Maximum Mesh Size Research Articles

Exploring the vulnerability of a commonly exploited fish stock, Galeoides decadactylus in the artisanal mixed capture fisheries of Sierra Leone

Galeoides decadactylus is a commonly exploited fish stock in Sierra Leone, and the study of its vulnerability to capture in the artisanal mixed fisheries of Sierra Leone has not gained the needed attention of researchers, for which the present study has come in handy particularly when such information is critical for sustainable management of the stock. The study utilized length-frequency data obtained from 865 specimens as input datasets of analytical models inscribed for the FAO Fish Stock Assessment Tool (FiSAT II) software. Vulnerability indices for this study were the Length Structured Virtual Population Analysis (LVPA) and the Probability of Capture (PC). Results revealed minimum and maximum total length of 11cm and 36cm respectively for the study species, and LVPA showed highest catch (in numbers) for the length range, 20 cm (n = 94, 0000) - 21 cm (n = 100, 000). Also, the probability of capture evinced greater selection probability (p = 0.9) of the larger sizes (17cm - 22 cm (mean, 19.5 cm TL) at a maximum mesh size of 8cm of bottom drift net utilised by the fishers. The results of LVPA implied that the smaller length groups of the assessed stock (TL are less vulnerable to fishing mortality, but most susceptible to natural mortality, and the probability of capture indicated that the gill nets used by the artisanal fishers for this study were highly selective to allow greater number (n = 4.8 x 106) of the smaller length group escape capture. In conclusion, G. decadactylus was efficiently exploited in the artisanal mixed fisheries. However, stringent measures on capture input and output controls are advised for the assessed stock.

A Hybrid Meshing Framework Adapted to the Topography to Simulate Atmospheric Boundary Layer Flows

A new topography adapted mesh generation framework tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and minimum surface mesh size, and the mesh size at the top of the ABL. The following contributions to the meshing workflow for ABL flow simulation are performed. First, we present a smooth topography modeling to query first and second-order geometry derivatives. Second, we propose a new adaptive meshing procedure to discretize the topography based on two different metrics. Third, we present the ABL mesher, featuring both prisms and tetrahedra. We extrude the triangles of the adapted surface mesh, generating prisms that reproduce the Surface Boundary Layer. Then, the rest of the domain is meshed with an unstructured tetrahedral mesh. In addition, we detail a hybrid quality optimization approach for both the surface and volume meshers, analyzing its impact on the solver for high-complexity terrains. We analyze the convergence of the triangle adaptive approach, obtaining quadratic convergence to the geometry and reducing to one-half the error for the same amount of degrees of freedom than without adaptivity and optimization. We also study the mesh convergence of our Reynolds-averaged Navier–Stokes (RANS) solver, obtaining quadratic mesh convergence to the solution, and using a 30% of the degrees of freedom while reducing a 20% of the error of standard semi-structured approaches. Finally, we present the generated meshes and the simulation results for a complete complex topographic scenario.

Dispersion and Stability Analysis for TLM Unstructured Block Meshing

The insatiable demand to optimize and engineer new functionalities in electromagnetic devices has risen their geometrical complexity to unprecedented levels. This usually results in computationally multiscale problems with some tiny components of great importance to the overall behavior of these devices. Block meshing is a powerful technique for treating such problems. The usage of variable mesh size is adaptable for adequately representing the geometrical details without exhausting the computational resources with a uniform fine grid in the entire computational domain. In addition, block meshing allows the use of cubic cells only for which time step in maximum and velocity error is minimal in each subregion. In this article, we present a mathematical formulation for stability and dispersion analysis when using block meshing in the transmission-line matrix (TLM) method. These relations permit us to compute the maximum mesh size and time step that guarantee a tolerable level of numerical dispersion, hence minimizing the computational expenditures. Moreover, we study the case of adopting the local time step and demonstrate the origins of the instability that may appear in this case. Finally, some numerical experiments are presented to show the advantages of the proposed approach when using TLM block meshing. A similar procedure can be used for FDTD or FIT with block meshing.

