Discontinuous Grid Research Articles

Evaluation Method of Average House Demand in Iraq’s Middle Territories

Iraqi householders are commonly interesting of hybrid power systems due to the considerable shortage of grid utility to meet there simple daily residential demands. Hybrid power systems that based on combination of multiple power sources (solar panels) and (diesel or gasoline) power generators are most favorable to use there, due to the small sizes and comparatively cheap initial prices of such systems. Renewable energy sources (RES) are intermittent in nature and change seasonally and daily, which make the hourly function evaluation, of electricity demand, is very important in the design of power systems based on these sources. In this work, average house electricity demand of Iraq’s middle territories is estimated, by considered Baghdad average house demand as representative for this region, in terms of appliances sizes and annual distribution of daily operation hours. Also, solar system is designed based on the estimated consumption profile. It’s found that the estimated profile with and without two tons of refrigeration air-conditioner system provide close results to the real values of Baghdad average house demand. Beside its reliability, independence and environmentally advantages, solar system that designed here show considerably cost effective than the private business diesel generator and discontinuous grid service in this area.

2-D seismic wave propagation using the distributional finite-difference method: further developments and potential for global seismology

SUMMARY We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth’s internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency.

Automatic surface mesh generation by a binary-tree method

In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize “dirty” geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems.

Direct implementation of discontinuous-grid finite-difference method using multiple point sources method and dynamic wavefield injection

SUMMARY The classical finite-difference (FD) method stimulates wave propagation in uniform grids. In models with considerable velocity variations, the computational efficiency is compromised by oversampling in time and space. Although adopting a discontinuous grid in different wave-speed regions can improve computational efficiency, such a technique is typically hindered by low accuracy in transition zones (i.e. in the vicinity of the discontinuous-grid interface) and is typically unstable in the long term. We propose a direct implementation of the discontinuous-grid FD method by performing two simulations simultaneously: one on a coarse grid and the other on a fine grid. The proposed method applies a dynamic injection strategy to manage wavefield communication between coarse and fine submodels. Compared with previous discontinuous-grid FD methods, where the number of layers required for wavefield communication is one-half that the order of the FD scheme, the proposed method only requires one single layer, which significantly reduces the communication overhead and suppresses wavefield errors. Numerical experiments show that the results yielded by our method are consistent with the reference solutions yielded by the uniform-grid FD method via a fine grid. Furthermore, our method does not encounter numerical instability in long-term simulations. Therefore, the proposed discontinuous-grid FD method can accelerate numerical simulations while retaining stable numerical accuracy, even for long-term simulations.

Dual interpolation boundary face method for 3-D potential problem based on binary tree grids

This paper presents the dual interpolation boundary face method (DiBFM) based on a binary tree grid for solving the 3-D potential problems. The subdivision method based on binary tree algorithm is capable to generate both continuous and discontinuous grids, and to achieve the grids​ generation for arbitrary complex model much easier and automatically. By adding virtual nodes on the vertices and edges of traditional discontinuous element, the dual interpolation elements are introduced while the order is increased by two. The values of physical variables are approximated by Lagrange interpolation polynomial in the first-layer interpolation, and meshless interpolation is used to condense the degree of freedom of virtual nodes in the second-layer interpolation. Since no requirement is needed for the continuity of grids in the DiBFM, the dilemma of discontinuous grids are avoidable. In this paper, the DiBFM is implemented based on the binary tree grids to solve general problems with thin-wall structures and “geometrical construction noise”.

Application of the finite volume method for geomechanics calculation and analysis on temperature dependent poromechanical stress and displacement fields in enhanced geothermal system

