Complex terrain wind field multi-scale numerical simulation real-time assimilation method fusing external field measurement data

Abstract

The invention discloses a complex terrain wind field multi-scale numerical simulation real-time assimilation method fusing external field measurement data, and the method comprises the steps: obtaining conventional meteorological and topographic data, determining a reference point, and carrying out the simulation of a complex terrain wind field numerical value based on a mesoscale WRF mode; acquiring external field observation data and high-precision terrain data, and improving the mesoscale numerical simulation precision of the complex terrain wind field based on a four-dimensional variational assimilation method by combining the high-precision terrain and the high-resolution grid until a first preset precision requirement is met; establishing a medium-micro scale coupling simulation framework based on WRF-CFD mode coupling, and performing high-fidelity CFD numerical simulation on the target wind field; and applying a four-dimensional variational assimilation technology to the CFD simulation process to improve the CFD numerical simulation precision to meet a second preset precision requirement. According to the invention, the precision of complex terrain wind field multi-scale numerical simulation can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power generation, and in particular to a real-time assimilation method for multi-scale numerical simulation of a complex terrain wind field integrating field measurement data. Background Art

[0002] With the rapid development of the global wind power industry, wind power generation has become a key technology for achieving energy transition and addressing climate change. However, wind fields in complex terrains are characterized by variable wind direction, high turbulence intensity, unsteady wind patterns, and multi-scale characteristics, posing significant challenges to the accurate assessment of wind energy resources. Traditional mesoscale and microscale coupled simulation methods, such as the combination of the WRF model and CFD technology, can account for both mesoscale atmospheric conditions and microscale terrain effects, but they still lack simulation accuracy.

[0003] While the WRF model can simulate spatiotemporally varying wind speeds and turbulence in mesoscale simulations, its accuracy is limited by numerous assumptions in the planetary boundary layer (PBL) model, large grid spacing, and insufficient terrain resolution. Data assimilation methods, particularly observational nudging based on four-dimensional variational assimilation, can improve the accuracy of mesoscale WRF simulations. However, when applied to wind simulations over complex terrain, the effects of grid spacing, terrain resolution, and assimilation frequency can lead to the loss of key terrain flow details and distorted wind simulations, limiting overall simulation accuracy.

[0004] In microscale simulations, RANS models based on the eddy viscosity assumption suffer from closed-loop model errors and inaccurate turbulence generation, limiting simulation fidelity. While LES-based data assimilation methods have shown potential for improving microscale CFD simulations, applying observational nudging methods to microscale CFD simulations of wind fields over complex terrain still faces numerous challenges, such as optimizing temporal parameters, defining horizontal and vertical spatial weighting functions, and determining horizontal and vertical influence ranges.

[0005] In summary, the existing technology lacks a multiscale simulation technology for wind fields over complex terrain that can simultaneously integrate data assimilation methods into both the WRF process and microscale CFD simulations, while fully accounting for factors such as grid resolution, terrain resolution, assimilation frequency, and unsteady effects. Therefore, developing a new meso-microscale coupled simulation technology based on data assimilation methods to improve the accuracy of numerical simulations of wind fields over complex terrain has important practical significance and application value. Summary of the Invention

[0006] The purpose of the present invention is to provide a real-time assimilation method for multi-scale numerical simulation of wind fields in complex terrain that integrates field measurement data. In the mesoscale assimilation process, high-precision terrain, high grid resolution and high-frequency observation data assimilation technology are adopted. In the microscale assimilation process, a multi-point real-time assimilation method is adopted, and the assimilation weight function and weight coefficient are optimized. A real-time assimilation method for multi-scale numerical simulation of wind fields in complex terrain that integrates field measurement data is proposed, which improves the accuracy of multi-scale numerical simulation of wind fields in complex terrain.

[0007] In order to achieve the above technical objectives, the technical solution adopted by the present invention is: A real-time assimilation method for multi-scale numerical simulation of wind fields in complex terrain by integrating field measurement data, the method comprising the following steps: S1, obtaining conventional meteorological and terrain data, determining a reference point, and numerically simulating the complex terrain wind field based on the mesoscale WRF model; determining the accuracy of the mesoscale numerical simulation of the complex terrain wind field; if it meets the first preset accuracy requirement, proceeding to step S3; otherwise, proceeding to step S2; S2: Acquire field observation data and high-precision terrain data, combine the high-precision terrain and high-resolution grid, and improve the accuracy of mesoscale numerical simulation of wind fields in complex terrain to meet the first preset accuracy requirement based on the four-dimensional variational assimilation method; S3, establishing a meso-microscale coupled simulation framework based on the WRF-CFD model coupling, and performing high-fidelity CFD numerical simulation of the target wind farm; judging the accuracy of the CFD numerical simulation; if it meets the second preset accuracy requirement, the process ends; otherwise, proceeding to step S4; S4, applying the four-dimensional variational assimilation technology to the CFD simulation process to improve the accuracy of the CFD numerical simulation to meet the second preset accuracy requirement.

[0008] Step S1 further includes the following steps: S11, determine conventional climate input data and topographic data; S12, selecting the center of the wind field as the reference point of the wind field to be simulated, obtaining its longitude and latitude; removing the start time of the mesoscale WRF model, and determining the simulation time period of the wind field to be simulated; S13, determine the computational domain range, grid scale, nesting method, parameterization scheme configuration, monitoring point locations and monitoring variables for the mesoscale WRF simulation; S14, perform mesoscale numerical simulation of wind fields over complex terrain and analyze the results.

