Grid Step Research Articles

Применение метода декомпозиции области для решения задачи контактного взаимодействия осесимметричных тел

Several variants of domain decomposition method are presented, including overlapping methods (multiplicative and additive Schwarz methods) and nonoverlapping methods (Neumann-Dirichlet and Neumann - Neumann). The results of their application for solving the two-dimensional problem of loading a section of an elastic pipe with pressure are considered. The dependence of the number of external iterations on the grid step and on the number of subdomains has been investigated. It has been shown that the best results are obtained for the two-level Schwarz additive method. This method is generalized to the case of solving the problem with the contact of the column of the body. To take into account the contact between the bodies when solving the local problem in each subdomain, the Neumann -Dirichlet method is used. Results of application of two-level Schwarz additive method for numerical simulation of stress-strain state of fuel element section are presented.

Аpplying prediction models for short-term hail forecasting in Southern Ukraine

Formulation of the problem. Often natural disasters cause significant damage to the economy and the population, having a devastating nature, especially when a complex of dangerous weather conditions are created, which mutually reinforce their negative impact: storm rains accompanied by storm winds, thunderstorms with hail, etc. Increasing the validity and timeliness of storm warnings about hail occurrence is one of the main urgent tasks of operational meteorological support. The geographical position of Ukraine, the diversity of climatic conditions and the features of the synoptic processes on its territory contribute to the complex spatial and temporal distribution of the occurrence of natural meteorological phenomena (NMP). In recent years, the frequency of extreme weather phenomena has increased due to significant climate fluctuations. Often natural disasters cause significant damage to the economy and the population, having a devastating nature, especially when a complex of dangerous weather conditions is created. These weather conditions mutually reinforce their negative impact: storm rains accompanied by storm winds, thunderstorms with hail, etc. Increasing the validity and timeliness of storm warnings about hail occurrence is one of the main urgent tasks of operational meteorological support. The purpose of the article to study the synoptic and thermodynamic conditions of large hail occurrence in the territory of southern Ukraine, as well as the possibility of using forecasting models for short-term forecast of hail. Methods. Using of high spatial resolution forecasting models and GFS objective data or other resources. Results. The conditions of occurrence of two cases of hailstorms in the territory of the south of Ukraine in 2017-2018 are determined. In the first episode hail was not forecasted by the weather forecasters, due to the lack of daily radio-sounding data and a rare network of aerological observations, in the other one, an extraordinary hail (D = 65 mm) was observed. As predictors in forecasting of hail and other convective phenomena it is rational to use quantitative characteristics of the atmosphere instability. Possibilities of applying different convective storm indices, as well as the use of the Global Forecast System (GFS) numerical simulation forecast data with a grid step of 0.25o × 0.25o meridians were evaluated. It has been found that the forecast of moving hail clouds is effectively implemented by using the Bunkers method. Scientific novelty and practical significance. The most informative parameters of the thermodynamic state of the atmosphere the day before hail formation have been identified - Severe Weather ThrEAT Index (abbreviated SWEAT), Convective Available Potential Energy (abbreviated CAPE), Li (Lifted Index), BRN (Bulk Richardson Number), and VI (Boyden I). Recommendations are given to improve the quality of short-term hail forecast, taking into account numerical simulation data.

Simulation of Dynamical Processes in Long Josephson Junctions: Computation of Current-Voltage Characteristics and Round Error Growth Estimation for a Second-Order Difference Scheme

The fourth-order Runge–Kutta method is commonly used to compute the current-voltage characteristics of stacks of Josephson junctions. The calculations are performed for long time intervals, and the results are updated four times at each time step. To reduce the calculation time, this study suggests using a second-order explicit scheme instead of the Runge–Kutta method. Good results are obtained in particular calculations. For all $$n$$, estimates of $$\left\| {{{G}^{n}}} \right\|$$ ensuring the bounded growth of the round errors are proved, where $$G$$ is the layer-to-layer transition operator. A specific feature of the scheme under consideration is that its coefficients depend not only on the grid step size ratio $$\gamma = \tau {\text{/}}h$$ but also on $$\tau $$ ($$\tau {\text{ and }}h$$ are the grid step sizes in $$t$$ and $$x$$). It is proved that, for all $$\gamma \leqslant 1$$, the eigenvalues of the characteristic matrix are within the unit disc ($$\left| {{{\lambda }_{j}}({{e}^{{i\phi }}})} \right| \leqslant 1$$ for all $$0 \leqslant \phi \leqslant 2\pi $$) at a distance $$O(\tau )$$ from the unit circle. The estimation method developed in this study can be used in studying other numerical methods.

