Variable Grid Size Research Articles

Numerical simulation study of sympathetic detonation in stages

A Direct Numerical Simulation (DNS) scheme for solving the temporal-spatial multiscale problem of sympathetic detonation is proposed. According to the physical and chemical properties, the SD process is divided into two stages in the numerical simulation. Two different grid sizes are used in the two stages to improve calculation accuracy and efficiency. The local Level Set Method is used to accurately track the multi-material interface, and the Harten Lax and van Leer Contact (HLLC) method is used to solve local Riemann problem. Based on the computing method mentioned above, choosing the high evolution Weighted Essentially Non-Oscillatory (WENO) scheme for the spatial discretization of governing equations in alliance with Total Variation Diminishing (TVD) Runge-Kutta for time discretization, the Eulerian code of SD is developed. It solves the data interaction between the two solvers with variable grid size and time step, and realizes the three-dimensional parallel computing of SD. Composition B is taken as the research object. The processes of SD in different stand-off distances are analyzed. The transmission and safety distances of Composition B are given. The test under the same conditions is designed to verify the numerical simulation. The numerical simulation results are in good agreement with the experiment, which proves the accuracy and feasibility of the numerical method.

A coupled atmospheric–hydrologic modeling system with variable grid sizes for rainfall–runoff simulation in semi-humid and semi-arid watersheds: how does the coupling scale affects the results?

Abstract. The coupled atmospheric–hydrologic modeling system is an effective way to improve the accuracy of rainfall–runoff modeling and extend the lead time in real-time flood forecasting. The aim of this study is to explore the appropriate coupling scale of the coupled atmospheric–hydrologic modeling system, which is established by the Weather Research and Forecasting (WRF) model and the gridded Hebei model with three different sizes (1 km×1 km, 3 km×3 km and 9 km×9 km). The Hebei model is a conceptual rainfall–runoff model designed to describe a mixed runoff generation mechanism, including both storage excess and infiltration excess, in the semi-humid and semi-dry area of northern China. The soil moisture storage capacity and infiltration capacity of different grids in the gridded Hebei model are obtained and dispersed using the topographic index. The lumped Hebei model is also used to establish the lumped atmospheric–hydrologic coupled system as a reference system. Four 24 h storm events occurring at two small- and medium-scale sub-watersheds in northern China are selected as case studies. Contrastive analyses of the flood process simulations from the gridded and lumped systems are carried out. The results show that the flood simulation results may not always be improved with higher-dimension precision and more complicated system, and the grid size selection has a strong relationship with the rainfall evenness. For the storm events with uniform spatial distribution, the coupling scale has less impact on flood simulation results, and the lumped system also performs well. For the storm events with uneven spatiotemporal distribution, the corrected rainfall can improve the simulation results significantly, and higher resolution leads to better flood process simulation. The results can help to establish the appropriate coupled atmospheric–hydrologic modeling system to improve the flood forecasting accuracy.

Expected Worth for 2 2 Matrix Games with Variable Grid Sizes

We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.

GIS-based logistic regression for rainfall-induced landslide susceptibility mapping under different grid sizes in Yueqing, Southeastern China

The logistic regression (LR) method was applied to assess landslide susceptibility in the northern Yueqing of Zhejiang Province, China. An inventory map of 323 landslides, digital elevation models (DEMs), remote sensing images, geological map, roads and rivers were collected and utilized in the analysis. LR models using partially continuous (LR-CON) and all categorized variables (LR-CAT) were carried out under different grid sizes of 5 m, 15 m and 30 m to investigate the influence of variable type and grid size on landslide susceptibility assessment. Ten different subsets of positive (landslide) and negative (non-landslide) cases were prepared for each kind of LR models. Receiver operation characteristic (ROC) curves were employed to evaluate the performance of the LR models while cross-validation was used to validate the effectiveness of susceptibility maps. The models with and without the rainfall factor were also compared. Among the three grid sizes, the result of 15 m shows the best performance with mean AUC (the area under a ROC curve) of 82.6%. The AUC values of LR-CON models with different grid sizes all demonstrated acceptable fit (0.7 < mean AUC <0.8) while those of LR-CAT models showed an excellent fit (mean AUC > 0.8), indicating that LR method has a better performance when using all categorical variables than using partially continuous variables. Random sampling is an adoptable method to generate training group and there is no significant difference of AUC values among different data subsets. The results also showed that the accuracy of the landslide susceptibility models is higher when rainfall is included in the analyses.