[0009] Furthermore, in step S13, the calculation domain range is determined according to the reference point position and the target wind field size; the grid scale and time scale of each nested domain are determined according to the complexity of the underlying surface terrain; the nesting method is bidirectional nesting; the parameterization scheme includes microphysical processes, shortwave and longwave radiation, surface and land surface processes, urban and ocean models, planetary boundary layer schemes and cumulus parameterization processes; the monitoring location is the wind tower location, and the monitored variables include wind speed, pressure and potential temperature.

[0010] Furthermore, in step S1, the process of judging the accuracy of the mesoscale numerical simulation of the complex terrain wind field includes: Obtain field observation data, which include the latitude and longitude and altitude of the observation location, as well as the wind speed, wind direction, temperature, humidity and air pressure variables of each observation location; use the observation data to verify whether the accuracy of the mesoscale numerical simulation of the complex terrain wind field meets the first preset accuracy requirement.

[0011] Furthermore, in step S2, the accuracy of mesoscale numerical simulation of complex terrain wind fields is improved based on the four-dimensional variational assimilation method. The data assimilation expression is: ; Where i is the index of the observation data, x, y, z are the spatial coordinates, t is the simulation time, q is the assimilated physical quantity, μ is the dry air static pressure, q0 is the observed value of the physical quantity, and q m (x i ,y i ,z i ,t) is the predicted value of the WRF model, G q is the assimilation intensity of q, N is the total number of observations, W q is a weighted function based on the distance between the grid cell and the observation point; W t 、W z and W xy Describes the assimilation strength of time and space; W xy and W z is the assimilation space weight function, W t is the time weight function; ; ; Where R is the maximum horizontal influence radius, D is the horizontal distance between the grid point and the observation point, t0 is the observation time point, and t is the simulation time. is the time window length of the observation data; W t The value range is 0 to 1.

[0012] Step S3 further comprises: S31: Establish a meso-microscale coupled simulation framework based on WRF-CFD model coupling, and use the boundary coupling method for WRF-CFD data transfer. Specifically, the spatiotemporal series of wind speed, temperature, and turbulent kinetic energy parameters corresponding to the microscale computational domain boundary are extracted from the WRF simulation results, and the extracted data are imported into the CFD simulation domain boundary through time and space interpolation for microscale calculations. S32, perform high-fidelity CFD numerical simulation of the target wind farm; S33, verify the WRF-CFD numerical simulation results based on field measured data.

[0013] In step S31, the process of establishing the coupling boundary includes the following steps: S311, determining the latitude, longitude and coordinates of a reference point, where the reference point is located at the center of the mesoscale computational domain and the microscale computational domain; S312, determining the boundary of the microscale computational domain according to the height of the mountain and the thickness of the atmospheric boundary layer; S313, extracting the boundary coordinates of the microscale computational domain; S314, extracting wind speed, turbulent kinetic energy, temperature, and pressure information corresponding to the boundary coordinates from the mesoscale numerical simulation results, and performing spatial interpolation and temporal interpolation on the extracted boundary variables, respectively. The interpolated boundary variables meet the requirements of the microscale grid in space and the requirements of the microscale simulation time step in time; S315, adding the derived boundary variables to the microscale computational domain boundary to complete the CFD numerical simulation, Step S4 further comprises: S41, add the source term F and the modified velocity field U to the momentum equation and modify the momentum equation to: ; Where: is the velocity component, subscript Represents flow direction, horizontal direction and vertical direction respectively. are coordinate components, For time, is the fluid density, is the static pressure, Indicates the position temperature, Representation is averaged in the horizontal plane; is the acceleration due to gravity, is the reference potential temperature, represents the Coriolis force coefficient, is the average angular velocity of the Earth's rotation, is the local latitude, 、 represent the directional and lateral components of the geostrophic wind, respectively; is the Dirac function, j=1, 2, 3, when hour, , 0 in other cases; is stress, is the source term for velocity correction.

[0014] S42, adjusting the flow field velocity to the target wind speed profile by updating the source term F.

[0015] Step S42 further includes: S421, calculate the weighted average wind speed within the specified grid volume at the target location: ; Where, represents the wind speed vector in the i-th grid cell corresponding to the j-th assimilation point, represents the volume within the i-th grid cell corresponding to the j-th assimilation point, j is a point to be assimilated, and m is the number of grids within the specified volume; after removing the vertical component, we get: ; Where, Represents the unit normal vector in the vertical direction; S422, read the wind speed vector of the target position at the nearest time point from the wind speed time series ; S423: Calculate the wind speed adjustment value ds based on the difference between the target wind speed and the current average wind speed, and perform normalization: ; ; ; Where α is the relaxation factor, is the volume-weighted average of the inverse of the momentum equation diagonal matrix rAU; S424, calculate and obtain the spatial and temporal weight functions; wherein the horizontal weight is: ; Where r xy is the maximum horizontal influence radius, d xy is the horizontal distance between the grid point and the observation point; The vertical weight is: ; Where r z is the maximum vertical influence range, d z is the vertical distance between the grid point and the observation point; The time weight is: ; Where t0 is the observation time point, t is the simulation time, is the time window length of the observation data; The total weight is: ; Where, 、 、 They represent the assimilation space weight function and time weight function of the j-th assimilation point respectively; S425, distribute the adjustment amount to the grid according to the weight, and update F and velocity field U as follows: ; ; The synchronously updated flux field φ is: ; Where n is the number of grids in the computational domain, The surface interpolation field of rAU, the inverse of the momentum equation diagonal matrix, is used to construct the pressure correction equation to ensure the numerical stability of velocity-pressure coupling. fvc represents finite volume convection, and interpolate represents the interpolation function, which is used to interpolate the physical quantity at the center of the grid cell to the grid interface. The area vector representing the mesh interface.