Numerical Modeling of Dust Propagation in the Atmosphere of a City with Complex Terrain. The Case of Background Eastern Light Air

Micro-scale processes of dust distribution in the city of Tbilisi with very complex topography are modeled using a 3D regional model of atmospheric processes and numerical integration of the transport-diffusion equation of the impurity. The Terrain-following coordinate system is used to take into account the influence of a very complex relief on the process of atmospheric pollution. Modeling is carried out using horizontal grid steps of 300 m and 400 m along latitude and longitude, respectively. Cases of the stationary background eastern light air are considered. In the model, motor transport is considered as a nonstationary source of pollution from which dust is emitted into the atmosphere. Modeling of dust micro-scale diffusion process showed that the city air pollution depends on the spatial distribution of the main sources of city pollution, i.e. on vehicle traffic intensity, as well as on the spatial distribution of highways, and micro-orography of city and relief of the surrounding territories. It is shown that the dust pollution level in the surface layer of the atmosphere is minimal at 6 a.m. Ground-level concentration rapidly grows with the increase of vehicle traffic intensity and at 12 a.m. reaches maximum allowable concentration (MAC = 0.5 mg/m3) in the vicinity of central city mains. From 12 a.m. to 9 p.m. maximum dust concentration values are within the limits of 0.9 - 1.2 MAC. In the mentioned time interval formation of the high pollution zones, the slow growth of their areas and the value of ground-level concentrations take place. These zones are located in both central and peripheral parts of the city. Their disposition and area sizes depend on the spatial distribution of local wind-generated under the action of complex terrain, as well as on the processes of turbulent and advective dust transfer. From 9 p.m. to 24 p.m. reduction of dust pollution and ground-level concentration takes place. After midnight the city dust pollution process continues quasi-periodically.

METHOD OF SIGNAL PARAMETERS ESTIMATION OF RADIOSTATIONS WITH FAST FREQUENCY HOPPING SPREAD SPECTRUM

Modern special-purpose radios utilize ultra-short burst mode with frequency hopping spread spectrum. Such digital radios operate, as a rule, in the fast frequency hopping spread spectrum mode and use a considerable number of frequency channels with frequency separation between adjacent channels, which is significantly less than the spectrum width of the frequency element. The main modulation in such radios is frequency manipulation. The identification of signals with fast frequency hopping spread spectrum and frequency manipulation is performed by estimating the speed of frequency tuning, the speed of information transmission, the number of frequency channels and the step of the frequency grid and comparing the obtained values with the corresponding characteristics of known radio stations with fast frequency hopping spread spectrum. The time limits and the duration of the frequency elements are calculated by the envelope of the received signal. For this purpose, a suitable method has been developed, which consists in filtering the envelope by means of a moving average window for suppression of the noise component and threshold processing. The threshold value is selected by the given probability of its exceeding by noise sample. The proposed approach to determining the time limits of frequency elements does not require any a priori signal information. To determine the frequencies of the frequency elements periodogram estimates are used. An exponential extrapolation of the discrete power spectrum was used to increase the frequency resolution at a fixed window length of the fast Fourier transform. It is shown that in order to uniquely determine the step of the frequency grid and the diversity of frequency manipulation frequencies, it is necessary to analyze the number of frequency elements not less than the number of frequency channels. By analyzing the histogram of the differences of sorted frequency vector of the frequency elements, determine the frequency grid, frequency diversity and the multiplicity of frequency manipulation. An approximate estimate of the number of frequency channels is calculated as the ratio of the magnitude of the frequency vector of the frequency elements to the step of the frequency grid. As a rule, symbol transmission at frequency manipulation is carried out at orthogonal frequencies, so it can be roughly assumed that the symbolic speed is equal to the frequency diversity of the frequency manipulation. The baud rate can be set only after signal demodulation and bit stream analysis, which can determine the frame structure and the number of service and information bits. The proposed method provides the estimation of the values of the parameters necessary for the identification of radio stations of signal parameters with a relative error not exceeding 0.3%, with values of signal to noise ratio not lower than 5 dB.

