Kinds Of Grids Research Articles

Discrete finite volume formulation for multidimensional fragmentation equation and its convergence analysis

The present work is focused on developing a finite volume scheme for a multidimensional fragmentation equation. The finite volume scheme is established using the concept of overlapping of the cells whose mathematical formulation is both straightforward and robust on any kind of grid. The numerical development is further supported by thorough discussion of the mathematical analysis using Lipschitz condition and consistency of the method. The proposed finite volume scheme conserves the total mass in the system and is shown to estimate several other moments accurately, even though no special measure is taken to capture these moments. The testing of the proposed scheme is investigated against the constant number Monte Carlo method and exact benchmarking problems. The new scheme shows second order convergence on both uniform and nonuniform grids irrespective of the breakage kernel and selection function.

The Influence of Grid Scale on the Tail Vortex Capture of Aircraft

The grid has appreciable impact on the simulation of the wake vortex. There is a big difference between the traditional aerodynamic estimation grid and the grid used for capture the main parameters of the trailing vortex in the far field. This paper compares the similarities and differences between these two kinds of grids. The main parameters of the coarse grid are quite different from those of the refined grid simulation in the far field. Sufficient quantity grids are required to simulate the flow field in the parameters of wake vortex prediction. Otherwise, it may draw the reverse conclusions with the physical truth.

Eternal dominating sets on digraphs and orientations of graphs

Eternal domination is a problem that asks the following question: Can we eternally defend a graph ? The principle is to defend against an attacked vertex, that changes every turn, by moving guards along the edges of the graph. In the classical version of the game (Burger et al., 2004), only one guard can move at a time, but in the m-eternal version (Goddard et al., 2005), any number of guards can move in a single turn. This problem led to the introduction of two parameters: the eternal and m-eternal domination numbers of the graph, that are the minimum numbers of guards necessary to defend against any infinite sequence of attacks.In this paper, we first study the (m-)eternal domination number on digraphs. We show that a lot of results proven for undirected graphs can be generalized to digraphs. Then, we introduce the problem of oriented (m-)eternal domination, that consists in finding an orientation of a graph that minimizes the eternal domination number. We prove that computing the oriented eternal domination number is a coNP-hard problem, and we give a complete characterization of the graphs for which the oriented m-eternal domination number is 2. We also study these two parameters on trees, cycles, complete graphs, complete bipartite graphs, and different kinds of grids and products of graphs.

Numerical analysis of the influence of the front heat shield separation process from the descent module on their aerodynamic characteristics

This paper considers aerodynamic characteristics of the descent module and the separable front heat shield (FHS) during its separation. FlowVision software was used to perform a numerical analysis of the flow around the front heat shield and descent module. The calculations were performed using dynamic and static meshes. The trajectory of the front heat shield after separation was calculated using dynamic mesh. The aerodynamic characteristics of the frontal heat shield in several positions on calculated trajectory were determined using static mesh. The results of the calculations using different kind of grids are compared.

Flexible discretization technique for DEM-CFD simulations including thin walls

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) method is regarded as a standard approach for a simulation of a gas-solid mixture system. In the DEM-CFD method, the local volume average technique is employed, and hence the fluid motion is calculated based on the void fraction. Although the accuracy of the DEM-CFD method has been improved through lots of studies, inflexibility may become a problem due to the local volume average technique. Specifically, calculations of a gas-solid flow involving thin walls is substantially impossible even by the improved DEM-CFD method. This is because the thin wall cannot be represented when its thickness becomes as large as one grid size due to usage of the local volume average technique. In order to solve this problem, a flexible discretization technique is newly proposed, where the signed distance function and the immersed boundary method are introduced into the dual grid model. In this technique, two kinds of grids are used to calculate the void fraction and the fluid flow. Thus, this technique makes it possible to simulate a gas-solid flow involving a thin wall. Verification and validation tests are performed to show the adequacy of this technique. Through this study, the proposed technique is illustrated to reproduce the exact solution and experimental results in the gas-solid flow involving the thin wall. Consequently, the proposed technique is shown to yield reasonable results in gas-solid flows involving the thin walls.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТРЕХМЕРНЫХ ПРОЦЕССОВ РАЗГОНА УПРУГОПЛАСТИЧЕСКИХ ТЕЛ ВЗРЫВОМ

