Orthogonal Mesh Research Articles

Reinforcement of Adobe Constructions with Toad Rush Mesh

Peru has a long history of mud constructions. The use of these techniques has been forgotten throughout time, and currently the adobe buildings lack a constructive system suitable for our seismic, economic and ecological characteristics. Current solutions to this problem, including the countrys normative, alter its natural characteristics and make it more expensive. To achieve a way of life that integrates cultural identity, dwelling, environment and health, a natural material of easy acquisition is studied: the toad rush (Juncus bufoniusL.) It is a plant that grows in humid areas of the country, between 0 and 4 000 AMSL, in order to address its use as reinforcement in the walls of adobe, based on structural proposals approved in Peru. An experimental methodology has been used under the modality of trial and error. The study was performed in three stages; in the first one, its elasticity coefficient and resistance to traction was determined in laboratory tests. The analysis were performed on simple fibers and braids (of up to 6 fibers), finding the following results: elasticity modulus = 36 kPa with 5% strain, maximum tension stress = 745 N in both directions with 12% elongation. Using these data, an orthogonal mesh of toad rushes, with 0.030 m of separation between braids, was designed to be attached to an adobe wall. This mesh was subjected to a test of horizontal impact, applying 84.49 MPa as a maximum force. In a third stage an adobe module of 2.40 x 2.40 x 2.40 m reinforced with the mesh was subjected to a mechanical seismic simulation test, supporting 26.1 kN without the mesh suffering any damage. As a last test, to comply with the requirements laid down in annex N°1 of the E.080 RNE of the Peruvian standard, a real scale module (2.40 x 2.40 x 2.40 m), was subjected to a cyclic test at the CISMID-UNI laboratory. The results showed that under a distortion from 1/1100 to 1/500 micro cracks were generated in the walls. Under a distortion of 1/400, 0.005 m cracks occurred at the bottom of the north side of the model and under a distortion of 1/280 the model suffered the detachment of the plaster of the lintel, without any damage to the mesh. All the tests allowed for the conclusion thatthe toad rush(Juncus bufoniusL.) is a material that,used as a mesh,can be used asreinforcement in adobe buildings. It is elastic and resistant to traction. It has as an advantage that it is very accessible, known throughout the country and easy to work with. The tests allowed us to proof the resistance of the toad rush mesh, in spite of the features of the adobe not conforming to the Peruvian standard E.080 RNE. We conclude that: it is feasible to use a mesh of toad rush (Juncus bufonius L.) as reinforcement in adobe buildings.

Full Core Reactor Analysis: Running Denovo on Jaguar

Fully consistent, full core, three-dimensional, deterministic neutron transport simulations using the orthogonal mesh code Denovo were run on the massively parallel computing architecture Jaguar XT5. Using energy and spatial parallelization schemes, Denovo was able to efficiently scale to more than 160 000 processors. Cell-homogenized cross sections were used with step characteristics, linear discontinuous finite element, and trilinear discontinuous finite element spatial methods. It was determined that using the finite element methods gave considerably more accurate eigenvalue solutions for large–aspect ratio meshes than using step characteristics.

A non-conforming multi-element DGTD method for the simulation of human exposure to electromagnetic waves

The great majority of numerical calculations of electric energy deposition in human tissues exposed to microwaves are performed using the finite-difference time-domain FDTD method and voxel-based geometrical models of the tissues. The straightforward implementation of the method and its computational efficiency are among the main reasons for FDTD being currently the leading method for numerical assessment of human exposure to electromagnetic waves. However, the rather difficult departure from the commonly used Cartesian grid and cell size limitations regarding the discretization of very detailed structures of human tissues are often recognized as the main weaknesses of the FDTD method in this application context. In particular, interfaces between tissues where sharp gradients of the electromagnetic field may occur are hardly modeled rigorously in these studies this is generally referred as the staircasing effect. We present here an alternative numerical dosimetry methodology that is based on a DGTD method designed to work with non-conforming cubic-tetrahedral meshes for more flexibility in the discretization process of complex propagation scenes. For example, in the context of head tissues exposure to mobile phone radiation, the computation domain is divided in two regions: an unstructured tetrahedral mesh-based heterogeneous model of head tissues and an orthogonal cartesian mesh of the vacuum part of the propagation domain. We present numerical results comparing this approach with strategies based on fully Cartesian and fully tetrahedral meshes of the whole computational domain. Copyright © 2013 John Wiley & Sons, Ltd.