Kinetic Methods for Solving Unsteady Problems with Jet Flows

The study of nonstationary rarefied gas flows is currently paid much attention. Such interest to these problems is caused by the creation of pulsed jets used for the deposition of thin films and special coatings on solid surfaces. However the problems of nonstationary rarefied gas flows have not been studied sufficiently fully because of their large computational complexity. In this paper the computational aspects of investigating the nonstationary flows of a reflected gas from a wall and flowing through a suddenly formed gap is considering. The objective of this study is to analyze the possible numerical kinetic approaches for solving such nonstationary problems and to identify the difficulties encountered in solving.When studying the gas flows in strong rarefaction regimes one should consider the Boltzmann kinetic equation, but its numerical implementation is rather laborious. In order to use more simple approaches based for example on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference of the solutions of the model equations and the Boltzmann equation. For this purpose two auxiliary problems are considered: reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas. Numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but a strong dependence on the velocity grid step . The detailed velocity grid is necessary to avoid non-monotonous behavior of macroparameters caused by the “ray effect”. To reduce numerical costs on detailed grid a hybrid method based on the synthesis of model equation and the Boltzmann equation is proposed. Such approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The results presented in this paper were obtained using two different software packages Unified Flow Solver (UFS) [13] and Nesvetay 3D [14-15]. Note that UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility of calculating both the Boltzmann equation and model equations is realized. The Nesvetay 3D complex was created to solve the Shakhov model equation, (S-model) and makes it possible to calculate on non-structured non uniform grids in velocity and physical spaces.Translated from Russian. Original text: Mathematics and Mathematical Modeling. 2018. no. 4. Pp. 27-44.

Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures

AbstractAn experimental quantification of the strength and volume of real, heterogeneous, fractured rock masses is crucial when assessing rock slope stability. In order to quantitatively characterize the internal structure of fractured rock slopes, we present three‐dimensional numerical simulations of seismic wave propagation and compare with observations. We introduce a simple, effective model for fractured rock mass, which can easily be applied to simulate weak‐motion seismic wave propagation. The macroscopic compliant fractures cutting the rock mass are modeled as finite‐width zones of reduced elastic parameters characterized by shear and normal stiffness. The widths of such zones are not fixed and can be adjusted to fit the grid step in the numerical method. The proposed rock mass model is applied and tested for the Walkerschmatt site in southwest Switzerland. Synthetic ambient vibrations are generated using a finite‐difference method for the fractured rock mass, shaped by the real terrain geometry, and compared with the measurements. The observed seismic response is satisfactorily reproduced in a broad frequency range (0.5–10 Hz). The synthetized response is primarily controlled by the stiffness, depth, number of fractures, and inertial mass of the fractured rock. The simulated amplification and ground‐motion directionality correspond with the observed levels, unless (1) the simplified cracks reach depths of 200–300 m; and (2) the fracture network is larger with respect to the mapped network. This illustrates the potential of ambient vibration methods in combination with numerical simulations to infer depth, volume, and mechanical characteristics of slope instability.

A GPU-Based Grid Traverse Algorithm for Accelerating Lightning Geolocation Process

Most lightning location networks are based on real-time analytical solutions of certain simplified models, while the reality is much more complicated. In this paper, we introduce a graphics processing unit (GPU)-based parallel computing algorithm that can extensively benefit lightning geolocation networks. For a network running this GPU-based algorithm, one can build up a geolocation database based on numerical solutions of certain complete models in advance, and lightning geolocations can then be easily determined with a grid-searching technique in real time. One such grid-searching technique, is the grid traverse algorithm (GTA) for the traditional time of arrival technique. By running GPU-based GTA in a six-station two-dimensional (2-D) and a five-station 3-D networks, we show that extremely high network performance can be achieved, with a processing speed of about 2700 times faster than CPU-based GTA. The location accuracy of GPU-GTA is examined with Monte Carlo simulations, showing that GPU-GTA can locate a lightning source in real time with high accuracy. We also find that when the grid step is comparable with the inherent time uncertainty of a network, the location accuracy cannot be improved further with a finer grid step.

