Meshes Of Different Sizes Research Articles

A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions

AbstractA numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined function spaces a well posed 3D-1D problem is obtained from the original fully 3D problem and the solution is then found by a PDE-constrained optimization reformulation. This is a domain decomposition strategy in which unknown interface variables are introduced and a suitably defined cost functional, expressing the error in fulfilling interface conditions, is minimized constrained by the constitutive equations on the subdomains. The resulting discrete problem is robust with respect to geometrical complexity thanks to the use of independent discretizations on the various subdomains. Meshes of different sizes can be used without affecting the conditioning of the discrete linear system, and this is a peculiar aspect of the considered formulation. An efficient solving strategy is further proposed, based on the use of a gradient based solver and yielding a method ready for parallel implementation. A numerical experiment on a problem with known analytical solution shows the accuracy of the method, and two examples on more complex configurations are proposed to address the applicability of the approach to practical problems.

Mesh convergence error estimations for compressible inviscid fluid flow over airfoil cascades using multiblock structured mesh

This work deals with estimations of errors, which are a consequence of a finite spatial discretisation that appears while solving differential equation numerically. More precisely, it deals with the estimation of errors that occur while computing compressible inviscid fluid flow over 2D airfoil cascades. This flow is described by the 2D Euler equations that are solved by the finite volume method in their conservative form. Numerical computations are performed on structured meshes consisting of four blocks, so the number of cells in the mesh can be easily adjusted. In this work, two estimation methods are used. Firstly, the grid convergence index is used to estimate the amount of cells needed to obtain certain accuracy of the solution. Secondly, the Richardson extrapolation is used to approximate the exact solution from a series of solutions obtained with meshes of different sizes. This analysis is performed on a well-known compressor cascade, which is composed of NACA 65 series airfoils. The obtained results should lead to a reasonable choice of the number of elements in a computational mesh based on the required accuracy of the solution and therefore also to computational time reduction while performing airfoil cascade computations. The results indicate that even for very precision demanding applications, 100 000 is a sufficient number of cells in a mesh.

Analysis of adaptive mesh refinement in a turbulent buoyant helium plume

AbstractThe study evaluates OpenFOAM's adaptive mesh refinement (AMR) capabilities and accuracy when applied to numerical simulations of turbulent buoyant flows. To this purpose, large eddy simulations of Sandia's turbulent helium plume test case are considered, a scenario with similar characteristics (in terms of air entrainment and vortex shedding) to those encountered in large‐scale fires. Comparison is made of the relative accuracy (in terms of both first and second order statistics), the predicted puffing frequencies and the computing times of numerical simulations using AMR and static meshes. Additionally, a sensitivity study on different AMR parameters is conducted and an evaluation of the performance of the dynamic Smagorinsky model when combined with AMR is made. Overall, the predictions of AMR are very satisfactory, in terms of both accuracy and computing times, compared to the use of static meshes of different sizes. Nevertheless, it is observed that a careful choice of a static mesh can result in equally accurate predictions with comparable, or even smaller, computing times than AMR for the case at hand. Additionally, the use of AMR slightly modified the entrainment characteristics in the near‐field region of the plume and (significantly) altered some of the, dynamically determined, turbulence model parameters.

EFFECT OF USING GEOPOLYMER MORTAR IN FERROCEMENT BY VARYING THE COMBINATION, NUMBER AND SIZES OF MESHES

Globally, Cement production contributes about 1.6 billion tons of CO2 or about 7% of global loading of CO2 into the atmosphere. The manufacture of Cement Releases Carbon dioxide that is significant contributor of Green house gas emissions to the atmosphere. So there was a need to develope and use eco-friendly material having similar properties as like of cement mortar. Geopolymer is produced without the presence of cement as a binder; instead, the base material such as fly ash, that is rich in Silicon (Si) and Aluminium (Al), is activated by alkaline solution to produce the binder. Hence Geopolymer mortar can be used instead of cement mortar which will have no adverse effect on our environment. Ferrocement is a composite material formed by closely spaced wire mesh which uses wire meshes as reinforcement and filled with rich cement mortar. Experimental investigation was carried out to study the effect of Geopolymer mortar in Ferrocement for variation in mesh size and number of layers. For this, tensile testing was done on Geo-ferrocement specimens of size 750 x 60 x 30 mm reinforced with single, double, triple layer using variation in meshes of different sizes. Similarly, compression testing of cubical specimens of side 70 mm reinforced with single, double, triple layer of meshes sizes was done. Results indicated an significant increase in tensile strength and compressive strength of specimens with increase in number of layer of meshes. Test results also provided the most suitable combination and size of mesh to be used for obtaining the maximum strength of different sizes was done.