[0016] Compared with the prior art, the present invention has the following beneficial effects: Comparison with measured wind field data shows that the wind speed, wind direction, and turbulence intensity obtained from the proposed method for real-time assimilation of multi-scale numerical simulations of complex terrain wind fields, which integrates field measurements, are highly consistent with observed data. This data assimilation method offers advantages such as simplicity, ease of coding, efficient computation, and high accuracy. It provides excellent prediction accuracy for wind speed, wind direction, and the spatiotemporal distribution of turbulence, surpassing numerical simulations based on the WRF model and the WRF-CFD coupled model. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1a This is a schematic diagram of the application process of the four-dimensional variational assimilation technology (Observational Nudging) in the mesoscale WRF model; Figure 1b This is a schematic diagram of the calculation of the horizontal weight function when the four-dimensional variational assimilation technology is applied to the WRF model; Figure 1c This is a schematic diagram of the time weight function calculation when the four-dimensional variational assimilation technology is applied to the WRF model; Figure 2 This is a schematic diagram of the process of establishing the coupling boundary under the WRF-CFD model coupling framework; Figure 3 This is a schematic diagram of the application process of four-dimensional variational assimilation technology (Observational Nudging) in the micro-scale CFD calculation process; Figure 4 It is a schematic diagram of the terrain at the location of a certain wind farm radar (radar is used to obtain field measurement data); Figure 5a This is a schematic diagram of static data for conventional terrain (USGS, when simulating wind fields in complex terrain based on the mesoscale WRF model); Figure 5b This is a schematic diagram of high-resolution terrain static data (SRTM 30, when simulating wind fields over complex terrain based on the mesoscale WRF model); Figure 6a This is a schematic diagram of the microscale CFD computational domain and grid when simulating wind fields in complex terrain based on the WRF-CFD model coupling framework; Figure 6b yes Figure 6a A partial enlarged view of the figure in the red rectangular box; Figure 7a This is a diagram showing the temporal changes in wind speed and direction at a certain wind farm radar location (first row: wind speed; second row: wind direction; wind speed and direction at 101m above the radar location, 2022.12.22 00:00-24:00, UTC+8, local time). Figure 7b This is a schematic diagram of the change of wind speed and wind direction with altitude at the radar location of a wind farm (left: wind speed; right: wind direction; 2022.12.22 15:00-16:00, UTC+8, local time); Figure 7c This is a schematic diagram of the change of turbulence intensity with height at the radar position of a certain wind farm (2022.12.22 15:00-16:00, UTC+8, local time); Figure 8 It is a schematic diagram of a real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to the present invention. DETAILED DESCRIPTION

[0018] The embodiments of the present invention are described in further detail below with reference to the accompanying drawings.

[0019] See also Figure 8 The embodiment of the present invention discloses a real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data, including: Step 1: Obtain conventional meteorological and terrain data, determine the reference point, and numerically simulate the wind field on complex terrain based on the mesoscale WRF model.

[0020] First, it is necessary to determine the conventional climate input data and terrain data; second, determine the latitude and longitude of the reference point of the wind field to be simulated and the simulation time period; then, determine the computational domain range, grid scale, nesting method, parameterization scheme configuration, monitoring point location and monitoring variables of the mesoscale WRF simulation; finally, based on the above configuration, complete the mesoscale numerical simulation of the complex terrain wind field and analyze the results.

[0021] Step 2: Obtain field observation data and high-precision terrain data, combine high-precision terrain and high-resolution grids, and further improve the accuracy of mesoscale numerical simulation of wind fields in complex terrain based on the four-dimensional variational assimilation method; First, obtain field observation data. Second, use the observation data to verify the mesoscale numerical simulation results in step 1. If the accuracy meets the requirements, skip step 2. Otherwise, combine high-precision terrain and high-resolution grids to further improve the accuracy of mesoscale numerical simulation of wind fields in complex terrain based on the four-dimensional variational assimilation method. Finally, after the data assimilation is completed, use the observation data to verify the assimilation effect.

[0022] Step 3: Establish a meso-microscale coupled simulation framework based on the WRF-CFD model coupling to perform high-fidelity CFD numerical simulation of the target wind field; First, a meso-microscale coupled simulation framework based on WRF-CFD model coupling was established; then, a high-fidelity CFD numerical simulation of the target wind field was carried out; finally, the WRF-CFD numerical simulation results were verified based on field measured data.

[0023] Step 4: Apply 4D variational assimilation to the CFD simulation process to further improve the accuracy of the WRF-CFD coupled simulation. If the WRF-CFD results in step 3 meet the accuracy requirements, skip step 4; otherwise, apply 4D variational assimilation to the CFD simulation process to further improve the accuracy of the WRF-CFD coupled simulation.

[0024] The preferred examples of each step are introduced in detail below.

[0025] 1. Obtain conventional meteorological and topographic data, determine reference points, and numerically simulate the wind field over complex terrain based on the mesoscale WRF model.

[0026] First, we need to determine the general climate input data and terrain data. For meteorological data, we can use the fifth generation (ERA5) data from the European Centre for Medium-Range Weather Forecasts (ECMWF), which has a spatial resolution of 0.25° and a temporal resolution of 1 hour. For static data on general terrain types and terrain heights, we can use data from the United States Geological Survey (USGS), which has a maximum spatial resolution of 30 inches.