Modeling the viscoelastic effects in P-waves with modified viscoacoustic wave propagation

Accurate full-waveform seismic modeling is a powerful tool for understanding wave propagation and building subsurface images. However, it can be computationally expensive for viscoelastic media. Viscoacoustic seismic modeling is much cheaper, but at the trade-off of using incomplete physics. We have developed a modified viscoacoustic wave simulation algorithm for modeling the viscoelastic effects of P-waves. The algorithm contains two viscoacoustic forward-modeling steps; the first is the same as the traditional viscoacoustic modeling, whereas the second propagation is generated using a residual error source, which is derived by comparing the viscoacoustic and viscoelastic wave equations in the form of stress-particle velocity formulations. The corrected P-wave particle velocities can be obtained by adding the wavefield from the second simulation step to the original (the first simulation step) viscoacoustic wavefield. Only P-waves are modeled. The overall cost is about twice that of viscoacoustic modeling, but it is significantly less than a viscoelastic propagation because there are fewer calculations, and we can use a coarser grid and larger time steps for the same accuracy. Numerical examples indicate that the P-wave waveforms, after correction, match those from viscoelastic wave modeling better than those from the original viscoacoustic simulation. Our method provides a cost-efficient alternative for approximating the viscoelastic effects in P-wave modeling.

Equivalent method of coarsening permeability in low permeability reservoirs

In view of considering reservoir segregation, it is preferred that the permeability coarsening method is of great importance. Based on the mesh coarsening technique, the conceptual model of low permeability reservoir segregation distribution is established, and different permeability coarsening methods are selected to simulate the daily production of oil field and other parameters and the error analysis. The most appropriate permeability equivalent method and the grid step size are selected at last. It is concluded that the harmonic-arithmetic mean method is the best method to simulate errors of the parameters, and it is also the best way to calculate the equivalent permeability in low permeability reservoir considering the reservoir segregation distribution. After the coarsening, the grid step on horizon is 20 m or so and on vertical is 4-6m.

Analysis of line loss status and loss reduction measures in eastern Inner Mongolia Area

Loss reduction, energy saving, safe and stable operation of power grid are two major themes of power companies, among them, line loss is a comprehensive technical indicator for measuring and assessing the production technology and management level of power supply enterprises. It is also a comprehensive indicator for evaluating the operation level and production level of power enterprises. The loss is the inevitable cost of the power grid when transmitting power, which related to the planning, operation level and operational efficiency of the power grid, the calculation and analysis of the loss can effectively indicate the direction for the next step of the power grid and provide effective guidance for the economic operation of the power grid.

ORIENTATION-BASED PAIRWISE COARSE REGISTRATION WITH MARKERLESS TERRESTRIAL LASER SCANS

Abstract. In this paper, pairwise coarse registration is presented using real world point cloud data obtained by terrestrial laser scanner and without information on reference marker on the scene. The challenge in the data is because of multi-scanning which caused large data size in millions of points due to limited range about the scene generated from side view. Furthermore, the data have a low percentage of overlapping between two scans, and the point cloud data were acquired from structures with geometrical symmetry which leads to minimal transformation during registration process. To process the data, 3D Harris keypoint is used and coarse registration is done by Iterative Closest Point (ICP). Different sampling methods were applied in order to evaluate processing time for further analysis on different voxel grid size. Then, Root Means Squared Error (RMSE) is used to determine the accuracy of the approach and to study its relation to relative orientation of scan by pairwise registration. The results show that the grid average downsampling method gives shorter processing time with reasonable RMSE in finding the exact scan pair. It can also be seen that grid step size is having an inverse relationship with downsampling points. This setting is used to test on smaller overlapping data set of other heritage building. Evaluation on relative orientation is studied from transformation parameter for both data set, where Data set I, which higher overlapping data gives better accuracy which may be due to the small distance between the two point clouds compared to Data set II.