A methodology for numerically modeling 3D processes of acceleration of deformable bodies by detonation products of solid explosives in the air is described. Simultaneous motion of the explosion products, the air and the elastoplastic medium is numerically analyzed in Euler variables, using a modified Godunov scheme, which is applicable for both fluid dynamics and elastoplastic flows, and an exact solution of Riemann problem of discontinuity breakage in the media and along the gas-elastic body interface. The methodology uses three types of spatial grids. The grids of the first type are sets of triangles (STL files) defining the surfaces of the objects and updating those surfaces in the process of motion. The grids of the second type are base fixed Cartesian grids nested into each medium. The grids of the third type are local orthogonal movable grids coupled with each of the triangles of the grids of the first type. The integration of dynamic equations of continua and mutual interpolation of parameters among the different kinds of grids is done on base and local grids. To simulate the detonation propagation process in a solid explosive, an algorithm based on Huygens principle and the account of energy release upon the arrival of the detonation wave into the integrated cell are used. Examples of numerically modeling propagation of elastic and elastoplastic disc-shaped, tetrahedral and cubic bodies of various materials adjacent to the charge are given. The results of the analyses testify to the applicability of the above methodology for modeling coupled processes of acceleration of deform-able bodies by detonation products up to deceleration in the ambient medium. Certain laws of the acceleration process have been found for the case where detonation is initiated in the center of a spherical charge. In particular, the duration of the acceleration of a body is comparable with the time of the arrival of the detonation wave at the surface of the contact; the major residual strains altering the geometry of the bodies occur at the initial stage of the acceleration and affect both the interaction with the detonation products and the parameters of the motion of the bodies; the final acceleration velocity is observed to depend considerably on the initial geometry of the accelerated body, its orientation relative to the detonation front and the deformation properties for the same mass.Keywords: modeling, detonation, 3D processes, multi-grid approach, interpolation, Godunov scheme, nonlinear coupled problems, aeroelastoplasticity, acceleration of bodies.

Effects of grid geometry on non-equilibrium dissipation in grid turbulence

A total of 11 grids in four families, including single- and multi-scale grids, are tested to investigate the development and decay characteristics of grid-generated turbulence. Special attention has been focused on dissipation and non-equilibrium characteristics in the decay region. A wide non-equilibrium region is observed for fractal square grids with three and four iterations. The distributions of the Taylor microscale λ, integral length scale Lu, and dissipation coefficient Cε show that a simple combination of large and small grids does not reproduce elongated non-equilibrium regions as realized by the fractal square grid. On the other hand, a new kind of grid, quasi-fractal grids, in which the region of the smaller fractal elements (N=2–4) of the fractal square grid is replaced by regular grids, successfully reproduce a similar flow field and non-equilibrium nature to that seen in the fractal square grid case. This suggests that the combination of large square grid and inhomogeneously arranged smaller grids produces an elongated non-equilibrium region. The dissipation coefficient Cε is better collapsed using Re0=t0U∞/ν (where t0 is the thickness of the largest grid bar, U∞ the inflow velocity, and ν the kinematic viscosity) as a global/inlet Reynolds number rather than ReM=MU∞/ν (where M is the mesh size) [P. C. Valente and J. C. Vassilicos, “Universal dissipation scaling for non-equilibrium turbulence,” Phys. Rev. Lett. 108, 214503 (2012)].