[0027] Next, determine the latitude and longitude of the reference point for the wind farm to be simulated, as well as the simulation time period. The reference point should be the center of the wind farm. The simulation time period should exclude the startup time of the mesoscale WRF model, also known as the spin-up time. This is typically recommended to be 6-12 hours, but can be extended to 24 hours for more complex cases.

[0028] Next, determine the computational domain, grid scale, nesting method, parameterization scheme configuration, monitoring point locations, and monitored variables for the mesoscale WRF simulation. The computational domain is determined based on the reference point location and target wind field size. The innermost nested domain grid scale can be 1 km or 3 km, while the outermost nested domain grid scale can be 20-30 km. Three or four layers of nesting are possible. A bidirectional nesting method is used for nesting. Parameterization schemes include microphysical processes, shortwave and longwave radiation, surface and land processes, urban and ocean models, planetary boundary layer schemes, and cumulus cloud parameterization. For mesoscale numerical simulations of wind fields over complex terrain, the Thompson graupel scheme and WDM6 are recommended for microphysical processes. For shortwave and longwave radiation, the combination of the RRTMG and RRTMG schemes is preferred. For near-surface layer simulations, the Monin-Obukhov scheme is generally used, combined with the MYJ planetary boundary layer scheme. For areas of China significantly affected by humidity, the MYNN 2.5 level TKE planetary layer scheme can be used, combined with the MYNN near-surface layer scheme. For land surface processes and cumulus convection parameterization, the Noah scheme and Kain-Fritsch (new Eta) are generally recommended. Monitoring locations are at wind towers, and monitored variables can include wind speed, pressure, and potential temperature. Finally, based on the above configuration, a mesoscale numerical simulation of wind fields over complex terrain is completed, and the results are analyzed.

[0029] 2. Acquire field observation data and high-precision terrain data, combine high-precision terrain and high-resolution grids, and further improve the accuracy of mesoscale numerical simulations of wind fields in complex terrain based on the four-dimensional variational assimilation method.

[0030] In step 2, the field observation data should include the latitude and longitude of the observation site and the altitude of the observation location (or the height above the ground of each observation layer). The observation data include variables such as wind speed, wind direction, temperature, humidity, and air pressure. The integrity and reliability of the observation data must be guaranteed, and the time resolution of the observation data must be less than or equal to 10 minutes.

[0031] The mesoscale numerical simulation results in step 1 are verified using observational data. If the accuracy meets the requirements, step 2 is skipped. Otherwise, the accuracy of mesoscale numerical simulation of wind fields in complex terrain will be further improved based on the four-dimensional variational assimilation method, combining high-precision terrain and high-resolution grids.

[0032] like Figure 1a As shown in Figure 2, the observational nudging method is used for data assimilation in the mesoscale WRF model, and its core expression is: ; Where i is the index of the observation data, x, y, z are the spatial coordinates, t is the simulation time, q is the assimilated physical quantity (which can be velocity, temperature, humidity, etc.), μ is the static pressure of dry air, q0 is the observed value of the physical quantity, and q m (x i ,y i ,z i ,t) is the predicted value of the WRF model, G q is the assimilation intensity of q, N is the total number of observations, W q is a weighted function based on the distance between the grid cell and the observation point. t 、W z and W xy Describes the assimilation intensity in time and space. Assimilation space weight function W xy and W z Define the spatial assimilation weight, and the time weight function W t Defines the duration and strength of the weight over time. Typically, W t It gradually increases from 0 to 1, and then gradually decreases back to 0.

[0033] The assimilation level weight function is defined as follows: ; Where R is the maximum horizontal influence radius, and D is the horizontal distance between the grid point and the observation point, as Figure 1b shown.

[0034] like Figure 1c As shown, the time weight function is defined as: ; Where t0 is the observation time point, t is the simulation time, is the length of the time window for observation data (in hours).

[0035] Allows you to specify how variables are assimilated vertically, either with full weights and / or with relaxation functions relative to the surface or the top of the boundary layer, and can be set in different states (stable or unstable). Vertical weights are typically set small so that data are assimilated only at their own eta level.

[0036] When using 4D variational assimilation in the mesoscale WRF model, the observational data must first be converted to the little_r format. Then, using the OBSGRID code, it must be further converted to the OBS_DOMAIN*01 format (where * represents the number of the nested domain to be assimilated). The data assimilation control parameters are then configured, including the start and end times of assimilation, the specific nested domain to be assimilated, the variables to be assimilated, the horizontal and vertical impact ranges during data assimilation, the data assimilation time window, and the data assimilation intensity. The horizontal impact range can be 180-240 km. During multi-layer assimilation, vertical impacts can be controlled by interpolating the observational data pressure. Interpolation will not be performed at model levels where the vertical interval of observations is greater than or equal to the maximum pressure interval (obs_max_sndng_gap). The data assimilation time window can be 0.11 hours (corresponding to a 10-minute temporal resolution for the observational data). The data assimilation intensity can be 6.0×10 -4 .

[0037] During data assimilation, the innermost nested domain uses the Shuttle Radar Topography Mission (SRTM) 30 high-precision topographic data to replace the USGS data. The innermost grid resolution can be 200-333 meters. Finally, after the data assimilation is completed, the assimilation results are verified using observational data.