Micro-computed tomography image-based evaluation of 3D anisotropy degree of polymer scaffolds

Anisotropy is one of the most meaningful determinants of biomechanical behaviour. This study employs micro-computed tomography (μCT) and image techniques for analysing the anisotropy of regenerative medicine polymer scaffolds. For this purpose, three three-dimensional anisotropy evaluation image methods were used: ellipsoid of inertia (EI), mean intercept length (MIL) and tensor scale (t-scale). These were applied to three patterns (a sphere, a cube and a right prism) and to two polymer scaffold topologies (cylindrical orthogonal pore mesh and spherical pores). For the patterns, the three methods provided good results. Regarding the scaffolds, EI mistook both topologies (0.0158, [ − 0.5683; 0.6001]; mean difference and 95% confidence interval), and MIL showed no significant differences (0.3509, [0.0656; 0.6362]). T-scale is the preferable method because it gave the best capability (0.3441, [0.1779; 0.5102]) to differentiate both topologies. This methodology results in the development of non-destructive tools to engineer biomimetic scaffolds, incorporating anisotropy as a fundamental property to be mimicked from the original tissue and permitting its assessment by means of μCT image analysis.

WE‐C‐WAB‐09: A Novel Volumetric Imaging Method Using a Sparse Subset of CBCT Projections

Purpose: : Over the preceding decade, onboard volumetric imaging utilizing cone beam CT (CBCT) has become an indispensible tool for image‐guided radiotherapy. A novel method has been developed to deform the planning CT to maximize the spatial congruence between the digitally reconstructed radiographs (DRRs) and CBCT projections. This method maps the planning CT images to the current anatomy using a sparse subset of CBCT projections. Methods: A finite element modeling methodology was developed to automatically generate adaptive meshes for a given region of interest without the need for segmentation. In this methodology, more control points are generated at organs boundaries, special tissues, contour boundaries, or high intensity gradients. The displacement of boundaries and important features is directly represented by the displacement of control points, instead of interpolation on regular grids. A splatting method was developed to generate DRRs of the deformed CT. These DRRs were compared with corresponding 2D projections from CBCT scans; as a Result, the displacement vector fields on the CT were optimized iteratively to obtain a final deformed CT image. A digital phantom was used to evaluate this method. Results: Typically 60 projections were needed to reconstruct a set of 3D images while several hundreds of projections were required for a conventional CBCT reconstruction. The feature‐based meshing method led to better results than either regular orthogonal or regular tetrahedral meshes. The image intensity results of the feature‐based meshing method were nearly identical to those of the voxel‐based method (normalized cross correlation efficient (NCC) ∼ 0.9858 vs 0.9872), while the feature‐based meshing method led to much better consistency of displacement vector fields relative to ground truth than voxel‐based method (NCC ∼ 0.8265 vs 0.6261). Conclusion: This feature‐based meshing method is capable of reconstructing volumetric images with significantly fewer projections while retaining the image quality of planning CT. This research is supported by CPRIT Individual Investigator Award RP110329.

Analysis of a finite volume method for a bone growth system in vivo

This paper is devoted to the convergence analysis of a finite volume method and numerical simulations of a reaction–cross diffusion system arising from a bone growth model. This model describes the evolution of mesenchymal stem cells, osteoblasts, bone matrix and osteogenic growth factor. We propose a numerical scheme based on an implicit finite volume method constructed on an orthogonal mesh. Lack of the regularity of the approximate system is overcome by stability results which allow to obtain estimates on the translates, apply the Kolmogorov theorem in order to get compactness and show the convergence of the proposed scheme. The efficiency and robustness of the scheme are shown in simulating a situation in bone growth: the healing of a skull fracture in rats.