The hot dry rock (HDR) development is a hot research field in recent years. Numerical simulation based on thermal-hydraulic-mechanical coupling model is a key technique for the HDR development evaluation. The calculation of geomechanics is an important part of the coupling thermal-hydraulic-mechanical simulation, and it is usually implemented by finite element method. However, meshing methods of geological modeling software are designed to serve seepage simulation, and grid quality cannot meet the requirements of finite element method. In this paper, finite volume method has been proposed to calculate the distribution of underground stress field, in order to solve the problem of discontinuous grid vertexes and calculation failure caused by finite element method. In addition, the mesh of geological modeling software is for finite difference method or finite volume method, which cannot be used directly by finite element method. In this paper, spatial discretization pattern of quasi static stress balance equation based on the finite volume method is obtained, the local grid refinement algorithm is proposed, the solution workflow of thermal-hydraulic-mechanical (THM) coupling model is presented, and the solution of displacement discretization equations and THM one way coupling model are implemented by C++ programming language. Finally, the feasibility and accuracy of the finite volume method of stress field calculation are verified through a series of numerical test examples compared with commercial finite element software. Several THM coupling simulation cases of enhanced geothermal system are presented by finite volume method. Numerical test results show that the calculation error between finite volume method and finite element method is less than 1%. Moreover, the variation of principal stress, induced by pore pressure and thermal stress, can reach 8 to 20 MPa. The finite volume method provides a unified technical framework for geomechanics and thermal-hydraulic calculation. Moreover, the method can be directly combined with geological modeling software without using two sets of grids. The results prove that the finite volume method would be a promising approach for thermal-hydraulic-mechanical simulation.

An optimal frequency-domain finite-difference operator with a flexible stencil and its application in discontinuous-grid modeling

We have developed an optimal method to determine expansion parameters for flexible stencils in 2D scalar-wave finite-difference frequency-domain (FDFD) simulation. Our stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, in which the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. Our method can work in an FDFD discontinuous grid with arbitrary integer coarse- to fine-grid spacing ratios. Numerical examples are developed to determine how to apply this optimal method to discontinuous-grid FDFD schemes with spacing ratios of 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, and the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, our discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging, and full-waveform inversion.

Solution-dependent predictor-corrector flux mapping algorithm for discrete ordinates calculation on multilevel discontinuous grids

The block-based and cell-based discontinuous Cartesian grid techniques have been one effective method to increase the geometric description accuracy for neutronics calculation codes using the discrete ordinates method. The reliability of the transport calculation on multilevel discontinuous grids depends on the accuracy and robustness of the spatial mapping algorithm for passing angular flux between neighboring meshes. In this work, we present a predictor-corrector algorithm together with multiple mapping schemes for the zeroth-order spatial discretization methods. This algorithm uses the shape and balance factors to predict the applicability of different mapping schemes, and an optimal method can be selected from the non-negative linear and nonlinear mapping techniques. We test this algorithm on three simple problems, where the average mapping errors, region-averaged flux and local flux are compared against the references of fine standard grids. The numerical results show that our method can control the mapping errors in an acceptable range of approximately 10% for optically thick grids twice as large as the mean free path. The accuracy degradation of spatial discretization method caused by the mapping errors can be mitigated to a great extent in our algorithm.

Effect of Processing Parameters on the Structure and Properties of Powder Fe–Al Intermetallic Compounds Obtained by Sintering and Impulse Hot Pressing

The paper examines the effect of high-energy grinding and post-treatment conditions on the structure and physical and mechanical properties of iron aluminide Fe–15 wt.% Al obtained by sintering and impulse hot pressing. It was shown that the grinding of a mixture of iron and aluminum powders in a planetary mill results in the formation of lamellar particles whose morphology is preserved in the alloy structure after sintering and impulse hot pressing. After grinding, sintered intermetallic compounds obtained from powder mixtures demonstrate low physical and mechanical properties due to the low quality of grain boundaries. The use of impulse hot pressing for compaction of samples from milled powders at temperatures of 850–1150°C significantly increases the density of intermetallic compounds compared to sintered materials of a similar composition—from 5 to 6.5 g/cm3. The increase in the temperature of impulse hot pressing contributes to an increase in mechanical characteristics, where the maximum values of bending strength and fracture toughness are 880 MPa and 21 MPa · m0.5, respectively. Subsequent hightemperature annealing (1350–1450°C) leads to an improvement of the quality of grain boundaries with the formation of a predominantly discontinuous grid, coagulation of impurity segregation, and, as a result, to a sharp increase in bending strength and fracture toughness, which are 1400 MPa and 27 MPa · m0.5, respectively. It was shown that the interparticle rupture observed in the samples after impulse hot pressing at relatively low temperatures changes to transcrystalline after hightemperature annealing.