Development of Parametric Acoustic Air FEA Mesh for Tire Noise Performance Calculations

<div class="section abstract"><div class="htmlview paragraph">Automobiles are one of the most significant discoveries of humankind and meant to transport goods and passengers from one place to other. The capability of the vehicle was mainly function of good powertrain and reliability. Above factors along with usability made automobiles successful in the earlier generations. Success of modern-day vehicles not just depend upon good power train or fine aesthetics, but on good levels of NVH (Noise Vibration and Harshness). The advent of electric vehicles has led to a quieter powertrain owing to lesser moving parts in the electric powertrain. Hence, the exterior tire noise becomes prominent. Consequently, the accurate measurement of tire noise is imperative to maintaining optimum noise level of the vehicle. The presented work focuses on the simulation of the measurement of external tire noise using Finite Element Analysis (FEA) approach.</div><div class="htmlview paragraph">The current procedure of FEA meshing used in the organization incurs a good amount of cost to company as a licensed software is being used and licenses are very limited. There is no standard method of creating acoustic air mesh. The proposed project aims to solve the above-mentioned limitations. A parametric acoustic air mesh will be developed in an open source tool which will be automated. In addition to this, the developed mesh will be cost effective and efficient with respect to time and performance. The parametric air mesh improves the precision of calculation of pass by noise by using a fine mesh near the tire surface and coarser mesh away from the tire surface. The mesh results are compared against various parameters to know the behavior of different mesh designs possible. Maximum mesh size was decided based on the physics of sound wave & was discussed in detailed.</div></div>

Local Discontinuous Galerkin Method for Time-Dependent Singularly Perturbed Semilinear Reaction-Diffusion Problems

Abstract Local discontinuous Galerkin method is considered for time-dependent singularly perturbed semilinear problems with boundary layer. The method is equipped with a general numerical flux including two kinds of independent parameters. By virtue of the weighted estimates and suitably designed global projections, we establish optimal ( k + 1 ) {(k+1)} -th error estimate in a local region at a distance of 𝒪 ⁢ ( h ⁢ log ⁡ ( 1 h ) ) {\mathcal{O}(h\log(\frac{1}{h}))} from domain boundary. Here k is the degree of piecewise polynomials in the discontinuous finite element space and h is the maximum mesh size. Both semi-discrete LDG method and fully discrete LDG method with a third-order explicit Runge–Kutta time-marching are considered. Numerical experiments support our theoretical results.

Finite Element Modelling of a Reflection Differential Split-D Eddy Current Probe Scanning Surface Notches

Differential eddy current probes are commonly used to detect shallow surface cracks in conductive materials. In recent years, a growing number of research works on their numerical modelling was conducted since the development of analytical or semi-analytical models for such a sensor may be prone to intractable complications. In this paper finite element modelling (FEM) has been employed to simulate the interaction of a reflection differential split-D probe with surface electrical discharge machined (EDM) notches in 3-dimensional (3-D) half-space. In order to attain a better insight into the correct setup of the FEM parameters, a simple multi-turn cylindrical absolute coil has also been modelled. The outcome generated through the simulated scan of this absolute coil over a surface notch in aluminum is validated with existing experimental impedance data taken from the literature. Parameters contributing to reliable FEM simulation results, such as maximum mesh size, mesh distribution, the extent of the surrounding air domain and conductivity of the air are investigated for the 3-D modelling of both absolute and differential probes. This study shows that the simulation results on a commercial reflection differential split-D surface pencil probe closely estimate the experimental measurements of the probe’s impedance variations as it scans three EDM notches having different depths in aluminum. The simulation results, generated by Comsol Multiphysics FEM package (COMSOL I, COMSOL multiphysics reference manual, version 5.3, COMSOL AB, 2018, www.comsol.com), for the cases of absolute and differential probes are checked for their extent of validity.