Model Predictive Control for Power Converters in a Distorted Three-Phase Power Supply

The interest on weak and micro-grid systems has grown up substantially last time, specially tied up to distributed power generation systems (DPGSs), isolated systems as aircraft, or islanding power systems. These kinds of grids are usually under significant variation in their quantities, specifically in their voltage amplitude and/or frequency. On this line, many studies about synchronization methods have been developed, which may work under variations on the frequency value, unbalanced voltage, and even with harmonic distortion. However, power converters connected to this class of systems are poorly documented-specifically controlled rectifiers. In fact, most of the controlled grid connected converters (GCCs) are defined to work in a fixed frequency and balanced system. This paper deals with a GCC connected to a variable-frequency and unbalanced voltage supply system control through a predictive algorithm with a fixed resolution sampling strategy. Furthermore, the current references are imposed in order to help the weak-grid source subjected to unbalancing, taking more power from the phase with highest voltage amplitude and relaxing the other phases. This issue makes to calculate every phase current reference independently and accordingly the voltage amplitudes keep the dc-link voltage in a desired value. The results show the feasibility of the proposed algorithm, where the performance is highlighted by simulated and experimental waveforms.

Grid independence in the study of boundary layer and its application in Hypergolic Propellants

Numerical simulation and experimental validation of a hypersonic flat plate and isothermal turning wall flow were conducted in the current study. The investigation was based on three kinds of grids (Grid1, Grid2, and Grid3) with laminar flow and three types of turbulence models (BL, SA, and SST). Under the same initiation and different turbulence models, the convergence process of the friction drag coefficient CP and the Stanton number St of a hypersonic flat plate flow revealed four results. First, the flow turbulence effect in the BL model simulation was responsive to CP and St. Second, the SA and SST model simulations both reflected the development process of flow turbulence. Third, the flow turbulence effect in the SST model simulation did not gradually emerge until the laminar flow simulation was sufficient. Moreover, the SA model simulation did not exist on such obvious hysteresis. Fourth, by comparing CP and St of a hypersonic flat-plate laminar simulation under the three grids, the errors of the calculation results of Grid2 and Grid3 were small.

Stochastic profit-based scheduling of industrial virtual power plant using the best demand response strategy

One of the main classified microgrids in a power system is the industrial microgrid. Due to its behaviors and the heavy loads, its energy management is challengeable. Virtual Power Plant (VPP) can be an important concept in managing such problems in this kind of grids. Here, a transmission power system is considered as a Regional Electric Company (REC) and the VPPs comprising Distributed Generation (DG) units and Demand Response Loads (DRLs) are determined in this system. This paper focuses on Industrial VPP (IVPP) and its management. An IVPP can be determined as a management unit comprising generations and loads in an industrial microgrid. Since the scheduling procedure for these units is very important for their participation in a short-term electric market, a stochastic formulation is proposed for power scheduling in VPPs especially in IVPPs in this paper. By introducing the DRL programs and using the proposed modeling, the operator can select the best DRL program for each VPP in a scheduling procedure. In this regard, a suitable approach is presented to determine the proposed formulation and its solution in a Mixed Integer Non-Linear Programming (MINLP). To validate the performance of the proposed method, the IEEE Reliability Test System (IEEE-RTS) is considered to apply the method on it, while some challenging aspects are presented.

Review of the modified finite particle method and application to incompressible solids

This paper focuses on the application of the Modified Finite Particle Method (MFPM) on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

Five novel Zn(ii)/Cd(ii) coordination polymers based on bis(pyrazinyl)-triazole and varied polycarboxylates: syntheses, topologies and photoluminescence