Nonmatching Discontinuous Cartesian Grid Algorithm Based on the Multilevel Octree Architecture for Discrete Ordinates Transport Calculation

Obtaining sufficiently accurate geometric descriptions is a crucial prerequisite for reliable particle transport calculations. Conventional transport algorithms on Cartesian grids use a highly efficient sweep technique and numerous mature discretization methods despite their modeling deficiency for complex geometries. To achieve a more accurate geometric description, a cell-based nonmatching Cartesian grid algorithm is proposed on the basis of the multilevel octree architecture. Transport sweep is performed according to the tree branch relationship of nested mesh distributions. The angular flux transmission between discontinuous grids is handled by the flux spatial moment mapping technique, and multiple zero-order mapping schemes are developed, including finite element interpolation, distance interpolation, and exponential fitting methods for treating upwind flux distributions of different relative shapes. The first-order mapping schemes are modified and improved for linear and exponential short characteristic discretization methods. The mapping accuracy is evaluated for polynomial and exponential functions, and a new spatial shape factor is presented for measuring the degree of nonlinearity. The multilevel octree grid (MLTG) algorithm is tested for neutron transport benchmarks, and good agreement with Monte Carlo and standard SN results is achieved. The number of meshes in the VVER shielding model is reduced from 18 million to 2 million using 3-level octree grids with the same geometric description accuracy. Numerical verification of a one-group fixed-source problem shows that 4-level and 5-level MLTG results with proper spatial discretization schemes can achieve relative deviations of less than 3% and 5% for detector region flux, respectively.

Representation of faults in reservoir-scale geomechanical finite element models – A comparison of different modelling approaches

Different approaches exist to incorporate faults in reservoir-scale geomechanical models. Challenges are the proper representation of the fault geometry as well as the small-scale variations in the internal architecture and the mechanical properties of the fault zone regarding the typical size of such models, i.e., kilometres to tens of kilometres. The present study utilizes a simple generic fault zone model to compare three different possibilities commonly used to represent faults in finite element reservoir models. Two differ in the basic grid geometry and the arrangement of mechanically weak fault zone elements, respectively. The third uses a discontinuous grid and contact elements to represent the fault. Modelling results show remarkable differences in the calculated stress and strain patterns. The relatively strongest perturbations result for a continuous curvilinear grid adapted to the fault geometry. In contrast, the fault implementation has the least impact on local stresses and strains if it is represented as a stair-step structure contained in a rectangular grid. The use of contact elements has an intermediate effect. Modelling results are used to infer some general recommendations concerning the appropriate approach of representing faults in a numerical-geomechanical reservoir models depending on fault geometry, model scale and scope of interest.

Path planning method based on discontinuous grid partition algorithm of point cloud for in situ printing

PurposePath planning is an important part of three-dimensional (3D) printing data processing technology. This study aims to propose a new path planning method based on a discontinuous grid partition algorithm of point cloud for in situ printing.Design/methodology/approachThree types of parameters (i.e. structural, process and path interruption parameters) were designed to establish the algorithm model with the path error and the computation amount as the dependent variables. The path error (i.e. boundary error and internal error) was further studied and the influence of each parameter on the path point density was analyzed quantitatively. The feasibility of this method was verified by skin in situ printing experiments.FindingsPath point density was positively correlated with Grid_size and negatively related to other parameters. Point_space, Sparsity and Line_space had greater influence on path point density than Indentation and Grid_size. In skin in situ printing experiment, two layers of orthogonal printing path were generated, and the material was printed accurately in the defect, which proved the feasibility of this method.Originality/valueThis study proposed a new path planning method that converted 3D point cloud data to a printing path directly, providing a new path planning solution for in situ printing. The discontinuous grid partition algorithm achieved controllability of the path planning accuracy and computation amount that could be applied to different processes.

From the Flat to the City: The Construction of Modern Greek Subjectivity

Athens is not built by large scale masterplans. Large public or private housing projects are nowhere to be found. Even an empirical observation of the city makes one thing immediately apparent: the city is defined by a construction model that is actualised by a singular building unit. The polykatoikia systems, is made of buildings, on average four to five storeys high, organized in irregular, fragmented plots in a patchwork of discontinuous grids, made of in situ, labour-intensive concrete frames, filled with bricks, plastered, something that ultimately looks like a stack of slabs with rather continuous balconies. The essay develops a critical reading of this model, presenting the way this domestic environment and distinct architectural typology mediated social conflict and economic development in post-war Greece. Architecture and urban management are presented here relating production with the role and the function of family and inheritance, the real estate market, law, and the construction industry.

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

The authors acknowledge the support of the King Abdullah University of Science and Technology through the project CCF/CAF/URF/1/2596.