Reconstruction of Large-Scale Sea Surface Temperature and Salinity Fields Using Sub-Regional EOF Patterns From Models

A method for reconstruction of gridded fields of sea surface variables from time-dependent observations, using sub-regional EOF (Empirical Orthogonal Functions) patterns from models, is presented and tested. Covariance fields, calculated from the model results over long enough time span, are used to find EOF modes. The gravest “observational” amplitudes and their first temporal derivatives are determined from the least-square minimization of fitting errors in relation to the observed values. The field is reconstructed by superposition of continuous model-based mode patterns multiplied by observational amplitudes that meet adopted statistical limits. If the observational amplitude exceeds the limits, gridded fields for this and higher modes are not produced. We applied the method in the northeastern Baltic over the model time series 2010-2015. Daily averages of sea surface temperature (SST) and salinity (SSS) from the high-resolution (grid step 0.5 nautical miles) sub-regional HBM model were spatially averaged over bins of 5x5 nautical miles. Three first modes cover 99% of variance of temperature and 61.4% of salinity. As shown by experiments with pseudo-observations (model values at these points reconstructed to the model grid and then compared with the original model data), reconstruction performance depends on the configuration of the observation points in the model domain. Still, a few first modes usually produce acceptable results. When removing the SST seasonal cycle prior to EOF analysis, spatial patterns of leading modes remained practically unchanged, share of variance of the three first modes was reduced to 88,6% and reconstruction errors were reduced by about 25%. Sufficient spatial data coverage of the larger basin with ship-born observations usually takes quite long time – of the order of month; therefore, time correction of the amplitudes using the found temporal derivatives improves the accuracy of reconstruction. The method is compared with the Optimal Interpolation (OI) by using the pseudo-observations. Results show that, for SST reconstruction, the OI method is significantly worse than the EOF method. For SSS, OI is slightly better than EOF. The superiority of EOF is that the remote correlation patterns can be used in the reconstruction, which is important when the observations are sparse.

Effect of grid and time step for predicting hydrodynamic resistance of blunt body

Taking the amphibious vehicle as an example, the hydrodynamic resistance was obtained by using computational fluid dynamics (CFD). This paper investigated the influent factors which contain mesh generation and time step which influences hydrodynamic calculation, and compared the calculation results with the relevant experimental results. This paper analyzed three factors which affecting amphibious vehicle’s resistance calculation, including the first grid thickness of boundary layer and ratio for extending surface mesh to the computational domain. By means of analyzing different factors, a high calculation precision strategy which could serve as reference for amphibious vehicle’s hydrodynamic resistance was obtained.

Enhanced air quality modelling through AUSTAL2000 model in Milan urban area

Atmospheric dispersion models are a useful tools to assess air quality and emission source contributions in urban areas. Eulerian chemical and transport models (CTMs) can assess the regional background, that is the baseline level in the region of the city, and the urban background, that is the increment of concentration due to the emissions of the city, but they are not able to properly assess the very local contribution of emission sources at pollution hotspots within the city, because of their relatively large grid step. For the assessment of local sources’ contribution, Lagrangian dispersion models can be profitably used, especially when high spatial resolution modelling is required. Actually, Lagrangian models rely on a more realistic spatialization of urban emissions, unevenly distributed because of the road network layout (for traffic emissions) and of the built environment structure (for space heating emissions); additionally, Lagrangian models also account for wind field modifications induced by buildings. In this work, air quality modelling results for fine particles (PM2.5) in the city centre of Milan obtained by means of the AUSTAL2000 Lagrangian model are compared with those of CAMx Eulerian model. Model simulations where performed for a 1.7x1.7 km2 area in Milan and focused on three receptor points selected in order to represent sites with both different features in terms of the surrounding built environment and different exposure to the local emission sources. Namely, the receptors correspond to a green area, to a residential and shopping area near Milan main square, and to a congested crossroad on the inner ring road of the city centre. Comparison results show that the outcome of the Eulerian model at the local scale is only representative of a background level, similar to Lagrangian model’s outcome for the green area receptor, but fails to reproduce concentration gradients and hot-spots, driven by local sources’ emissions.