Five novel Zn(II)/Cd(II) coordination polymers (CPs) based on the V-shaped ligand 1H-3,5-bis(pyrazinyl)-1,2,4-triazole (Hbpt) and different polycarboxylates, {[Cd(bpt)(H2O)]·ClO4·H2O} (1), {[Cd4(bpt)2(suc)2.5(OH)]·3H2O} (2), {[Cd4(bpt)3(1,3-bdc)2.5]·4H2O} (3), {[Cd9(bpt)6(1,4-bdc)6(H2O)2]·4H2O} (4) and {[Zn2(bpt)(H3bhc)(H2O)6]·H2O} (5) (H2suc = succinic acid, 1,3-H2bdc = isophthalic acid, 1,4-H2bdc = terephthalic acid, H6bhc = benzene-1,2,3,4,5,6-hexacarboxylic acid), have been successfully synthesized. Their structures have been characterized using single-crystal X-ray crystallography, powder X-ray diffraction (PXRD) analyses, elemental analyses, IR spectroscopy, and thermogravimetric analyses (TGA). Complex 1 bears a two-dimensional (2D) layered (3,3) network, which is further extended into the resulting three-dimensional (3D) supramolecular architecture via π⋯π stacking interactions between the terminal pyrazine groups of bpt− ligands. In 2, Cd(II) ions and bpt− ligands construct a 2D Cd-bpt layer and two 1D zigzag chains, which are further connected by suc2− ligands to form a 2D + 1D → 3D (4,5)-connected framework. Complex 3 contains two kinds of grids, and their alternating arrangement gives a final complicated 3,4,5-connected network with a stoichiometry of (3-c)6(4-c)9(5-c)2. In 4, the bpt− ligands act as tetradentate ones to connect neighbouring Cd(II) ions into an infinite 1D Cd-bpt chain. The completely deprotonated 1,4-bdc2− ligands further link the adjacent Cd-bpt chains to generate a novel 3,4,6-connected 3D topological network with (3-c)2(4-c)14(6-c). Complex 5 displays an infinite 1D coordination chain. There are strong π⋯π stacking interactions between adjacent chains in 5 with a centroid–centroid distance of 3.860 Å and 3.862 Å, resulting in a 3D supramolecular structure. The results show that Hbpt can act as a versatile building block for the construction of various coordination polymers. Moreover, the fluorescence properties of 1–5 in the solid state have also been investigated.

An Algorithm for Mesh Simplification Based on Energy-Aware

Mesh simplification should not only emphasize high compression ratio, but also maximize retention of a mesh representation which is another objective of mesh compression. In one of our 3D projects, in order to pursue the optimization model display, we proposed a new mesh simplification algorithm. This article describes the algorithm based on energy-aware which used to simplify a mesh of 3D model. Our approach has two major contributions. Firstly, we used an optimization method based on energy-aware, which seeks to collect low energy value vertexes of a mesh. Vertex energy is calculated by an energy function that describes the potential energy between the vertex and its directly related vertexes in a space. Secondly, our optimization method transforms a mesh into a series of triangle stripes, and reduces low energy vertexes of those stripes effectively. The process of compression is simple, efficient and adjustable for users. From the result of experiments, we can learn that our algorithm is suitable for processing several kinds of grid, and retains the characterization from original mesh very well. Our approach solved the problem of obvious distortions of a simplified mesh of 3D model, and significantly improved the efficiency of simplification process.

Maxwell + TDDFT multi-scale simulation for laser-matter interactions

We are developing a theoretical and computational method to describe interactions between an intense laser pulse and a solid. The laser-solid interactions are extensively investigated in current frontiers of optical sciences. There are two spatial scales in the problem: the scale of laser wavelength typically a μm and the scale of electron dynamics in a solid less than a nm. We have developed a multi-scale simulation for this problem, describing propagation of the electromagnetic fields by the Maxwell equations and the electron dynamics in a unit cell of a solid by the time-dependent density functional theory. In calculating the coupled dynamics, we employ a finite difference scheme for both space and time variables. Two kinds of grids with different grid spacings are used for space, while a single time step is used for time. We present our theoretical framework, numerical implementation, and parallelization of our multi-scale simulation. It will be shown that high parallel efficiency and computing performance are realized in our computational code.

Computational Fluid Dynamics Simulation and Experimental Validation of Hypersonic Turbulence Boundary Layer