Using the Cartesian Discrete Ordinates Code DORT for Assembly-Level Calculations

For the sake of a high-fidelity representation of the curved surfaces characteristic of fuel pins, the standard reactor design process employs the method of collision probabilities (CP), the method of characteristics (MOC), or unstructured-grid discrete ordinates (SN) transport solvers for assembly-level calculations. In this work we provide a proof of principle using highly simplified assembly configurations that an approximate staircased representation of the fuel pin’s circumference via an orthogonal mesh is accurate enough for reactor physics computations. For the purpose of comparing the performance of these approaches, we employ the orthogonal-grid SN code DORT and the lattice code DRAGON (CP and MOC) to perform k-eigenvalue-type computations for both a boiling water reactor (BWR) and pressurized water reactor (PWR) test assembly. In the framework of a computational model refinement study, the multiplication factor and the fission source distribution are computed and compared to a high-fidelity multigroup MCNP reference solution. The accuracy of the considered methods at each considered model refinement level (fidelity of curved surface representation in DORT, number of tracks in MOC, etc.) is quantified via the difference of the multiplication factor from its reference value and via the root-mean-square and maximum norm of the error in the fission source distribution. We find that for the BWR assembly DORT outperforms MOC and CP in both accuracy and computational efficiency, while for the PWR test case, MOC computes the most accurate fission source distribution but fails to compute the multiplication factor accurately.

A phase field model for simulating the precipitation of multi-variant β-Mg17Al12 in Mg–Al-based alloys

A phase field model for simulating the precipitation of multi-variant β-Mg17Al12 phase during the aging process of Mg–Al-based alloys was developed in which the interface anisotropy and the elastic strain energy were taken into account. A special numerical technique based on a hexagonal and an orthogonal mesh was employed to deal with the precipitate orientation and calculate the elastic strain energy. The model reveals the contribution of the interface anisotropy and the elastic strain energy in the evolution of the precipitates.

Implementation of slip boundary conditions in the finite volume method: new techniques

SUMMARYTwo different techniques for the implementation of the linear and nonlinear slip boundary conditions into a finite volume method based numerical code are presented. For the linear Navier slip boundary condition, an implicit implementation in the system of equations is carried out for which there is no need for any relaxation, especially when handling high slip coefficients. For three different nonlinear slip boundary conditions, two different methods are devised, one based on solving a transcendental equation for the boundary and the other on the linearization of the slip law. For assessment purposes, comparison is made between these new methods and the usual iterative process. With these new methods, the convergence difficulties, typical of the iterative procedure, are eliminated, and for some of the test cases, the convergence rate even increased with the slip velocity. The details of these implementations are given first for a simple geometry using orthogonal meshes and Cartesian coordinates followed by their generalization to non‐Cartesian coordinates and nonorthogonal meshes. The developed code was tested in the benchmark slip‐stick and 4:1 contraction flows, evidencing the robustness of the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd.

An Optimized Forward Problem Solver for the Complete Characterization of the Electromagnetic Properties of Biological Tissues in Magnetic Induction Tomography

A new method for solving the magnetic induction tomography forward problem is presented. It is based on the combination of an OcTree type multi-level adaptive orthogonal mesh generation algorithm with a conformal finite integration technique-like formulation. The results obtained were compared with both analytical solutions and the response from a previously validated method. The presented method was proven to be capable of dealing with both complex electrical conductivity and magnetic permeability, giving a response with a low relative error, even when fairly coarse grids are used, thus reducing the overall system size and consequently the time for the attainment of the solution. This method is shown to be sensitive enough to be useful for image reconstruction in biological applications, where very small conductivities and relative permeabilities are usually found.