[0038] 3. Establish a meso-microscale coupled simulation framework based on WRF-CFD model coupling to perform high-fidelity CFD numerical simulation of the target wind field.

[0039] In step 3, first, a meso-microscale coupled simulation framework based on WRF-CFD model coupling is established. Figure 2 This is the process for establishing a coupled boundary within the WRF-CFD model coupling framework. WRF-CFD data transfer is performed using the boundary coupling method. The spatiotemporal series of parameters such as wind speed, temperature, and turbulent kinetic energy corresponding to the microscale computational domain boundary are extracted from the WRF simulation results. These are then imported into the CFD simulation domain boundary through temporal and spatial interpolation for microscale calculations. Establishing the coupled boundary is accomplished in the following steps: 1) Determine the latitude, longitude and coordinates of the reference point, which is generally located at the center of the mesoscale and microscale computational domains; 2) Determine the boundary of the microscale computational domain, which is generally determined by the height of the mountain and the thickness of the atmospheric boundary layer; 3) Extracting the coordinates of the microscale computational domain boundary using the OpenFOAM data monitoring tool combined with Python scripts; 4) Extract wind speed, turbulent kinetic energy, temperature, pressure, and other information corresponding to the boundary coordinates from the mesoscale numerical simulation results. Here, the (x, y, z) coordinates need to be converted to longitude, latitude, and altitude. Both coordinates are assumed to be in the UTM projection system. Due to the large difference between the mesoscale and microscale grids, spatial interpolation is required. This is accomplished using a combination of Fortran scripts and Python scripts. 5) During microscale calculations, the boundary variables derived in step 4) are added to the microscale computational domain boundary to complete the CFD numerical simulation. Since the time steps of mesoscale and microscale simulations also deviate, time interpolation is required here.

[0040] Linear interpolation is used to assign values ​​to time steps between any two moments. Mesoscale data is extracted based on altitude. Spatial interpolation uses triangulation / linear interpolation.

[0041] In order to ensure the consistency between the mesoscale simulation output data and the microscale simulation boundary input data, meso-microscale terrain fusion is required.

[0042] In order to solve the problems of insufficient pulsation in mesoscale numerical simulation and slow development of near-ground turbulence, artificial synthetic turbulence driven by measured data is added on the basis of the inlet and outlet boundaries.

[0043] The main steps of microscale computational domain mesh generation technology are as follows: 1) Prepare terrain files (convert the .map format terrain files to .stl format terrain files in advance); 2) Prepare blockMeshDict and snappyHexMeshDict files; 3) Run the script to generate the mesh file (after the mesh is generated, perform a mesh quality check).

[0044] The east, south, west, and north sides of the microscale computational domain are all inlet and outlet boundary conditions, and the vertical top and bottom are the top and bottom boundaries, respectively. In the inlet and outlet boundary conditions, the variables U and T adopt time-varying boundary conditions.

[0045] Time discretization uses the time domain backward difference method (backward, second order, implicit), the gradient term discretization uses the Gaussian linear interpolation format (Gauss linear, second order accuracy, unbounded), the numerical formats of the convection term and the divergence term are basically the same, using the Gaussian linear interpolation format (Gauss linear, restrictions can also be used in the upwind direction of the linear format, such as div(phi,nuTilda) using Gauss limitedLinear 1), and the Laplace term discretization uses the Gaussian linear interpolation corrected format (Gausslinear corrected, explicit non-orthogonal grid correction).

[0046] The main methods for solving linear systems include iterative solvers based on the conjugate gradient method (PCG, for the variable p_rgh) and iterative solvers based on the biconjugate gradient method (PBiCG, for variables U, T, k, nuTilda, etc.). Preconditioners include the geometrically clustered algebraic multigrid preconditioner (GAMG, for the variable p_rgh) and the diagonally incomplete LU preconditioner (DILU, for variables U, T, k, nuTilda, etc.). A smoothing solver (using the DICGaussSeidel method for the variable p_rgh) is also used.

[0047] The solver uses PISO-SIMPLE to implicitly solve the momentum and pressure equations. The prediction-correction method employs the Rhie-Chow interpolation method, and the temperature equation is incorporated into the correction loop. A high-fidelity CFD simulation of the target wind field is then performed. Finally, the WRF-CFD simulation results are validated against field measurements.

[0048] Fourth, apply four-dimensional variational assimilation technology to the CFD simulation process to further improve the accuracy of WRF-CFD coupled simulation.

[0049] If the accuracy of the WRF-CFD results in step 3 meets the requirements, step 4 is skipped; otherwise, the four-dimensional variational assimilation technique is applied to the CFD simulation process to further improve the accuracy of the WRF-CFD coupled simulation.

[0050] In step 4, when the 4D variational assimilation technique is applied to the CFD simulation, a source term F is added to the momentum equation to modify the velocity field U. The calculation of the source term is based on the time and space weights and the difference between the current velocity field and the target velocity field. The momentum equation is now expressed as: ; Where: is the velocity component, subscript Represents flow direction, horizontal direction and vertical direction respectively. are coordinate components, For time, is the fluid density, is the static pressure, Indicates the position temperature, Characterizes the average value in the horizontal plane. Other parameters: is the acceleration due to gravity, is the reference potential temperature, represents the Coriolis force coefficient ( is the average angular velocity of the Earth's rotation, is the local latitude), 、 represent the directional and lateral components of the geostrophic wind, respectively. is the Dirac function, j=1, 2, 3, when hour, , and 0 in other cases. is stress, is the source term for velocity correction.