Numerical simulation and experimental validation of a hypersonic flat plate and isothermal turning wall flow were conducted in the current study. The investigation was based on three kinds of grids (Grid1, Grid2 and Grid3) with laminar flow and three types of turbulence models (BL, SA and SST). Under the same initiation and different turbulence models, the convergence process of the friction drag coefficient <em>C</em>_P and the Stanton number <em>St</em> of a hypersonic flat plate flow revealed four results. First, the flow turbulence effect in the BL model simulation was responsive to <em>C</em>_P and <em>St</em>. Second, the SA and SST model simulations both reflected the development process of flow turbulence. Third, the flow turbulence effect in the SST model simulation did not gradually emerge until the laminar flow simulation was sufficient. Moreover, the SA model simulation did not exist on such obvious hysteresis. Fourth, by comparing <em>C</em>_P and <em>St</em> of a hypersonic flat-plate laminar simulation under the three grids, the errors of the calculation results of Grid2 and Grid3 were small. In contrast, the error on Grid1 was large. By comparing <em>C</em>_P and <em>St</em> of the BL model for the three grids, we found that the result of Grid3 was slightly better than the result of Grid2. The deviation between them basically remained within 10%. However, the result of Grid1 had a large deviation with oscillation. <em>C</em>_P and <em>St</em> of the SA model for the three grids were then compared. A large difference was found only on the transition zone location between the result of Grid2 and Grid3. Nevertheless, the error and calculation of reference between them was maintained within 10%. Grid1 not only had a large deviation, but also had certain oscillation on the laminar flow area. Finally, <em>C</em>_P and <em>St</em> of the SST model for the three grids were compared. There was a large difference only on the transition zone location between the result of Grid2 and Grid3, but the error between them was maintained within 10%. Grid1 had a large deviation. The hypersonic flat-plate laminar flow was also compared with <em>C</em>_P and <em>St</em> calculated from the three turbulence models for the three grids. Evidently, the grids near the wall must be encrypted to an appropriate extent to simulate more accurately the boundary laminar flow as well as obtain proper surface friction and heat flow. The calculation in the present study showed that the Reynolds number in the first layer of the grid was more reasonable when it was about 20. The simulation result for the hypersonic isothermal two-dimensional turning wall flow showed that the calculation and experiment results from the different turbulence model were consistent. There was little difference between the location of the simulated heat flow peak and the position given by experiment. However, the peak, the curve trend after the peak and the experimental result widely differed. The curve and experimental results for pressure distribution greatly varied because of the existence of an isolated area in the calculation of the laminar flow. The calculation and experimental results from different turbulence models were close. The curve trend, the peak and the experimental result basically matched.

Methodology for Droop Control Dynamic Analysis of Multiterminal VSC-HVDC Grids for Offshore Wind Farms

This paper addresses the control of multiterminal voltage-source converters at high-voltage direct current in the context of offshore wind farms. Droop control is commonly used to regulate the dc voltage in this kind of grid, and droop parameters are selected on the basis of steady-state analyses. Here, a control design methodology is proposed based on the frequency-response analysis. This methodology provides a criterion to select the droop gains, taking into account the performance specifications [i.e., the desired voltage errors and the maximum control inputs (currents)]. The application of the methodology is illustrated with a four-terminal grid.

Study of dynamic behavior of ceramic–metal FGM under high velocity impact conditions using CSPM method

In Problems with large deformation including fracture and fragmentation, the grid based methods have some limitations which make them unsuitable for simulating these types of problems. An example is extreme mesh distortion in a lagrangian approach like Finite element method. Another situation is the inability of Eulerian based formulations in tracking the history of a desired physical property at the interface of multi materials including impact problems. A promising solution is taking the advantage of meshless and particle based methods which do not use any kind of grid in the physical domain of problem. In this paper, corrective smoothed particle algorithm (CSPM) as a meshless particle method is used to study the mechanical behavior of a ceramic–metal functionally graded material (FGM) under high velocity impact conditions. A mixed strength model with sigmoid formulation has been used to describe both yielding and fracture phenomena in the FGM. The strength model includes the JC dynamic yield relation and Johnson–Holmquist–Beissel (JHB) fracture model with a continuum damage description approach. An efficient renormalization in continuity density approach is used to improve the smoothed particle hydrodynamics (SPH) approximation of boundary physical variables. This study shows that CSPM in combination with the proper strength model describing the FGM dynamic behavior, can predict the mixed plastic and brittle response of a ceramic–metal functionally graded material under high impact velocities.

