered water bodies, as some of the most vulnerable aquatic habitats to anthropogenic influence. The CPET method could be a useful tool for the ecological studies and bioassessment of water quality in Croatia.

Testing best practices in small scale fisheries management: Evidence from a collaborative intervention in two marine protected areas of the central Mediterranean Sea

Adopting best practices (BPs) in small scale fisheries (SSF) is generally acknowledged to enhance ecological and social conditions, improving SSF management overall. Yet studies that empirically assess the effects of BPs on social-ecological outcomes (e.g., fishers' catches, revenues, and level of support towards management measures) remain limited. This study aimed to assess the effects of adopting BPs on catch per unit of effort (CPUE), revenue per unit of effort (RPUE) and small-scale fishers' perceptions in two Marine Protected Areas (MPAs) in Campania, Italy (Santa Maria di Castellabate (CAS-MPA) and Regno di Nettuno (NET-MPA)). Two BPs were implemented and tested in the two MPAs: i) five selective gears with three different mesh/hook sizes and ii) a participatory approach to increase dialogue between fishers and managers. The results from 36 surveys with small scale fishers and 158 SSF operations monitored using photo-sampling and image analysis techniques (between 2020 and 2022) are presented. Analyses of landings showed that significant differences in CPUE and RPUE between mesh/hook sizes were found in a limited number of cases (i.e., combination of fishing gears used in the 2 MPAs). Significant but divergent effects were found on CPUE in the two MPAs for gillnet used to target amberjack (GNA) only. RPUE was significantly higher in the NET-MPA when adopting the largest mesh size for GNA and the largest hook size for bottom longlines (BLL). When analyzing perceptions, fishers generally reported that the BPs adopted had a positive impact on their revenues, improved their relationship with MPA managers and increased their support for the MPA. In addition, eight stakeholder focus groups were held which helped investigators better understand the context, feedback the data gathered from the research and open up dialogue between the relevant stakeholders. The study concluded that increasing mesh/hook sizes, within the range tested here, does not negatively impact fishers’ revenues, while likely improving the status of target populations. Moreover, increasing dialogue between fishers and decision-makers can generate more positive perceptions towards the MPA and improve mutual understanding, helping to reconcile biodiversity conservation with human wellbeing for SSF.

Mesh Refinement for Dynamics Airflow in Health Care

This studyexplores using computational fluid dynamics(CFD) tooptimize ventilation in healthcare, with a focus on mesh refinement for accurate airflow analysis. The goal is to reduce airborne contaminant spread, which is crucial during COVID-19. Ventilation in healthcare ensures air quality and minimizes pathogen transmission. The research analyzer analyzes mesh element size's impact on airflow accuracy in simulated hospital wards with two coughing patients. The optimal mesh size is determined for reliable predictions. Mesh refinement enhances accuracy in critical zones. The k-epsilon turbulence model is chosen for low error. Experimental validation shows temperature discrepancies, likely due to simulated manikins lacking clothing insulation. Air velocity measurements show minor variations within an acceptable range. Further research on various ventilation configurations and airflow rates in real hospital conditions is crucial. Addressing these limitations optimizer optimizeshealthcare ventilation, enhancing safety and infection control.

Study on the adsorption process and kinetic, thermodynamic of bio-based waste cattle hair powder toward acidic complex dye.

In this paper, cattle hair waste (CHW) was collected and physically milled into different meshes of ultrafine cattle hair powder (UCHP). The reuse of CHW reaches the purpose of treating pollution with waste by using bio-base adsorbent. It was characterized by using scanning electron microscope-energy dispersive spectrometer (SEM-EDS), Fourier transform infrared (FT-IR) spectroscopy, X-ray photoelectron spectroscopy (XPS), thermogravimetric analysis (TGA), differential scanning calorimeter (DSC), and X-ray diffraction (XRD). The adsorption studies were carried out under different conditions of temperature, time, pH, concentration of dye solution, mesh size, and dosage of cattle hair powder, respectively. The pseudo-first and pseudo-secondary kinetics and intra-particle diffusion models were employed to analyze the adsorption kinetic. The Langmuir, Freundlich, and Temkin adsorption isotherm was used to analyze the adsorption isotherm. The results showed that the adsorption capacity of UCHP for acidic metal complex (Trupoxane Brown R6) dyes increased with the decreasing pH solution. The adsorption capacity of 200 mesh UCHP was 379.5mg.g-1 when the adsorption conditions were as follows: 100mL dye solution with the initial concentration of 1000mg·L-1, the dosage of adsorbent was 0.1g, the pH was 3 for 12h at 40°C. The kinetic model fitting results showed that the adsorption of dyes by UCHP conformed to the pseudo-second-order kinetic model. Adsorption thermodynamics study showed that the Langmuir model has the highest fitting result. The amino group contained on the surface of cattle hair powder and the amide bond contained in the molecular chain of peptide chain have better electrostatic adsorption binding force for acid metal complex dyes, and the binding between them is mainly electrostatic attraction. The experimental results show that the ultrafine powder has better adsorption property, which provides a high-value conversion way for recycling waste cattle hair.