[0051] The terms in the momentum equation represent: represents the non-constant term, represents the convection term, represents the pressure gradient term, represents stress (viscous + SGS / Reynolds), Indicates buoyancy, represents the Coriolis force, Represents a source term.

[0052] During the CFD simulation, the flow field velocity is adjusted to the target wind speed profile by updating the source term F. Figure 3 The application process of four-dimensional variational assimilation technology (Observational Nudging) in micro-scale CFD calculation process includes the following steps: 1) Calculation of average wind speed at target location: Calculate the weighted average wind speed within a specified grid volume at the target location: ; Where, represents the wind speed vector in the i-th grid cell corresponding to the j-th assimilation point, It represents the volume within the i-th grid cell corresponding to the j-th assimilation point, where j is a point to be assimilated and m is the number of grids within the specified volume.

[0053] Remove the vertical component (assuming the adjustment only affects the horizontal direction): ; Where, Represents the unit normal vector in the vertical direction.

[0054] 2) Reading the measured wind speed at the target location: Read the wind speed vector at the nearest time point of the target location from the wind speed time series .

[0055] 3) Calculation of source adjustment: Based on the difference between the target wind speed and the current average wind speed, the wind speed adjustment ds is calculated and normalized by rAU (the inverse of the momentum equation diagonal matrix): ; ; ; Where α is the relaxation factor, is the volume-weighted average of rAU.

[0056] 4) Calculation of spatial and temporal weight functions: Weight w j It consists of three parts: A. Horizontal weight (inversely proportional to horizontal distance, consistent with the Observational Nudging method): ; Where r xy is the maximum horizontal influence radius, d xy is the horizontal distance between the grid point and the observation point.

[0057] B. Vertical weight (linear decay, inconsistent with the Observational Nudging method): ; Where r z is the maximum vertical influence range, d z is the vertical distance between the grid point and the observation point.

[0058] C. Time weight (piecewise function, consistent with the Observational Nudging method): ; Where t0 is the observation time point, t is the simulation time, is the length of the time window for observation data (in seconds).

[0059] The total weight is: ; in, 、 、 Respectively represent the assimilation space weight function and time weight function of the j-th assimilation point; the maximum horizontal influence radius r xy The maximum vertical influence range r can be taken as half of the microscale calculation domain. z It is advisable to use the same height as the microscale calculation, and the determination of the time window is consistent with the observational nudging method in the mesoscale WRF model.

[0060] 5) Source item update: Distribute the adjustment amount to the grid according to the weight, and update F and velocity field U: ; ;

[0061] The flux field φ is updated synchronously: ; Where n is the number of grids in the computational domain, The surface interpolation field of rAU, the inverse of the momentum equation diagonal matrix, is used to construct the pressure correction equation to ensure the numerical stability of velocity-pressure coupling. fvc represents finite volume convection, and interpolate represents the interpolation function, which is used to interpolate the physical quantity at the center of the grid cell to the grid interface. The area vector representing the mesh interface.

[0062] Examples Select a wind farm with complex terrain (such as Figure 4 This wind farm serves as a prime example for studying wind flow characteristics in complex terrain. The wind farm's terrain is characterized by rolling hills, with the highest elevation reaching 1,824 meters and the lowest reaching 1,222 meters. The primary vegetation within the wind farm includes farmland, grassland, shrubland, and forest. The average roughness length of the area is 0.0624 meters.

[0063] Step 1: Obtain conventional meteorological and terrain data, determine the reference point, and numerically simulate the wind field in complex terrain based on the mesoscale WRF model. First, it is necessary to determine the conventional climate input data and terrain data. The meteorological data is selected from the fifth generation data (ERA5) of the European Centre for Medium-Range Weather Forecasts (ECMWF), with a spatial resolution of 0.25° and a temporal resolution of 1 hour; the static data of conventional terrain categories and terrain heights can be selected from the data of the United States Geological Survey (USGS) (such as Figure 5a The highest spatial resolution is 30".

[0064] Next, determine the latitude and longitude of the reference point for the wind field to be simulated, as well as the simulation time period. The reference point coordinates are (37.2286°N, 112.7075°E). The WRF simulation period is from 08:00 on December 20, 2022, to 00:00 on December 23, 2022 (local time, UTC+8). The WRF simulation time resolutions are 60 seconds, 20 seconds, 6.67 seconds, and 2.22 seconds, respectively. For this example, a 16-hour spin-up period is selected.

[0065] Next, the computational domain, grid scale, nesting method, parameterization scheme configuration, monitoring point locations, and monitored variables for the mesoscale WRF simulation were determined. For this case, the innermost nested domain grid scale was 1 km, and the outermost nested domain grid scale was 27 km. The projection method was set to Lambert, with spatial horizontal resolutions of 27 km, 9 km, 3 km, and 1 km, respectively, for a four-layer nesting scheme. A bidirectional nesting method was used. For this case, the WDM6 microphysical process scheme was selected. For shortwave and longwave radiation, a combination of RRTMG and RRTMG schemes was used. For the near-surface layer scheme, the Monin-Obukhov scheme was used, combined with the MYJ planetary boundary layer scheme. For land surface processes and cumulus convection parameterization, the Noah format and Kain-Fritsch (new Eta) were used. Monitoring locations were at the wind mast (which is also the radar location), and monitored variables included wind speed, pressure, and potential temperature.

[0066] Finally, based on the above configuration, a mesoscale numerical simulation of the wind field in complex terrain was completed, and the results were analyzed.