Разностная схема с оптимальным весом для уравнения диффузии-конвекции

Исследована разностная схема с весами для однородного пространственно-одномерного уравнения диффузии-конвекции. Выполнено исследование погрешности аппроксимации разностной схемы в зависимости от шага по времени на основе разложения функции решения и погрешности аппроксимации по тригонометрическому базису. Разработан алгоритм нахождения оптимального значения веса, обеспечивающий минимум погрешности аппроксимации решения исходной начально-краевой задачи для заданных значений шагов временной сетки. Улучшенная точность построенной схемы с оптимальным весом по сравнению с явной схемой и эффективность алгоритма поиска оптимального значения весового параметра продемонстрированы на примере тестовой задачи. A difference scheme with weights for a homogeneous spatially one-dimensional diffusion-convection equation is studied. An analysis of the approximation error for the difference scheme as a time step function is performed on the basis of the expansion of the solution and approximation error in a trigonometric basis. An algorithm is proposed to find the optimal weight value that ensures the minimum approximation error of the solution to an initial boundary value problem for the given values of the time grid steps. A better accuracy of the constructed scheme with the optimal weight compared to the explicit scheme as well as the efficiency of the algorithm for finding the optimal weight value is shown using a test problem.

INVESTIGATION OF THE POSSIBILITY OF THERMAL CONTROL OF POLYMER COMPOSITE STRUCTURES WHILE HEATING BY THE INTERNAL SOURCE

Dynamic temperature fields on the surface of a polymer composite material under the action of an internal heat source are considered. It is shown that the use of thermal control based on the measurement and analysis of the temperature field parameters allows detecting a defect (heat source) in the material and determining its depth and coordinates. The studies have shown the possibility of using thermal control to detect internal defects in products made of polymer composite materials when creating internal heat sources in the vicinity of defects with the use of modern thermograph systems that provide the registration of changing the temperature field of 0.1 deg and higher. The numerical solution using the finite element method and the time difference scheme is in good agreement with the analytical solution when choosing grid steps: the error is reduced to 2.4% already at a distance of three grid steps from the source. It is shown that on the basis of the measurement of the parameters of dynamic temperature fields, it is possible to determine the location of the depth of the defect (internal heating source) and its area coordinates that makes it possible significantly to extend the scope of application of thermal control.

Conditions for the Appearance and Short-Time Prediction of Strong Squalls and Tornadoes in the European Part of Russia

Conditions for the occurrence and the possibility of a short-term prediction of strong squalls, as well as several tornadoes (mainly, weak), which caused major damage in the European part of Russia May 30, 2018, are considered. The information on the squalls is gathered from the data from the network of weather stations. In addition, data about cases of tornadoes are refined, in particular, based on the analysis of windthrows caused by them in forested regions. Synoptic and aerologic prerequisites for the appearance of squalls are considered. Squalls are modeled using the WRF model (version 3.9.1.1, the grid step is 3 km). Predicted data of the GFS and ECMWF global atmospheric models (from the ERA-5 archive) have been obtained as initial conditions. It has been established that squalls are comparatively successfully reproduced by the model.

Aeroheating reduction for blunt body using aerodome jet

A novel thermal protection concept that combines the aerodome and cooling nitrogen is introduced for aeroheating reduction in high-speed flights. Study involves the fluid–thermal interaction between the blunt body and surrounding fluid. After detailed grid and time step verification and numerical validation with available experimental results, the influence of jet pressure and jet distance on the aeroheating reduction performance are analyzed comprehensively. Results indicate that the advantages of the novel combination of aerodome and cooling nitrogen over the conventional opposing jet are mainly embodied in the following three aspects. Firstly, the stability of both the aerodome-jet and the flow field structure can be ensured in wide ranges of flight speed and jet pressure, due to the existence of aerodome. Secondly, on the premise of providing overall thermal protection for the blunt body, emphasis is placed on the direct and continuous cooling of the front part of blunt body where severe aeroheating occurs. Thirdly, the thermal protection performance can be improved without sacrificing the drag reduction performance by selecting a suitable set of jet pressure and jet distance.

Continuous Optimization and Economic Evaluation of Wind Farm Layout Based on Genetic Algorithm with Elitist Strategy

To improve the overall output power and efficiency of the wind farm, considering the cost model of a wind turbine and the multi-turbine wake interference model, using genetic algorithm with elitist strategy, the real-coded method is used to optimize the wind farm layout. The optimal calculation results of three typical flow conditions show that: Compared with the results of the discrete optimization method, the continuous optimization can increase the output power and efficiency of a wind farm by about 1.05% ∼ 4.27% in the same amount of wind turbines, increase the economy of a wind farm by about 1.04% ∼ 4.10%, and avoid the influence of grid step size on the optimization results, so that it is possible to perform a finer micro-siting.