On the Babuška–Osborn approach to finite element analysis: $$L^2$$ L 2 estimates for unstructured meshes

This paper is devoted to a long standing issue in the finite element analysis for elliptic problems. The standard approach to $$ L^2$$ bounds uses the $$H^1$$ bound in combination to a duality argument, known as Nitsche’s trick, to recover the optimal a priori order of the method. Although this approach makes perfect sense for quasi-uniform meshes, it does not provide the expected information for unstructured meshes since the final estimate involves the maximum mesh size. Babuska and Osborn (Numer Math 34:41–62, 1980), addressed this issue for a one dimensional problem by introducing a technique based on mesh-dependent norms. The key idea was to see the bilinear form posed on two different spaces; equipped with the mesh dependent analogs of $$L^2$$ and $$H^2$$ and to show that the finite element space is inf-sup stable with respect to these norms. Although this approach is readily extendable to multidimensional setting, the proof of the inf-sup stability with respect to mesh dependent norms is known only in very limited cases. We establish the validity of the inf-sup condition for standard conforming finite element spaces of any polynomial degree under certain restrictions on the mesh variation which however permit unstructured non quasiuniform meshes. As a consequence we derive $$L^2$$ estimates for the finite element approximation via quasioptimal bounds and examine related stability properties of the elliptic projection.

Stability and Dispersion Analysis of a TLM Unified Approach for Dispersive Anisotropic Media

With the advancement of technology, modern equipment involves new functionalities that require complex media (e.g., anisotropic dispersive media such as ferrite, lossy dielectrics, or graphene) for a variety of applications. This imposes the necessity to extend simulation techniques capable of solving Maxwell’s equations in such media. However, as far as discrete time-domain models are concerned, their performance in terms of dispersion and stability criterion has not been thoroughly investigated in the presence of complex media. More particularly, a question arises about which maximum mesh size can be used and the resulting time step to ensure stability. Starting from a transmission-line matrix method algorithm for the general linear media, procedures for dispersion and stability analysis are given and special cases are presented. It is found that the proposed approach allows, in certain cases, some significant reduction in the computer cost compared to the approximate rules generally used. The same procedures can be easily extended to other time-domain schemes such as FDTD.

SANS investigation of water adsorption in tunable cyclodextrin-based polymeric hydrogels.

The focus of this work is on addressing how the adsorption properties of cyclodextrin (CD) based polymeric hydrogels (cyclodextrin nanosponges, CDNS) can be regulated by a precise control of a crucial parameter such as the characteristic pore size of the polymer network. With this aim, Small Angle Neutron Scattering (SANS) experiments are performed on different CDNS polymer formulations, differing by (i) the chemical structure of the cross-linking agent used for the polymerization of CD, which affects the flexibility of the strands between two crosslinking junctions, (ii) the relative molar ratio of cross-linker to monomer, affecting the cross-linking density, and (iii) the dimension of the CD macrocycle, regulating the steric hindrance and number of available reactive sites on the monomer. The analysis of the experimental data in terms of a two-correlation-length model allows one to extract a correlation length ζ that is interpreted as an experimental assessment of the average mesh-size of the cross-linked polymer, confirming the effective nano-size of the cavities formed in the network of CDNS. The hydration-dependence of ζ is modelled by an empirical functional form, that provides as key parameters the swelling rate of the polymeric network and the upper limit for the mesh size of the material. These parameters are useful for the characterization of the dynamic response of the hydrogel to swelling and the maximum mesh size compatible with the chemical structure of the polymer.