Design of optimized architected structures with exact size and connectivity via an enhanced multidomain topology optimization strategy

With the rapid developments of modern fabrication techniques, architected structures are increasingly used in many application areas, e.g., lightweight structures, heat exchangers, energy absorption components, aircraft engines, etc. To systematically design optimized architected structures with favorable manufacturability in terms of exact sizes and good connectivity, in the present work, an enhanced multidomain topology optimization method is developed. The design domain is divided into several subdomains and boundary layers between them first. Periodic base cells with exact sizes are distributed in each subdomain, and analyzed and optimized approximately based on the homogenization method with coarse meshes to reduce the numerical efforts. Besides, gradient boundary layers discretized by fine meshes are optimized between subdomains and boundaries to connect adjacent base cells with different patterns and address the boundary effect. Quadtree technology is used to match the meshes of different sizes. Numerical examples verify both the effectiveness and efficiency of the proposed approach for designing manufacturable optimized architected structures.

Modelling the effect of mesh size and opening angle on size selection and capture pattern in a snow crab (Chionoecetes opilio) pot fishery

Size selection in commercial snow crab (Chionoecetes opilio) pot fisheries is important for reducing on-board sorting and unintended mortality of undersized individuals. In this paper, we tested whether snow crab of various sizes geometrically could pass through diamond meshes of different sizes and opening angles, to estimate a model for predicting the effect of mesh size and mesh opening angle on snow crab size selectivity. The model was able to explain the size selection results from earlier sea trials using commercial snow crab pots. Size selection was strongly dependent on mesh opening angle, making it less well-defined for the conical pots often used in snow crab fisheries where mesh opening angle varies. We predicted the optimal mesh size for the Norwegian snow crab fishery is 140 mm with a 65° opening angle, resulting in high capture efficiency for target size snow crab (larger than 100 mm carapace width) and low sorting effort, with approximately 10% of the catch consisting of undersized snow crab. Our model can potentially be used for other snow crab fisheries.

Prediction of square mesh panel and codend size selectivity of blue whiting based on fish morphology

Abstract Square mesh panels (SMPs) are selective devices used extensively to supplement codend size selectivity in trawl fisheries. Therefore, predictions of the effect of mesh size in both SMPs and codends on size selectivity are valuable. Here, we established a framework to predict the size selection of blue whiting through different SMPs and diamond mesh codends based on the morphological characteristics of this species. We hypothesized that size selection for an SMP is determined by different fish contact angles, whereas different mesh opening angles determine size selection for the codend. Based on these hypotheses, we first developed a model that enabled us to predict which sizes of blue whiting are able to pass through meshes of different sizes and shapes. We then tested whether the selectivity for blue whiting of the SMP, the codend, and the combination of both could be explained by the models. Finally, we predicted the size selectivity of multiple combinations of SMPs and diamond mesh codends. The method presented here can potentially be applied to make predictions for species other than blue whiting.

Prediction of size-dependent risk of salmon smolt (Salmo salar) escape through fish farm nets

The escape of small smolt through farm cage netting is a major challenge faced by the Norwegian salmon farming industry. Escape can occur when the smolt placed in the cages are smaller than the size estimated by the farmers. Furthermore, one may assume wrong mesh-properties as the cage netting change shape and/or state from stiff (mesh bars with tension) to slack (mesh bars without tension) due to sea currents or waves and become more suitable for penetration. The latter represents an increased risk for cages placed in more exposed sea areas, which is a growing trend in the industry due to increased demand for farming sites. The potential influence of mesh shape and state on the risk of escape from salmon farm cages is predicted. The morphological characteristics of salmon smolt are assessed and used to determine the risk of potential escape through meshes of different sizes, shapes and states. The results showed that fish smaller than 47 g and 201 g have the potential to escape through 30 mm and 50 mm meshes, respectively. In general, the risk of smolt escape is highest when the meshes in the netting are slack. Semi-slack meshes with mesh openness of between 65 and 95 % also present a higher risk of smolt escape than square stiff meshes. The highest risk of escape was identified at approximately 80 % mesh openness. This study illustrates the importance of mesh states in fish farming cage nettings. In many cases the minimum smolt size needed to maintain an escape risk below 1 % was approximately twice as large for slack square meshes than for stiff square meshes of the same size.