Design of compression reinforcement in reinforced concrete membrane

This paper presents a method to design membrane elements of concrete with orthogonal mesh of reinforcement which are subject to compressive stress. Design methods, in general, define how to quantify the reinforcement necessary to support the tension stress and verify if the compression in concrete is within the strength limit. In case the compression in membrane is excessive, it is possible to use reinforcements subject to compression. However, there is not much information in the literature about how to design reinforcement for these cases. For that, this paper presents a procedure which uses the model based on Baumann's [1] criteria. The strength limits used herein are those recommended by CEB [3], however, a model is proposed in which this limit varies according to the tensile strain which occur perpendicular to compression. This resistance model is based on concepts proposed by Vecchio e Collins [2].

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry

In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable θ), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uθ.

An Upstream Finite Volume Scheme for a Bone Healing Model

This paper is devoted to the introduction of a numerical scheme for a bone healing model and simulation of skull fractures. The mathematical model describes the evolution of mesenchymal stem cells, osteoblasts, bone matrix and osteogenic growth factor. WeВ propose a numerical scheme based on an implicit finite volume method constructed on an orthogonal mesh. The efficiency and robustness of the scheme are shown in simulating a skull fracture in rats.

New Multicomponent Porous Architecture of Self-Assembled Porphyrins/Calixarenes Driven by Nickel Ions

A new multicomponent material with nanoporous structure has been synthesized by co-crystallization of a mixture of cationic meso-tetrakis(4-N-methylpyridyl)porphyrin (H2T4) and meso-tri(4-N-methylpyridyl)porphyrin (H2T3py) with polyanionic 5,11,17,23-tetrasulfonato-25,26,27,28-tetrakis(hydroxylcarbonylmethoxy)calix[4]arene (C4TsTc) in the presence of Ni2+ ions. The structural analysis indicates that the overall architecture is assembled by interpenetrated two-dimensional (2D) meshes where the nodes are built up by a central tetracationic H2T4 porphyrin with arms hosted in sulphonated rims of four cavitands. The approximately 2D square network is formed by Ni2+ ions bridging the calixarene carboxylate rims in a tail-to-tail fashion. The central H2T4 stacks with two external H2T3py molecules having the neutral pyridine arm N-coordinated to Ni2+ ions. These metal centers interconnect the orthogonal 2D meshes by further coordination of calixarene–carboxylate groups. Self-organization of the new multicomponent material, featuring large channels (60% of volume accessible to solvent molecules) and potential readily accessible metal active sites, has been driven by both supramolecular host–guest recognition and coordinative assembly. The thermal behavior of native and nickel-containing crystals was studied by hot stage microscopy and differential scanning calorimetry. The decomposition temperatures of the multicomponent materials, 465–470 °C, are about 100 °C higher than those of the single building blocks.

Reduced order mesh optimisation using proper orthogonal decomposition and a modified cuckoo search

SUMMARYA new mesh optimisation scheme, reduced order mesh optimisation, is introduced. The technique uses proper orthogonal decomposition to reduce the number of dimensions in a mesh optimisation problem. This reduction in dimensionality allows the expression of the optimisation problem globally rather than the more traditional local mesh optimisation or smoothing algorithms. To perform the optimisation, the recently developed gradient‐free technique modified cuckoo search is applied. The effectiveness of the algorithm is shown by considering the problem of optimising meshes for use in co‐volume techniques. Co‐volume techniques require the existence of two mutually orthogonal meshes; this is achieved by utilising the Delaunay–Voronoi dual. A combination of considering the problem globally and the use of a gradient‐free technique results in a scheme that significantly outperforms previous methods in solving this particular problem. Although the examples presented in this paper are specific to optimising dual meshes, the technique is general and can be simply modified to any mesh optimisation problem. Copyright © 2012 John Wiley & Sons, Ltd.