Error estimates of Runge–Kutta discontinuous galerkin methods for the Vlasov–Maxwell system

In this paper, error analysis is established for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve the Vlasov-Maxwell system. This nonlinear hyperbolic system describes the time evolution of collisionless plasma particles of a single species under the self-consistent electromagnetic field, and it models many phenomena in both laboratory and astrophysical plasmas. The methods involve a third order TVD Runge-Kutta discretization in time and upwind discontinuous Galerkin discretizations of arbitrary order in phase domain. With the assumption that the exact solution has sufficient regularity, the $L^2$ errors of the particle number density function as well as electric and magnetic fields at any given time $T$ are bounded by $C h^{k+\frac{1}{2}}+C\tau^3$ under a CFL condition $\tau /h \leq \gamma$. Here $k$ is the polynomial degree used in phase space discretization, satisfying $k \geq \left \lceil \frac{d_x + 1}{2} \right \rceil$ (the smallest integer greater than or equal to $\frac{d_x+1}{2}$, with $d_x$ being the dimension of spatial domain), $\tau$ is the time step, and $h$ is the maximum mesh size in phase space. Both $C$ and $\gamma$ are positive constants independent of $h$ and $\tau$, and they may depend on the polynomial degree $k$, time $T$, the size of the phase domain, certain mesh parameters, and some Sobolev norms of the exact solution. The analysis can be extended to RKDG methods with other numerical fluxes and to RKDG methods solving relativistic Vlasov-Maxwell equations.

Sea duck predation in mussel farms: the best nets for excluding common eiders safely and efficiently

Shellfish aquaculture is a growing food-producing sector. The blue mussel Mytilus edulis is the primary farmed shellfish and is also a main prey for various species of sea ducks. With their large density of high-quality mussels, mussel farms attract these predators, and consequent depredation by ducks represents a substantial economic loss among mussel growers worldwide. Total exclusion with nets seems to be the only method that provides complete and long-term control of bird predation. The best nets for duck exclusion must be cost effective, efficient, easy to handle, and safe for bird populations. In order to identify the best net type, we tested 8 different nets under controlled conditions using captive common eiders Somateria mollissima, the largest sea duck species in the Northern Hemisphere. We identified a net with a maximum mesh size of 6 inches (~15 cm) and large twine size to be best in excluding common eiders considering the above-mentioned criteria. Nets with thin twine and large mesh size were more likely to cause bird entanglement. In addition to using the best nets for sea duck exclusion, it is necessary to identify a target zone where such nets are the most effective. Good knowledge of the predation problem as well as collaboration among mussel growers, bird specialists, and government authorities are essential to reduce the costs and effort of installing and maintaining exclusion nets.

A Numerical Proof-Test of Finite Element Method to Simulate Wave Propagation in Ground Soil

A numerical case study is presented in this paper to demonstrate the feasibility of a finite element method with artificial boundary condition to simulate the wave in 3D ground soil. An unit centralized harmonic excitation at surface is adopted with four frequencies. The calculated vibration amplitudes are compared with the corresponding results by dynamic Green Function in frequency-wave number domain. The result shows a clear calculation error phenomena that the smaller mesh adopted, the smaller error is for a given frequency, and the lower frequency excited so the smaller error is for a given mesh size. A preliminary suggestion is presented as that the maximum mesh size of a 3D discrete grid must be no larger than 1/25 of the minimum wave length.

Recommendation for maximum allowable mesh size for plant combustion analyses with CFD codes