[0067] Step 2: Obtain field observation data and high-precision terrain data, combine high-precision terrain and high-resolution grids, and further improve the accuracy of mesoscale numerical simulation of complex terrain wind fields based on the four-dimensional variational assimilation method. First, obtain field observation data. The observation data used in this study comes from a wind lidar located at (112.70750004°E, 37.22866700°N) at a terrain altitude of 1,670 meters, with a sampling frequency of 1 Hz. The observation data covers temperature, air pressure, humidity, wind speed, and wind direction. The lidar measurement altitudes are 40 meters, 44 meters, 47 meters, 58 meters, 61 meters, 73 meters, 91 meters, 101 meters, 113 meters, and 121 meters, respectively. The time range of the data used in this study is from 0:00 on December 21, 2022, to 0:00 on December 23, 2022 (local time, UTC+8).

[0068] Secondly, the mesoscale numerical simulation results in step 1 were verified using observational data, and the accuracy was found to be low. Figure 5b ) and high-resolution grids (the grid scale of the outermost nested domain is 25 km, the grid scale of the innermost nested domain is 200 m, and there are 56 vertical layers, which are encrypted near the ground, including 10 layers below 100 meters, 10 layers within the range of 100-500 meters, 5 layers within the range of 500-1000 meters, and 31 layers above 1000 meters. Other configurations are the same as in step 1), based on the four-dimensional variational assimilation method to further improve the accuracy of mesoscale numerical simulation of complex terrain wind fields.

[0069] Assimilation starts at 17:00 UTC on December 21, 2022, and ends at 15:00 UTC on December 23, 2022. Data assimilation is performed in all four nested domains. The maximum horizontal influence radius is 180 km in the third and fourth nested domains and 240 km in the first and second nested domains. The data assimilation time window can be 0.11 h (corresponding to a 10-minute temporal resolution for observational data); the data assimilation intensity is 6.0×10 -4 .

[0070] During data assimilation, the innermost nested domain uses the high-precision topographic data SRTM 30 from the Space Shuttle Radar Topography Mission to replace the USGS data, and the innermost grid resolution is 200m. Figure 5b shown.

[0071] Finally, after the data assimilation is completed, the observation data is used to verify the assimilation effect.

[0072] Step 3: Establish a meso-microscale coupled simulation framework based on WRF-CFD model coupling to perform high-fidelity CFD numerical simulation of the target wind field First, a meso-microscale coupled simulation framework based on WRF-CFD mode coupling is established.

[0073] The WRF-CFD data transfer is performed using the boundary coupling method. The spatiotemporal series of wind speed, temperature, and turbulent kinetic energy corresponding to the microscale computational domain boundary are extracted from the WRF simulation results. These series are then imported into the CFD simulation domain boundary through temporal and spatial interpolation for microscale calculations.

[0074] Linear interpolation is used to assign values ​​to time steps between any two moments. Mesoscale data is extracted based on altitude. Spatial interpolation uses triangulation / linear interpolation.

[0075] In order to ensure the consistency between the mesoscale simulation output data and the microscale simulation boundary input data, meso-microscale terrain fusion is required.

[0076] In order to solve the problems of insufficient pulsation in mesoscale numerical simulation and slow development of near-ground turbulence, artificial synthetic turbulence driven by measured data is added on the basis of the inlet and outlet boundaries.

[0077] Microscale computational domain grid (such as Figure 6a and 6b ) The main steps of the generation technology are as follows: 1) Prepare terrain files (convert the .map format terrain files to .stl format terrain files in advance); 2) Prepare blockMeshDict and snappyHexMeshDict files; 3) Run the script to generate the mesh file (after the mesh is generated, perform a mesh quality check).

[0078] For this example, the microscale computational domain was set at an altitude of 2 km and a horizontal dimension of 5 km × 5 km. The uniform background grid had a horizontal resolution of 16.5 m and a vertical resolution of 10 m. The grid was refined in the near-surface area covering the mountain, with a horizontal resolution of 4 m and a vertical resolution of 2.5 m.

[0079] The east, south, west, and north sides of the microscale computational domain are all inlet and outlet boundary conditions, and the vertical top and bottom are the top and bottom boundaries, respectively. In the inlet and outlet boundary conditions, the variables U and T adopt time-varying boundary conditions.

[0080] Time discretization uses the time domain backward difference method (backward, second order, implicit), the gradient term discretization uses the Gaussian linear interpolation format (Gauss linear, second order accuracy, unbounded), the numerical formats of the convection term and the divergence term are basically the same, using the Gaussian linear interpolation format (Gauss linear, restrictions can also be used in the upwind direction of the linear format, such as div(phi,nuTilda) using Gauss limitedLinear 1), and the Laplace term discretization uses the Gaussian linear interpolation corrected format (Gausslinear corrected, explicit non-orthogonal grid correction).

[0081] The main methods for solving linear systems include iterative solvers based on the conjugate gradient method (PCG, for the variable p_rgh) and iterative solvers based on the biconjugate gradient method (PBiCG, for variables U, T, k, nuTilda, etc.). Preconditioners include the geometrically clustered algebraic multigrid preconditioner (GAMG, for the variable p_rgh) and the diagonally incomplete LU preconditioner (DILU, for variables U, T, k, nuTilda, etc.). A smoothing solver (using the DICGaussSeidel method for the variable p_rgh) is also used.

[0082] The solver uses PISO-SIMPLE to "implicitly" solve the momentum and pressure equations, and the prediction-correction method uses the Rhie-Chow interpolation method, and the temperature equation is included in the correction loop.