Activity concentrations of 60 Co, 137Cs and 241Am in sieved soil and soil inclusions from the «Taiga» peaceful nuclear explosions site

The article presents results of comparative study of 137Cs, 60Co, and 241Am activity concentrations in components of the soil samples collected in 2009 on the territory adjacent to the «Taiga» peaceful nuclear explosions site (the Perm region, Russia). The objective of the study was to identify differences between: 1) non fractionated native soil, 2) the soil passed through a sieve with a mesh size of 1.2 mm, and 3) the screened out coarse components. Measurements of the radionuclides activities in counting samples were performed using a semiconductor gamma spectrometer. Statistically significantly lower activity concentrations of 137Cs (factor of 1.2), 60Co (factor of 2.2) and 241Am (factor of 2.6) were found in the finely dispersed sieved fraction of soil compared to the native soil. On the opposite, in the solid radioactive inclusions selected from the screened out coarse fraction, the activity concentrations of 137Cs, 60Co and 241Am were significantly higher compared to those in the native soil. Especially large differences (up to a factor of 10 and more) between the native soil and radioactive inclusions were observed for the refractory and low-volatile 60Co and 241Am. Presumably, these radionuclides were concentrated predominantly in the glassy substance of the radioactive inclusions. For 137Cs, the unevenness in the contamination of different soil components was less pronounced. The results obtained will be used to standardize methods for assessing radioactive contamination of the territory at the sites of peaceful nuclear explosions

Element behavior during autoclave oxidation of polymetallic sulfide flotation concentrate containing tungsten and molybdenum

In this paper, we investigate the behavior of associated elements (tungsten, molybdenum, and bismuth) contained in a sulfide gold-bearing concentrate during its autoclave oxidation. The process is studied using a sulfide flotation concentrate, crushed to a particle sieve mesh size of minus 0.045 mm and containing 22.1 g/t of gold, 133.2 g/t of silver, 2.7% of tungsten, 13% of molybdenum, and 0.7% of bismuth. The process was carried out in a 2 dm3 autoclave at a temperature of 220ºC and an oxygen partial pressure of 0.7 MPa. The concentrations of sulfuric acid and iron ions in the solution were determined by titrimetric analysis. Inductively coupled plasma atomic emission spectroscopy was used to determine the concentrations of bismuth, tungsten, molybdenum, copper, silver, and arsenic in the solution, as well as the content of bismuth, tungsten, molybdenum, copper, arsenic, lead, and iron and sulfur forms in the cake. The cake was also examined using diffraction analysis. Experiments on cyanidation of oxidized cake were carried out in the pH range of 10.0–10.5 and a NaCN concentration of 1 g/dm3 with a PuroliteS992 ion exchange resin for 24 h. Autoclave oxidation experiments showed the sulfide oxidation degree to be higher than 99%. Extraction of molybdenum into solution in the form of [MoO2(SO4)n]-(2n-2) and MoO 2+ amounted to 95%. The decrease in the solid mass led to an increase in the concentration of bismuth and tungsten in the cake, with their contents reaching 1.66% and 12.7%, respectively. The main phases in the cake were established to be scheelite, anhydrite, plumboyarosite, and bedantite. The extraction of precious metals at the subsequent cyanidation stage amounted to 97.5% of gold and 91.6% of silver. Therefore, autoclave cyanide processing of sulfide gold-containing concentrates leads to a molybdenum extraction in the autoclave oxidation solution at the level of 95%. During cyanidation, more than 90% of gold and silver are extracted. Due to the significant amount of tungsten (17%), bismuth (0.9%), lead (5.3%), and molybdenum (3.3%), the obtained cake cannot be considered a waste product.

Per-recruit analysis and proposed sustainable harvest strategy for rednose labeo Labeo rosae and Mosambique tilapia Oreochromis mossambicus in Flag Boshielo Dam, Olifants River, South Africa

Inland fisheries development in South Africa has been proposed to improve rural livelihoods and food security. However, inland fisheries are susceptible to collapse through overfishing. Therefore, establishing biological reference points for these fisheries is essential for long-term sustainability. Here, spawner-biomass-per-recruit (SBR) analysis was used to set biological reference points for a gillnet fishery targeting the rednose labeo Labeo rosae and Mozambique tilapia Oreochromis mossambicus at Flag Boshielo Dam on the Oliphants River in Limpopo Province, South Africa. Both species are currently exploited at the impoundment by subsistence fishers that keep their entire catch. The current yields are estimated at 59 and 172 g yr−1 for L. rosae and O. mossambicus, respectively. The per-recruit analysis showed that age-at-first-capture for both species should be 4 years, at minimum lengths of 280 mm TL and 250 mm TL for L. rosae and O. mossambicus, respectively, with fishers using a minimum mesh size of 100 mm to reduce the risk of stock collapse. To maintain a SBR value greater than 25% of a pristine population, the L. rosae yield could be increased to 98 g yr−1, while the O. mossambicus yield could be increased to 176 g yr−1, following implementation of the recommended mesh size and size limits. A per-recruit analysis for O. mossambicus that includes recruitment variability and error to accurately calculate the biological reference points is recommended.

Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation

Abstract In [L. Bourhrara, A new numerical method for solving the Boltzmann transport equation using the PN method and the discontinuous finite elements on unstructured and curved meshes, J. Comput. Phys. 397 2019, Article ID 108801], a numerical scheme based on a combined spherical harmonics and discontinuous Galerkin finite element method for the resolution of the Boltzmann transport equation is proposed. One of its features is that a streamline weight is added to the test function to obtain the variational formulation. In the present paper, restricting our attention to the advective part of the Boltzmann equation, we prove the convergence and provide error estimates of this numerical scheme. To this end, the original variational formulation is restated in a broken functional space. The use of broken functional spaces enables to build a conforming approximation, that is the finite element space is a subspace of the broken functional space. The setting of a conforming approximation simplifies the numerical analysis, in particular the error estimates, for which a Céa’s type lemma and standard interpolation estimates are sufficient for our analysis. For our numerical scheme, based on ℙ k {\mathbb{P}^{k}} discontinuous Galerkin finite elements (in space) on a mesh of size h and a spherical harmonics approximation of order N (in the angular variable), the convergence rate is of order 𝒪 ⁢ ( N - t + h k ) {\mathcal{O}(N^{-t}+h^{k})} for a smooth solution which admits partial derivatives of order k + 1 {k+1} and t with respect to the spatial and angular variables, respectively. For k = 0 {k=0} (piecewise constant finite elements) we also obtain a convergence result of order 𝒪 ⁢ ( N - t + h 1 2 ) {\mathcal{O}(N^{-t}+h^{\frac{1}{2}})} . Numerical experiments in one, two and three dimensions are provided, showing a better convergence behavior for the L 2 {L^{2}} -norm, typically of one more order, 𝒪 ⁢ ( N - t + h k + 1 ) {\mathcal{O}(N^{-t}+h^{k+1})} .

A Mesh Convergence Study for 2D Axisymmetric Pipe Wall Thickness

A meshing size study is essential for any simulation, as it affects the accuracy of the results by approximating the real-world geometry. This paper presents a detailed mesh convergence study for a 2D axisymmetric pipe model. The model incorporates a one-quarter cross-section due to the axisymmetric nature of the pipe. Four pipe wall thicknesses were investigated: 3.40 mm, 7.11 mm, 10.97 mm, and 18.26 mm. The results revealed a significant advantage for simulations involving thin pipes. They achieved convergence, a state with stable solution values, by utilizing a less dense mesh, leading to reduced computational time. This trend was exemplified by the fact that a thinner pipe with thickness, t = 3.40 mm has converged with only 8 mesh elements, whereas a significantly thicker pipe, t = 18.26 mm necessitated 14 elements for convergence. This suggests that more complex geometries, with intricate details, may require a larger and denser mesh for convergence, leading to increased computational time. In conclusion, the mesh convergence study confirms that the finite element analysis (FEA) model has achieved a converged solution.

Controlled stiffness and diffusivity of poly(ethylene glycol) hydrogel formed with cellulose-nanofiber framework

Hydrogels composed of polymer networks are widely used in industry and scientific research for high water retention and unique mechanical properties. Nevertheless, in ordinary hydrogel formation, the trade-off relationship between stiffness and mesh size remains a crucial consideration for practical applications. This study describes a facile approach to controlling hydrogel stiffness and mesh size by hybridizing poly(ethylene glycol) diacrylate (PEGDA) and methacrylated TEMPO-oxidized cellulose nanofibers (T-CNFMA). After disintegrating T-CNF by ultrasonication, T-CNFMA was synthesized resulting in a degree of substitution of 2.04 mmol/g. Incorporation of T-CNFMA in the PEGDA network allowed for independent control of hydrogel stiffness and mesh size by reinforcing the whole hydrogel network as a framework. Consequently, the swelling ratio and shear modulus could be manipulated by controlling the PEGDA/T-CNFMA ratio. Structural analyses revealed that an increase in the T-CNFMA content in the presence of a low amount of PEGDA resulted in a large mesh size with a constant stiffness. The diffusivity test was also consistent with the properties of the hydrogels. This result indicates that the incorporation of T-CNF in hydrogel network is useful to control the physical property of the hydrogel, especially for varying mesh size, regardless of stiffness alteration.