A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface

PurposeThe purpose of this paper is to develop a new finite difference method for solving the seismic wave propagation in fluid-solid media, which can be described by the acoustic and viscoelastic wave equations for the fluid and solid parts, respectively.Design/methodology/approachIn this paper, the authors introduced a coordinate transformation method for seismic wave simulation method. In the new method, the irregular fluid–solid interface is transformed into a horizontal interface. Then, a multi-block coordinate transformation method is proposed to mesh every layer to curved grids and transforms every interface to horizontal interface. Meanwhile, a variable grid size is used in different regions according to the shape and the velocity within each region. Finally, a Lebedev-standard staggered coupled grid scheme for curved grids is applied in the multi-block coordinate transformation method to reduce the computational cost.FindingsThe instability in the auxiliary coordinate system caused by the standard staggered grid scheme is resolved using a curved grid viscoelastic wave field separation strategy. Several numerical examples are solved using this new method. It has been shown that the new method is stable, efficient and highly accurate in solving the seismic wave equation defined on domain with irregular fluid–solid interface.Originality/valueFirst, the irregular fluid–solid interface is transformed into a horizontal interface by using the coordinate transformation method. The conversion between pressures and stresses is easy to implement and adaptive to different irregular fluid–solid interface models, because the normal stress and shear stress vanish when the normal angle is 90° in the interface. Moreover, in the new method, the strong false artificial boundary reflection and instability caused by ladder-shaped grid discretion are resolved as well.

Variable-grid reverse-time migration of different seismic survey data

With an increasing demand for high-resolution imaging of complex subsurface structures, thin layers and hidden reservoirs, borehole and cross-well seismic migration methods have become important. However, large differences are observed in the frequency bandwidth between the surface, borehole, and cross-well surveys. Thus, variable-gridbased algorithms have been adapted to reverse-time migration. Further, we introduce Lanczos filtering to ensure the stability of wavefield calculations as well as to decrease the artificial reflections that are caused due to the variable grid size. Finally, we observe that the application of this method to surface survey, borehole, and cross-well seismic data suggests improvements in the delineation of minor fractures and steeply dipping faults.

Development of real-time laser-scanning system to detect tree canopy characteristics for variable-rate pesticide application

Improving pesticide application efficiency is increasingly important in orchard spraying. In this study, a laser-scanning system was designed to acquire gridding volumes of a tree to quantify the geometry characteristics of the tree canopy in real-time. A laser-scanning sensor mounted on a linear guide was utilized to measure the structure of a target tree canopy. A computer was used to receive measurement data from the laser scanner and obtain the movement distance of the laser-scanning sensor from a controller. An algorithm written with VC# program was designed to calculate gridding volumes of trees by recognizing valid measurement data from the laser scanner. Laboratory evaluations were conducted on three kinds of regular objects, and the maximum relative errors of section volumes of the cuboid, triangular prism and cylinder objects were 3.3%, 7.9% and 9.4%, respectively, which illustrated that the algorithm could calculate the section volumes in different parts of the objects with high accuracy. A conifer tree and an apple tree were chosen to verify detecting accuracy of the laser-scanning system at variable speeds and grid sizes. The variation coefficients of total volumes for each kind of the tree were 0.078 and 0.041, respectively, which indicated that the laser-scanning system could be applied to provide the gridding volumes of different canopy densities in real-time with good reliability for guiding a variable-rate sprayer. Keywords: laser-scanning system, sensor, tree canopy, variable-rate spray, pesticide application efficiency, gridding volumes, calculation algorithm DOI: 10.25165/j.ijabe.20171006.3140 Citation: Cai J C, Wang X, Song J, Wang S L, Yang S, Zhao C J. Development of real-time laser-scanning system to detect tree canopy characteristics for variable-rate pesticide application. Int J Agric & Biol Eng, 2017; 10(6): 155–163.

Excitonic mass gap in uniaxially strained graphene

We study the conditions for spontaneously generating an excitonic mass gap due to Coulomb interactions between anisotropic Dirac fermions in uniaxially strained graphene. The mass gap equation is realized as a self-consistent solution for the self-energy within the Hartree-Fock mean-field and static random phase approximations. It depends not only on momentum, due to the long-range nature of the interaction, but also on the velocity anisotropy caused by the presence of uniaxial strain. We solve the nonlinear integral equation self-consistently by performing large scale numerical calculations on variable grid sizes. We evaluate the mass gap at the charge neutrality (Dirac) point as a function of the dimensionless coupling constant and anisotropy parameter. We also obtain the phase diagram of the critical coupling, at which the gap becomes finite, against velocity anisotropy. Our numerical study indicates that with an increase in uniaxial strain in graphene the strength of critical coupling decreases, which suggests anisotropy supports formation of excitonic mass gap in graphene.