Discontinuous Grid Current Control of Motor Drive System With Single-Phase Diode Rectifier and Small DC-Link Capacitor

In this paper, a control method for motor drive system without electrolytic capacitor is proposed. Since dc-link capacitor of this motor drive is about 1% of the conventional one, it can satisfy the grid current regulation of IEC61000-3-2 without bulky filter circuits by directly controlling the electric output power of the inverter. However, dc-link voltage of this drive fluctuates as the rectified grid voltage. It causes higher motor current, especially at the low dc-link voltage area, and severely harms the drive efficiency. To solve this problem, proposed method keeps the dc-link voltage higher than certain limit while controlling the output power. It can improve the efficiency of the drive by lowering the d-axis current at low dc-link voltage area, with satisfying the regulation with small grid current harmonics. The proposed method includes the motor current reference generation for the limited dc-link voltage and selection of the limitation value. The improved performance of the proposed method was verified by the experimental results.

Postshock Oscillations on Non-Uniform Mesh

An investigation of postshock oscillations on non-uniform grids is performed in this paper. These oscillations are generated as shock passes through the grid interfaces. The LLF scheme is checked for 1D and 2D problems on the discontinuous grids. Oscillations are observed only for nonlinear systems and the solutions of the scalar conservation laws and linear systems behave logically. The integral curves suggest underlying properties of these oscillations. The results of the paper reveal a flaw that adaptive methods for conservation laws have to refine grids at each time step.

Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization

AbstractThis paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model–Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAM-Fluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as ). ATHAM-Fluidity operates on two- and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite–Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.

Seismic‐Hazard Analysis of Long‐Period Ground Motion of Megathrust Earthquakes in the Nankai Trough Based on 3D Finite‐Difference Simulation

The 3D wave propagation simulation is suitable for the long‐period ground‐motion hazard analysis, because the realistic seismic source and velocity structure models are applicable and ground motion at any point can be obtained. However, large‐scale simulations for various scenarios are needed to adopt uncertainty due to the source model of a large earthquake. Here we show our approach to overcome a problem of heavy computational expense. We improve computation performance of the 3D finite‐difference method by using discontinuous grids and by adapting to multigraphics processing units technique. Then, we simulate long‐period ground motion of many scenarios of a hypothetical megathrust earthquake in the Nankai trough. We use the characterized source models based on the “recipe” in the simulation. Finally, we apply the simulation results based on about 400 scenarios to a technical framework of the probabilistic seismic‐hazard analysis. The hazard maps of velocity response spectra for a given conditional exceedance probability show that the long‐period ground motion is more significant with respect to the underground structure than is the distance from the source area.

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

A translating discontinuous-grid-block model for moving boundaries of finite thickness based on multi-relaxation time version of lattice Boltzmann method has been developed. The implementation of this model to simulate moving boundary flows has been demonstrated for the cases of a cylinder in simple shear flow, a single rigid wing executing ‘clap and fling’ motion, and the propulsion of a plunging flat plate. A number of interpolation schemes of linear, quadratic and cubic natures are assessed around the discontinuous grid interface. It is shown that the implementation of a body-fitted refined mesh that moves along with the object reduces the spurious oscillations registered in the force and velocity measurements compared to a single coarse grid block. Moreover, use of multiple relaxation times helps overcome stability issues at high Reynolds number, normally encountered in the single-relaxation time model. Significantly, in the former model the same base grid could handle flows with good accuracy for 10 ≤ Re ≤ 1000. The proposed technique offers significant advantage in terms of capturing flow around moving solids at lower computational cost and simulation time as compared to the stationary discontinuous-grid-block method.

Mesh grading approach for wave propagation in high velocity-contrast media

A mesh grading approach based on investigated lump method has been presented for simulating wave propagation in high velocity-contrast media. Unstructured fine grids are used to discretize the low wave-velocity medium in order to ensure the accuracy of numerical computation, and unstructured coarse grids are used for the high wave-velocity medium in order to substantially reduce the computational cost. On the interface, one coarse grid can match the fine grids of arbitrary odd number. The key feature of the proposed method is the constructions of investigated lumps on the interfaces of media. The transition zone, which is commonly used in the discontinuous grid scheme based on the staggered-grid finite-difference method, will not be used any more. Moreover, the computational instability that the discontinuous grid schemes frequently encountered does not arise in the proposed method. The comparisons with the analytical solutions and the application in studying the effects of sedimentary basin demonstrated that the mesh grading approach is a valid, accurate, convenient and flexible algorithm in simulating wave propagations in high velocity-contrast media with irregular interfaces.