The selection of the maximum allowable mesh size for a fluid dynamic calculation with Computational Fluid Dynamic (CFD) codes is essential for the reliability of the results assuming suitable physical and numerical models are used. Calculations with CFD codes are necessary for the assessment of the consequences of pressure loads on containment structures due to possible hydrogen combustion in nuclear power plants in a severe accident and on piping system due to pressure wave propagation in case of a pipe break accident or fast closing of a valve in a pipe with forced flow.CFD simulations of the transport and distribution of the released hydrogen/steam as well as the possible combustion during the transient in the containment require an appropriate mesh size to resolve the relevant phenomena and loads.The determination of the mesh size has to take into account:•adequate delineation of the containment geometry for accurate hydrogen distribution calculations,•sufficient conservative resolution of the combustion phenomena for the determination of pressure wave propagation and pressure loads,•no loss of pressure wave loads with relevant frequencies for the structural response analysis of the containment during the combustion calculation.In this paper, it is found that the accuracy of the calculated pressure wave associated with its frequency depends on the mesh size and a simple and easily useable analytical formula for the determination of the maximum allowable mesh size is derived. This formula can be used as a criterion to find out easily and simply the appropriate mesh size for accurate determination of the pressure wave load function with sufficient resolved frequencies relevant for structural response analyses. This criterion in form of a relation is deduced in this theoretical treatment from the connection between the structural characteristic associated with the relevant frequency and fluid property associated with mixture quality and gas temperature as well as numerical determination of the pressure wave load function associated with the accuracy of the approximation.This criterion gives the CFD code users the ability to determine the upper limit of the mesh size during the preparing of the geometry simulation specially for performing a combustion calculation.Applying the criterion presupposes that the used CFD code can calculate correctly the turbulent combustion, flame and pressure wave propagation for the predicted maximum allowable mesh size.The mesh size can be calculated from the analytical formula using:•the mixture quality and temperature in the cloud surrounded by structures (containment),•the highest relevant frequency for the structural analysis of the containment and•the number of points for the accurate approximation of the pressure wave function.The methodology can be applied also for the assessment of the frequency content of the determined pressure wave load function for the response analysis of a piping system like main coolant or steam lines in case of a break accident or other accidents with occurrence of pressure waves.

Modeling of wall pressure fluctuations for finite element structural analysis

This paper investigates a modeling technique of wall pressure fluctuations (WPF) due to turbulent boundary layer flows on a surface for finite element structural analysis. This study is motivated by critical issues of structural vibrations due to turbulent WPF over the surface of a body. The WPFs are characterized with random behavior in time and space. The temporal and spatial random behavior of the WPFs is mathematically expressed in the form of the auto- and cross-power spectral density functions (PSDF) in the frequency domain (e.g., Corcos Model). For finite element modeling of the random distributed fluctuations, the cross-PSDF is properly modeled over the finite element structural mesh. The quality of modeling of the cross-PSDF is directly affected by the structural mesh size. We first examine the maximum mesh size required for reliable finite element analysis. The reliability of the FEA results is confirmed by the theoretical results. It is found that the maximum mesh size should be determined under consideration of the spatial distribution of the cross-PSDF in addition to the representation of dynamic behavior of the structure in the frequency range of interest. It is also recognized that the requirement of the maximum mesh size is unrealistic in many practical cases. We then investigate practical modeling schemes under a realistic mesh size condition. We found that the WPF can be modeled without the exact consideration of cross-correlation if the power due to the wall pressure fluctuation can be properly compensated. This is owing to the feature of decreasing the cross-correlation of WPFs at high frequencies and the fact that the WPF does weakly couple into the structural modes at high wavenumbers such that 2 π f / U c < k max . The wall pressure fluctuations can therefore be modeled as uncorrelated loadings with power compensations.

A framework for cohesive element enrichment

It was shown in a previous work by the same authors that the stringent mesh size requirement on cohesive, interface elements, can be alleviated through enrichment of the finite element basis functions. In this paper, some limitations of the enriched formulation are discussed and a new maximum mesh size requirement is established. The enriched formulation is also applied here to the simulation of mixed-mode delamination for the first time.