Dimensional distribution control of elongate mineral particles for their use in biological assays

The aim of the present method is to reduce the dimensional variability of asbestos, elongate mineral particles, and other asbestiform minerals for use in biological assays. Here, the pristine mineral sample is filtered through two nylon meshes of different sizes to obtain a narrower dimensional distribution following a power law. Furthermore, we show that anoxic preparation, autoclaving and storage of the mineral prior to addition into biological cultures did not affect the mineral's chemical properties. This approach avoids the use of highly reactive chemicals modifying mineralogical characteristics and surface properties, which can affect to a major extent mineral toxicity as well as interactions between minerals and biological matter or biofluids. The method can be combined with additional selective approaches to further refine the dimensional range of the minerals. The advantages of this protocol over previous methods are:•Exclusive use of distilled water and 2-propanol, thus eliminating chemicals that can modify bulk or surface properties of the studied minerals.•Successful sterilization of the resulting mineral particles for use in biological assays without compromising mineralogical characteristics.•Applicability of this method across various types of asbestos, elongate mineral particles and, potentially, other hazardous minerals.

An in-depth comparative study of three-dimensional angularity indices of general-shape particles based on spherical harmonic reconstruction

An in-depth comparative study is conducted on four three-dimensional (3D) angularity indices, namely, the radius-based angularity index (AIr), gradient-based angularity index (AIg), deviation angle-based angularity index (AId), and Gaussian curvature-based angularity index (AIG). An innovative modification is carried out to ensure that all the indices equal zero for spheres and ellipsoids. Each AI is evaluated on particle surfaces reconstructed through spherical harmonic analyses with regular polyhedral meshes of different sizes. This comprehensive comparative study revealed that AIg and AIG better reflect the local morphological characteristics of the particles than AIr and AId. To obtain a convergent value of the overall AI of the particles, a relatively coarse mesh is sufficient for estimating AIr and AId, whereas a fine mesh is required to estimate AIG and AIg. Among the four indices, only AIG and AIg are well correlated, and their relationship can be described by a power function.

Sensitivity of acoustic predictions on the mesh size of large-eddy simulation of supersonic jet

Intense noise produced by the supersonic jet plume from a rocket can cause damage to its structural system and even a failure during launch. In order to predict the acoustic loading by rocket jet noise, large-eddy simulation (LES) is commonly employed for analysis of the jet flow field that is subsequently used as a source condition for predicting the acoustic field. Although desirable from the accuracy standpoint, LES of a supersonic jet is often burdened by an overwhelming computational cost in both runtime and memory. In this talk, we discuss the sensitivity of acoustic predictions on the spatial resolution of LES, and propose a guideline for reducing the mesh requirement. . Here, the flow field of a supersonic jet is calculated using a hybrid RANS/LES scheme on meshes of different sizes, and is fed into the Helmholtz-Kirchhoff integral for prediction of the acoustic farfield. Changes in overall sound pressure level (OASPL) and directivity of the Mach radiation are monitored as the LES mesh varies in size. The study suggests that (a) the accuracy of the acoustic prediction is not much affected by the use of a coarser mesh to a certain extent and (b) the resulting improvement in computation speed and economy thus outweighs the loss of details in LES, given the prediction of acoustic loading as the ultimate goal. (This work was conducted at High-Speed Vehicle Research Center of KAIST with the support of the Defense Acquisition Program Administration and the Agency for Defense Development under Contract UD170018CD.)Intense noise produced by the supersonic jet plume from a rocket can cause damage to its structural system and even a failure during launch. In order to predict the acoustic loading by rocket jet noise, large-eddy simulation (LES) is commonly employed for analysis of the jet flow field that is subsequently used as a source condition for predicting the acoustic field. Although desirable from the accuracy standpoint, LES of a supersonic jet is often burdened by an overwhelming computational cost in both runtime and memory. In this talk, we discuss the sensitivity of acoustic predictions on the spatial resolution of LES, and propose a guideline for reducing the mesh requirement. . Here, the flow field of a supersonic jet is calculated using a hybrid RANS/LES scheme on meshes of different sizes, and is fed into the Helmholtz-Kirchhoff integral for prediction of the acoustic farfield. Changes in overall sound pressure level (OASPL) and directivity of the Mach radiation are monitored as the LES mesh varies in s...