Large Eddy Simulation and the effect of the turbulent inlet conditions in the mixing Tee

Abstract Thermal fatigue in Pressurized Water Reactor plants has been found to be very acute in some hot/cold Tee junction mixing zones. Large Eddy Simulation (LES) can be used to capture the unsteadiness which is responsible for the large mechanical stresses associated with thermal fatigue. Here one LES subgrid model is studied, namely the Dynamic Smagorinsky model. This paper has two goals. The first is to demonstrate some results obtained using the EDF R&D Code Saturne applied to the Vattenfall Tee junction benchmark (version 2006) and the second is to look at the effect of including synthetic turbulence at the Tee junction pipe inlets. The last goal is the main topic of this paper. The Synthetic Eddy Method is used to create the turbulent inlet conditions and is applied to two kinds of grids. One contains six million cells and the other ten million. The addition of turbulence at the inlet does not seem to have much effect on the bulk flow and all computations are in good agreement with the experimental data. However, the inlet turbulence does have an effect on the near wall flow. All cases show that the wall temperature fluctuation and the wall temperature/velocity correlation are not the same when a turbulent inlet condition is used. Inclusion of the turbulent inlet condition moves the downstream location of the maximum temperature/velocity correlation by 1 cm and reduces its magnitude by 10%. This result is very important because the temperature/velocity correlation is closely related to the turbulent heat transfer in the flow, which is in turn responsible for the mechanical stresses on the structure. Finally we have studied in detail the influence of the turbulent inlet condition just downstream of the mixing zone. We show the influence of including turbulent inlet condition on the structure of the flow Walker et al. (2009).

Grids with Unusual, High Nuclearity – A Structural Approach

AbstractPolynuclear supramolecular homoleptic grid‐like architectures containing s2 (s = 3, 4, 5) metal ions arranged like the elements of a square matrix and located in the coordination spheres generated at the intersection points (“nodes”) of the 2s bridging s‐topic ligands (the “bars” of the grid), are quite rare, but they are fascinating by their formation by self‐assembly, their structures and properties. Moreover, heteroleptic hexanuclear complete [2 × 3] grids, as well as other kinds of grids containing more than four metal centres were reported. The access to such grids necessitates the design of appropriate polytopic ligands. However, in several cases, incomplete grids were obtained instead of the expected complete grids. The structural diversity of the grids with unusual, high nuclearity reported until now is herein reviewed. (© Wiley‐VCH Verlag GmbH &amp; Co. KGaA, 69451 Weinheim, Germany, 2009)

Spatial Dynamics of Soil Moisture in a Complex Terrain in the Semi‐Arid Loess Plateau Region, China1

Abstract: Soil moisture is an important hydrological variable in reforestation practices in a water‐limited region of the Loess Plateau of northwestern China. The objective of this study was to quantify the spatial dynamics of soil moisture on a complex terrain. During 2004‐2006, a total of 313 sample points in two kinds of grid (2 × 2 m and 20 × 20 m) were arranged for soil moisture measurements (two soil layers: 0‐30 and 30‐60 cm) with Time Domain Reflectometry. The geostatistical properties of soil moisture patterns, the variance and correlation structure of the soil moisture, and the effects of terrain factors on soil moisture were analyzed. The results suggested that our sampling grid captured the spatial variability of soil moisture distributions for this complex terrain. Principal Component Analysis and Cluster Analysis statistics showed that soil moisture decreased as slope gradient increased; that sunny aspects (112.5°‐292.5°) had relatively lower soil moisture than did shady aspects (292.5°‐112.5°); that soil moisture was lowest in the SWW direction and highest in the NWN direction; and that hillslope aspect was the main factor affecting soil moisture in the 0‐ to 30‐cm soil layer, whereas the main factor for the 30‐ to 60‐cm layer was slope gradient. It was found that the relative values of soil moisture for steep slopes (&gt;36%) with shady aspect (292.5°‐112.5°), gentle slopes (&lt;36%) with sunny aspect (112.5°‐292.5°), and steep slopes with sunny aspect were 99, 82, and 80, respectively – assuming a soil moisture value of 100 for gentle slopes with shady aspect. The results of this study are expected to be relevant to and useful for reforestation planning and design, parameterization of distributed hydrology models, and land productivity assessment in the study region.