A critical assessment of standard processing methods for the preparation of palynological samples

Standard processing techniques for the isolation of organic walled dinoflagellate cysts from geological samples are examined, with particular attention to the size and type of sieve mesh used. Variations within the ‘standard’ processing techniques used by different laboratories are identified, and an assessment of the retention capacities of meshes of different sizes and different materials is carried out. Some dinoflagellate cysts and large numbers of Lycopodium spores, used for the calculations of absolute abundance data, were found to pass through 20 μm meshes. This is due to a combination of factors including: the diagonal aperture diameter of a 20 μm mesh measuring over 28 μm; the three-dimensional properties of different mesh weaves (nylon and polyester); and the non-spherical shape of the particles. Experiments demonstrate that the maximum mesh size that should be used in palynological processing is 15 μm. Nylon mesh is more practical to use than polyester as processing time is reduced, but nylon is degraded by contact with acid solutions. Meshes with apertures < 15 μm may be used, though this may be impractical for large samples containing significant quantities of fine siliciclastic or organic material.

A mathematical theory for numerical treatment of nonlinear two-point boundary value problems

This paper gives a unified mathematical theory for numerical treatment of two-point boundary value problems of the form −(p(x)u′)′ +f(x,u,u′) = 0,a ≤x ≤b, α0 u(a) − α1 u′(a) = α, β0 u(b) + β1 u′(b) = β, α0, α1, β0, β1 ≥ 0, α0 + α1 > 0, β0 + β1 > 0, α0 + β0 > 0. Firstly, a unique existence of solution is shown with the use of the Schauder fixed point theorem, which improves Keller’s result [6]. Next, a new discrete boundary value problem with arbitrary nodes is proposed. The unique existence of solution for the problem is also proved by using the Brouwer theorem, which extends some results in Keller [6] and Ortega-Rheinboldt [10]. Furthermore, it is shown that, under some assumptions onp and ƒ, the solution for the discrete problem has the second order accuracyO(h 2), whereh denotes the maximum mesh size. Finally, observations are given.

A simple method to determine the time‐step size to achieve a desired dispersion accuracy in ADI‐FDTD

AbstractThis paper presents a simple approach to determine the time‐step size required in the alternate‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD) method in order to obtain a desired numerical dispersion accuracy. The Courant number, the desired dispersion accuracy, and the maximum mesh size Δmax = max(Δx, Δy, Δz) are governed by the numerical dispersion relation, which can be solved by a simple root‐finding algorithm to evaluate the Courant number and hence the time‐step size for a given mesh size and accuracy. The time‐step size is independent of the aspect ratio. To determine if ADI‐FDTD is more efficient than the Yee's FDTD, this paper provides a simple relation to evaluate the relative Courant–Friedrich–Levy number (CFLN) from the Courant number and the aspect ratio. The ADI‐FDTD method is more efficient than Yee's FDTD when the aspect ratio is high or the mesh density is very large. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 487–490, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20012

Transport Properties of Comb-Type Grafted and Normal-Type N-Isopropylacrylamide Hydrogel

Transport properties of the comb-type grafted and normal-type N-isopropylacrylamide (NIPA) gel are investigated by gel filtration chromatography and a pulsed field gradient NMR technique with known standard probe molecules in terms of molecular weight cutoff and diffusion coefficient in and through the gels, respectively. The incorporation of NIPA grafted chains into NIPA gel makes the effective mesh size smaller and induces the additional friction between the probe molecule and gel network. One may control the maximum mesh size of the NIPA gel and thus the effective diffusivity of a probe molecule within a gel by incorporating grafted chains and by adjusting the temperature.

Size selectivity of sole gill nets fished in the North Sea

The size selectivity of sole nets was measured indirectly on a Danish commercial gill net vessel in the North Sea by using nets made in seven different mesh sizes fished simultaneously. Maximum likelihood procedure was used to fit different forms for the selection curve to the catch data for sole, plaice and cod for each setting of the gear. It was found that a bi-normal form for the selection curve gave the best fits. Mean selection curves were then estimated by combining sets using a model of between-set variation. The ratio between length of maximum retention and mesh size was estimated to be 3.28 for sole, 2.60 for plaice and 4.56 for cod. Selection curves were also fitted to the catch data pooled over all sets. The model deviance for the sole and plaice data indicated lack of fit when pooling the catch data.