CREELSELECT—A method for determining the optimal creel mesh: Case study on Norway lobster (Nephrops norvegicus) fishery in the Mediterranean Sea

In the laboratory, we investigated which sizes of Nephrops (Nephrops norvegicus) could pass through the meshes of different size and shape to establish a predictive model for the creels size selectivity. Predictions agreed well with the results from experimental fishing, demonstrating the reliability of this simple method. Nephrops minimum target size is 20 mm carapace length in the Mediterranean creel fishery, with some areas having restrictions on the mesh size, minimum being 36 or 40 mm. The model predicts that Nephrops below 28 and 32 mm carapace length would escape from creels with respectively 36 and 40 mm mesh size, implying a suboptimal exploitation pattern. Our method provides easy and quick identification of optimal mesh size and shape without the exhaustive sea trials with various creel designs. It was predicted that a square mesh of 30 mm would better match the desired exploitation pattern. The method could easily be adopted to other species and different creel fisheries, helping to determine optimal mesh matching a prescribed exploitation pattern.

Improving the reconstruction image contrast of time-domain diffuse optical tomography using high accuracy Jacobian matrix

An algorithm for time-domain diffuse optical tomography using a high accuracy Jacobian matrix has been developed. The Jacobian matrix has been calculated using a new direct method that uses two finite element meshes of different sizes. A low density mesh has been used for the inverse calculations where the tissue optical properties are reconstructed at its nodes’ locations. The second mesh has a bigger size and is used to calculate the high accuracy light fluence rates and the Jacobian matrix. The high accuracy light fluence is interpolated to obtain its values at the nodes of the low density mesh and at the detectors’ locations. The high accuracy Jacobian matrix at the nodes of the low density mesh are obtained by integrating the Jacobian calculated using the high density mesh. The integration of the Jacobian using the proposed method does not require calculating the Jacobian explicitly at all nodes of the high density mesh which is inefficient in memory requirement and computation speed. The improvement of the Jacobian accuracy while using a low density mesh for the inverse calculations improves the reconstructed image contrast and the computation speed. The optical properties are reconstructed in a region of interest by solving iteratively a self-regularized minimization problem. The minimization problem uses the calculated Jacobian and the light fluence at precisely selected points on the temporal profile of each source-detector pair for the reconstruction. The algorithm has been applied to a three-dimensional model of a neonatal brain and to a three-dimensional model of the mouse for a small animal model. The reconstruction results by the proposed method have been compared with the results using a single mesh for the Jacobian calculations. The effect of using different sizes of the low density mesh for the inverse calculations on the image contrast has been reported.

Numerical simulation of the viscoelastic flow in a three-dimensional lid-driven cavity using the log-conformation reformulation in OpenFOAM®

In this work we implement the log-conformation reformulation for viscoelastic constitutive equations as proposed by Fattal and Kupferman (2004) in the open-source CFD-software OpenFOAM®, which is based on the collocated finite-volume method (FVM). The implementation includes an efficient eigenvalue and eigenvector routine and the algorithm finally is second-order accurate both in time and space, when using it in conjunction with an adequate convection scheme such as the CUBISTA scheme (Alves et al., 2003). The newly developed solver is first validated with the analytical solution for a startup Poiseuille flow of a viscoelastic fluid and subsequently applied to the three-dimensional and transient simulation of a lid-driven cavity flow, in which the viscoelastic fluid is modeled by the Oldroyd-B constitutive equation. The results are presented for both the first-order upwind scheme and the CUBISTA scheme on four hexahedral meshes of different size in order to check for mesh convergence of the results and a tetrahedral mesh to show the applicability to unstructured meshes. The results obtained for various values of the Weissenberg number are presented and discussed with respect to the location of the primary vortex center, streamline patterns and velocity and stress profiles besides others. We are able to obtain sufficiently mesh converged results for Weissenberg numbers, which would have been impossible to obtain without use of the log-conformation reformulation. An upper limit for the Weissenberg number in terms of stability could not be found.

Computational Fluid Dynamics Simulations of the Complex Geometry of a Technical Textile

The use of virtual prototypes for the prediction of relevant flow related parameters is well established in many industries such as the automotive industry. For the development of technical textiles an analogous approach is anticipated as being beneficial. However, so far the complex geometry of textiles consisting of a very large number of filaments has impeded this approach. We utilize this approach for the first time investigating a fabric, which is used during the paper forming process. The most challenging aspect for the simulation is the the process of geometry creation by use of single filaments together with the indispensable simplifications for a currently marketed fabric. Meshes of different sizes up 20 million cells have been generated and results from CFD calculations will be displayed together with an analysis of the numerical accuracy. The individual relevance of the simulation experiments will be discussed. Physical experiments at ambient temperature of laminar water flow through the same fabric under comparable conditions with a Reynolds Number of 15 based on pipe diameter of 9.0 mm and pipe volume flow rate averaged velocity magnitude of 0.00172 m/s were performed. The Reynolds Number based on the diameter of the different filaments of 0.2 mm up to 0.45 mm is approx. between 0.34 and 0.77. The experimental set up using Magnetic Resonance Imaging (MRI) will be explained. The use of this experimental approach as a means to validate the results of the simulation will be critically evaluated.