An improved nearly-orthogonal structured mesh generation system with smoothness control functions

This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are capable of relaxing the local strong orthogonal conditions so that nearly orthogonal but smooth mesh can be achieved. Examples and applications are also investigated in this paper to demonstrate the effects of the proposed mesh generation system.

Two-Dimensional Mathematical Modelling of a Dam-Break Wave in a Narrow Steep Stream

The paper deals with hydraulic aspects of a wave, emerging as a result of a potential dam break of the upper storage reservoir of the pumpedstorage hydropower plant Kolarjev vrh. A two-dimensional depth-averaged mathematical approach was used. The upper storage reservoir and its dam failure were modelled with the mathematical model PCFLOW2D, which is based on the Cartesian coordinate numerical mesh. The results of PCFLOW2D were used as the upper boundary condition for the mathematical model PCFLOW2D-ORTHOCURVE, based on the orthogonal curvilinear numerical mesh. The model PCFLOW2D-ORTHOCURVE provided a tool for the analysis of flood wave flow in a steep, narrow and geometrically diversified stream channel. The classic Manning’s equation fails to give good results for streams with steep bed slopes and therefore, a different equation should be used. The application of the Rickenmann’s equation was chosen, presented in a form similar to Manning’s equation. For the purpose of the example given here, the equation was somewhat simplified and adapted to the data available. The roughness coefficient used at each calculation cell depended on the slope of that cell. The results of numerical calculations were compared to measurements carried out on a physical model in the scale of 1 : 200. Regarding the complexity of the flow phenomenon a rather good correlation of maximum depth was established: only at one gauge the difference in water depth was up to 27% while at the other four it was 7% of water depth on average.

Three-Dimensional Diffusion in Arbitrary Domain Using Generalized Coordinates for the Boundary Condition of the First Kind: Application in Drying

This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. For this end, the diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. The computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (orthogonal and non-orthogonal meshes). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. The developed computational code was applied in the simulation of the drying of ceramic roof tiles for the following temperature: 55.6 °C. The analysis of the results makes it possible to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature.

A fuzzy set approach of an analytical solution of non-steady two-dimensional drainage

A new analytical solution for soil water two-dimensional movement to an orthogonal mesh of parallel drains is presented, as an extended case of the one-dimensional flow problem of the same nature. An equation is provided, that gives the profile of the water surface as well as the volume that has passed through the drains at a given time moment. Non-dimensional profiles of the piezometric surface are given for various values of time and space parameters. The water volume versus time derived from the respective equation is in very good accordance with the volume derived from surface profile integration. We also explore the possibility to solve this problem by using the fuzzy set approach, to cope with the uncertainties of the hydraulic parameters. Triangular fuzzy numbers are used to represent the hydraulic conductivity of the soil as well as the storativity of the aquifer. The drained water volume derived from the fuzzy set after defuzification, approaches the one calculated by the analytical solution, included in the interval of presumption level @a=0.8.

Multi-objective analysis of dam release flows in rivers downstream from hydropower reservoirs

This paper assesses dam releases from hydropower reservoirs in order to optimize power production and fish habitat protection. A multi-objective programming model includes output from 2-D hydraulic simulation for habitat assessment to optimize power production and fish habitat suitability as a Pareto set. To identify the optimal Pareto set two different approaches are used and compared: ε-constraint methods and non-dominant-sorting genetic algorithm (NSGA II). To formulate the ecological objective the river habitat quality is quantified by the weighted usable area (WUA). The relation between the WUA and the river flow-rate is obtained by using a 2D hydraulic model in which the hydraulic characteristics of river current – depth and velocity – are calculated by a finite difference numerical integration of two-dimensional shallow water equations on a boundary fitted non orthogonal curvilinear mesh. This approach allows the integration of motion equations on geometrically complex domains as those representing the morphology of natural watercourses. The performance of the proposed methodology is analyzed in a case study of a stretch of the Piave river downstream of the dam of the Pieve di Cadore reservoir (Belluno, Italy).