Physically, Fully-Distributed Hydrologic Simulations Driven by GPM Satellite Rainfall over an Urbanizing Arid Catchment in Saudi Arabia

A physically-based, distributed-parameter hydrologic model was used to simulate a recent flood event in the city of Hafr Al Batin, Saudi Arabia to gain a better understanding of the runoff generation and spatial distribution of flooding. The city is located in a very arid catchment. Flooding of the city is influenced by the presence of three major tributaries that join the main channel in and around the heavily urbanized area. The Integrated Multi-satellite Retrievals for Global Precipitation Measurement Mission (IMERG) rainfall product was used due to lack of detailed ground observations. To overcome the heavy computational demand, the catchment was divided into three sub-catchments with a variable model grid resolution. The model was run on three subcatchments separately, without losing hydrologic connectivity among the sub-catchments. Uncalibrated and calibrated satellite products were used producing different estimates of the predicted runoff. The runoff simulations demonstrated that 85% of the flooding was generated in the urbanized portion of the catchments for the simulated flood. Additional model simulations were performed to understand the roles of the unique channel network in the city flooding. The simulations provided insights into the best options for flood mitigation efforts. The variable model grid size approach allowed using physically-based, distributed models—such as the Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model used in this study—on large basins that include urban centers that need to be modeled at very high resolutions.

Numerical simulation of groundwater measurement using alternating direction methods

The groundwater measurement is obliged to take care of the issue of need water assets in numerous dry season ranges for agricultural use. In this study, we propose a groundwater stream model demonstrate that gives the pumping rates and the infusion rates individually. The objective are to propose a simply and flexible groundwater simulation using the implicit and explicit traditional finite difference methods and alternating direction methods. The groundwater model is giving the water driven head that gives the groundwater level. The understood limited distinction technique is utilized to surmise the groundwater flow. The complex geometry in the model is considered by variable grid sizes aquifer parameters, sinks and source terms. The proposed alternating direction methods are shown that they are able to use in groundwater simulation for the real-world cases.

A sharp interface method for coupling multiphase flow, heat transfer and multicomponent mass transfer with interphase diffusion

Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder–Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.

Expected Worth for 2 2 Matrix Games with Variable Grid Sizes

We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.

Finite difference method for analyzing band structure in semiconductor heterostructures without spurious solutions

To stably employ multiband k·p model for analyzing the band structure in semiconductor heterostructures without spurious solutions (SSs), the Hermitian forward and backward difference (HFBD) scheme for finite difference method (FDM) is presented. The HFBD is the discretization scheme that eliminates the difference instability and employs the Burt-Foreman Hermitian operator ordering without geometric asymmetry. The difference instability arises from employing Foreman's strategy (FS). FS removes SSs caused by unphysical bowing in bulk dispersion curve meanwhile the HFBD is the only difference scheme that can accurately adapt for it. In comparison with other recent strategies, the proposed method in this paper is as accurate and reliable as FS, along with preserving the rapidness and simplicity of FDM. This difference scheme shows stable convergence without any SSs under variable grid size. Therefore, a wide range of experiment-determined band parameters can be applied to large-scale stable simulation with this method regardless of the SSs they originally generate.

Three-dimensional viscoelastic finite-difference code and modelling of basement focusing effects on ground motion characteristics

This paper consists of two parts. The first part of the paper is concerned with developing a 3D staggered grid time-domain finite-difference (FD) code with fourth-order spatial accuracy for simulating the responses of viscoelastic geological models with a continuous variable grid size in all the directions. The 3D FD code is written in Fortran 90. In the developed code, the realistic damping in the time-domain simulation is incorporated based on the generalized Maxwell body rheological model proposed by Emmerich and Korn (GMB-EK) Geophysics 52,1252–1264, 1987 with improvements made by Kristeck and Moczo Bull Seism Soc Am 93, 2273–2280, 2003. The accuracy of implementation of the realistic damping is validated by comparing the numerically computed phase velocity, quality factors and spatial spectral damping with the same based on GMB-EK model and Futterman’s relations. It is also concluded that the grid spacing ratio up to 5.0 can be used unharmed. The second part of the paper presents the application of the developed code to simulate the basement focusing effects on ground motion characteristics in an unbounded medium. The combined effects of sediment damping and the focusing caused by the hemi-spherical (HS) and hemi-cylindrical (HC) synclinal basement topography (SBT) on the ground motion characteristics are studied. The simulated responses and the computed snapshots revealed the SBT focusing and defocusing phenomenon, intense mode conversion and diffractions of the incident waves. A good match of the spectral amplifications caused by the HS and HC basement topography models at their focus with the same computed analytically also reveals the accuracy of the developed FD code. The response of elastic HS and HC basement topography models revealed an increase of spectral amplification with an increase of frequency. Further, an increase of rate of frequency-dependent amplification towards the focus was inferred. The average spectral amplification (ASA) caused by the elastic HS basement topography model at the focus is more than the square of the same caused by the elastic HC basement topography model, and this ratio of ASA is increasing with an increase of sediment damping.

Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

Robust inverse mask synthesis is computationally intensive, and its turnaround time continues to rise hand-in-hand with the ever-shrinking integrated circuit feature size. We report the development of a cascadic multigrid (CMG) algorithm for robust inverse mask synthesis, which starts from a relatively coarse mask grid and refines it iteratively in stages, so as to achieve significant speedup without compromising numerical accuracy. Since the CMG algorithm entails frequent changes of the computational grid size, we need to intentionally introduce an analytical circle-sampling technique for modeling the forward lithography imaging and employ an edge distance error as metric to guide mask synthesis. These two techniques work nicely with variable grid sizes and are well suited for our CMG algorithm. As a result, our algorithm achieves more than four times speedup over conventional methods that synthesize a mask on a fixed fine grid. Numerical results are presented to demonstrate the validity and efficiency of the proposed method.

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

A study into extraction of geothermal energy from tailings ponds

Assessing the performance of ground-coupled heat exchangers (GCHE) of closed-loop geothermal systems installed in tailings ponds is studied. A heat transfer model is constructed, taking into account heat conduction as well as groundwater advection. A three-dimensional finite volume discretisation method over a structured mesh with variable grid size is used to solve the governing equations. The performance of a GCHE system installed in tailings ponds is assessed based on the rate of energy extraction and the outlet fluid temperature. The geothermal capacity of mine tailings ponds and its sustainable rate of heat extraction are estimated. Effects of tube network configuration and horizontal and vertical underground advection on the performance of the system are investigated. It is found that two-dimensional heat transfer models may lead to over-designed systems and the effect of advection cannot be neglected in highly pervious tailings.

Verification of the grid size and angular increment effects in lung stereotactic body radiation therapy using the dynamic conformal arc technique

The dosimetric effects of variable grid size and angular increment were systematically evaluated in the measured dose distributions of dynamic conformal arc therapy (DCAT) for lung stereotactic body radiation therapy (SBRT). Dose variations with different grid sizes (2, 3, and 4 mm) and angular increments (2, 4, 6, and 10°) for spherical planning target volumes (PTVs) were verified in a thorax phantom by using EBT2 films. Although the doses for identical PTVs were predicted for the different grid sizes, the dose discrepancy was evaluated using one measured dose distribution with the gamma tool because the beam was delivered in the same set-up for DCAT. The dosimetric effect of the angular increment was verified by comparing the measured dose area histograms of organs at risk (OARs) at each angular increment. When the difference in the OAR doses is higher than the uncertainty of the film dosimetry, the error is regarded as the angular increment effect in discretely calculated doses. In the results, even when a 2-mm grid size was used with an elaborate dose calculation, 4-mm grid size led to a higher gamma pass ratio due to underdosage, a steep-dose descent gradient, and lower estimated PTV doses caused by the smoothing effect in the calculated dose distribution. An undulating dose distribution and a difference in the maximum contralateral lung dose of up to 14% were observed in dose calculation using a 10° angular increment. The DCAT can be effectively applied for an approximately spherical PTV in a relatively uniform geometry, which is less affected by inhomogeneous materials and differences in the beam path length.

A three-dimensional hydrodynamic model for shallow waters using unstructured Cartesian grids

This paper presents a three-dimensional unstructured Cartesian grid model for simulating shallow water hydrodynamics in lakes, rivers, estuaries, and coastal waters. It is a flux-based finite difference model that uses a cut-cell approach to fit the bottom topography and shorelines and, at the same time, has the flexibility of discretizing complex geometries with Cartesian grids that can be arbitrarily downsized in the two horizontal directions simultaneously. Because of the use of Cartesian grids, the grid generation is very simple and does not suffer the grid generation headache often seen in many other unstructured models, as the unstructured Cartesian grid model does not have any requirements on the orthogonality of the grids. The newly developed unstructured Cartesian grid model was validated against analytical solutions for a three-dimensional seiching case in a rectangular basin, before it was compared with another three-dimensional model named LESS3D for circulations and salinity transport processes in an idealized embayment that is driven by tides and freshwater inflows. Model tests show that the numerical procedure used in the unstructured Cartesian grid model is robust. Similar to other unstructured models, a variable grid size has resulted in a smaller number of grids required for a reasonable model simulation, which in turn reduces the CPU time used in the model run.

Absorbing boundary conditions in a fourth-order accurate SH-wave staggered grid finite difference algorithm

This article presents the implementation of two well known absorbing boundary conditions in a fourth-order accurate staggered grid SH-wave finite difference (FD) algorithm with variable grid size, in a very simplified manner. Based on simulated results, it was confirmed that the Clayton and Engquist absorbing boundary condition causes edge-reflections in case of larger angle of incidence of body waves on the model edges. The results of various numerical experiments revealed that the Israeli and Orszag sponge boundary condition is efficient enough to avoid edge-reflections for any angle of incidence of the body. We recommend the use of both the Clayton and Engquist and Israeli and Orszag absorbing boundary conditions simultaneously to avoid any edge-reflections.