‘The mesh method’ in lightning protection standards – Revisited

At present the design of the Lightning protection systems (LPS) for structures as stipulated in standards is based on the electro – geometrical method, which was initially used to protect power lines from lightning. A derivative of the electro-geometrical method is the rolling sphere method. This method together, with the protection angle method and mesh method are used almost in all lightning standards as the measure in installing the lightning protection systems of grounded structures. In the mesh method, the dimension of the cell size in different levels of protection is determined using the rolling sphere method. Since the rolling sphere method does not take into account the physics of the lightning attachment process there is a need to evaluate the validity of the stipulated value in standards of the minimum lightning current that can penetrate through the mesh in different levels of protection. In this paper, meshes of different sizes as stipulated in the lightning protection standards were tested for their ability to intercept lightning flashes using a lightning attachment model that takes into account the physics of connecting leaders on. The results are in reasonable agreement with the specifications given in the lightning protection standards.

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.

3D mesh design to evaluate sense of place in closed spaces

The waveguide mesh defines ideal numerical schemes for the simulation of acoustic linear pressure wave fields, characterized by having constant parameters along the propagation domain. Using the waveguide mesh it is possible to accurately simulate closed spaces of arbitrary size and dimensions. We propose a real-time implementation of the 3D waveguide mesh which runs under the Pure data platform. The parameters the user can control, in real-time, are the mesh dimensions, the damping characteristics of the surfaces and the listening point and sound source positions. In previous experiments, we tested the listeners’ ability to evaluate distance, by placing different sound sources inside an acoustic tube simulated by using the 3D mesh. In this paper we are interested in evaluating humans’ ability to perceive the size of an acoustic enclosure. We calculated the impulse response of 3D meshes of different sizes and shapes, and asked the listener to rate such responses according to the perceived size of the enclosure. Results of this experiment will be shown during the presentation.

Analysis and application of new quasi-network characteristics of nonuniform mesh in FDTD simulation

The equation of computing the reflection coefficient between two meshes of different sizes is derived. Using the equation, quasi-network characteristics of nonuniform mesh for the finite-difference time-domain technique is found and analyzed. The so-called mesh network (MN) here is a kind of structure composed of the sections of mesh in cascade. The cell sizes of these sections change regularly. By means of choosing the number of mesh sections, length of each section, and cell sizes, some novel network characteristics are obtained, which can be used to match the reflecting wave of nonuniform mesh or improve the transmitted characteristics for a mesh wave to travel along the nonuniform mesh. Formulas for analyzing the MN are given. The characteristics are realized in both one- and three-dimensional cases. The applications and advantages of the MN are shown by computing three different structures, i.e., microstrip-gap capacitor, parallel-coupling filter, and microstrip slot-line transformer.

How to Trammel up the Consequence and Catch Success: "Macbeth" 1.7.3-4

Macbeth's metaphor, in his utterance if th'assassination / Could trammel up the consequence, and catch, / With his surcease, success (1.7.24), is not quite clear. Is the image taken from fishing, or horse hobbling, or bird catching? And what does the 'up' stand for? A passage from Gervase Markham's treatise Hungers Preuention: Or, The whole Arte Of Fowling By Water and Land (London, 1621) helps to elucidate the passage as a metaphor drawn from fowling. Gervase Markham (ca. 1568-1637) was a hack writer, scholar, poet, dramatist, and expert in agriculture and horse-breeding who has been linked with Shakespeare's Don Armado and the rival poet of the sonnets.1 In the chapter in question, Markham describes a special way of fowling with the help of a trammel net. This is a large rectangular net with at least two layers of meshes of different sizes. It is held up in two corners by several men and trailed along the ground, its lower end kept down by lead plummets. This is done by night, on unenclosed ground and in open fields, called champion or champaigne (grass, heather, stubble fields, fallow land, etc.). Other men walk beside the net, with lights and torches, carrying long poles. The birds press closely to their cover at first. When the party approaches, some try to run away, but the lights keep them toward the middle. There they are put up by the poles and become entangled in the trammel. Those birds that manage to escape, scatter and hide and can no longer be taken in one catch. The birds stalked are, in Markham's words, Partriges, Rayles, Larkes, Quailes, or any other small Birdes of