[0083] Then, a high-fidelity CFD numerical simulation of the target wind field is performed; Finally, the WRF-CFD numerical simulation results were verified based on field measured data.

[0084] Step 4: Apply 4D variational assimilation technology to the CFD simulation process to further improve the accuracy of WRF-CFD coupled simulation In this case, since the accuracy of the WRF-CFD results in step 3 can be improved, the four-dimensional variational assimilation technology is applied to the CFD simulation process to further improve the accuracy of the WRF-CFD coupled simulation.

[0085] When 4D variational assimilation is applied to CFD simulations, a source term F is added to the momentum equation to modify the velocity field (U). The source term is calculated based on time and space weights and the difference between the current velocity field and the target velocity field.

[0086] In this case, observation data (wind speed vectors) from radar altitudes of 40, 101, and 143 meters are assimilated to calculate the average velocity within a 20-meter sphere around the observation point.

[0087] Maximum horizontal influence radius r xy In this case, 3000m is used. The maximum vertical impact range r z In this case, 1500m is used. The observation time point t0 is every 10 minutes; the time window length of the observation data is The unit is seconds. In this case, 1200.5s is used (to accelerate convergence).

[0088] After analysis Figure 7a 、 Figure 7b and Figure 7cIt can be seen that when the mesoscale WRF model is used to simulate wind fields over complex terrain without observational data assimilation, the simulated wind speed and direction results differ significantly from the observed data, necessitating data assimilation to improve numerical simulation accuracy. When high-precision terrain and a high-resolution grid are combined with four-dimensional variational assimilation techniques, the mean absolute errors of wind speed, wind direction, and turbulence intensity at the radar location are reduced by 40.1%, 27.4%, and 6.1%, respectively (compared to the mesoscale WRF numerical simulation method without observational data assimilation). Furthermore, insufficient turbulence generation in the mesoscale WRF model was found. To further improve the accuracy of wind field simulation over complex terrain and reflect the capture of flow details by high-precision terrain, the assimilated WRF results were added to the CFD boundary, and a numerical simulation method for wind fields over complex terrain based on the WRF-CFD coupling framework was established. At this time, the mean absolute errors of wind speed, wind direction and turbulence intensity at the radar position were reduced by 51.1%, 45.5% and 36.2%, respectively (compared with the mesoscale WRF numerical simulation method without assimilation of observational data), especially the simulation accuracy of turbulence intensity was significantly improved. Furthermore, after applying the four-dimensional variational assimilation technology to the CFD simulation process, the average absolute errors of wind speed, wind direction and turbulence intensity at the radar position were reduced by 97.6%, 90.7% and 86%, respectively (compared with the mesoscale WRF numerical simulation method without observational data assimilation). At this time, the average absolute errors of wind speed, wind direction and turbulence intensity were 0.15m / s, 3.2° and 0.04, respectively, while the average absolute errors of wind speed, wind direction and turbulence intensity in the mesoscale WRF numerical simulation method without observational data assimilation were 6.22m / s, 34.4° and 0.29, respectively.

[0089] In summary, the present invention is a complex terrain wind field simulation technology that can simultaneously integrate the data assimilation method into the WRF process and micro-scale CFD simulation, and fully consider factors such as grid resolution, terrain resolution, assimilation frequency and unsteady effects. It can greatly improve the accuracy of numerical simulation of complex terrain wind fields and effectively improve the accuracy of wind resource assessment, thereby laying a solid foundation for wind farm planning and operation control.

[0090] Comparisons with measured wind field data indicate that the proposed real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields, which integrates field measurements, can effectively simulate wind speed, wind direction, and turbulence intensity in complex terrain wind fields, achieving good consistency with observed data. This data assimilation method offers advantages such as simplicity, ease of coding, efficient computation, and high accuracy. It achieves excellent prediction accuracy for wind speed, wind direction, and the spatiotemporal distribution of turbulence, surpassing numerical simulations based on the WRF model and the WRF-CFD coupled model.

[0091] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0092] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A real-time assimilation method for multi-scale numerical simulation of wind fields in complex terrain by integrating field measurement data, characterized by: The method comprises the following steps: S1, obtaining conventional meteorological and terrain data, determining a reference point, and numerically simulating the complex terrain wind field based on the mesoscale WRF model; determining the accuracy of the mesoscale numerical simulation of the complex terrain wind field; if it meets the first preset accuracy requirement, proceeding to step S3; otherwise, proceeding to step S2; S2: Acquire field observation data and high-precision terrain data, combine the high-precision terrain and high-resolution grid, and improve the accuracy of mesoscale numerical simulation of wind fields in complex terrain to meet the first preset accuracy requirement based on the four-dimensional variational assimilation method; S3, establishing a meso-microscale coupled simulation framework based on the WRF-CFD model coupling, and performing high-fidelity CFD numerical simulation of the target wind farm; judging the accuracy of the CFD numerical simulation; if it meets the second preset accuracy requirement, the process ends; otherwise, proceeding to step S4; S4, applying the four-dimensional variational assimilation technology to the CFD simulation process to improve the accuracy of the CFD numerical simulation to meet the second preset accuracy requirement.

2. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 1 is characterized in that: Step S1 further includes the following steps: S11, determine conventional climate input data and topographic data; S12, selecting the center of the wind field as the reference point of the wind field to be simulated, obtaining its longitude and latitude; removing the start time of the mesoscale WRF model, and determining the simulation time period of the wind field to be simulated; S13, determine the computational domain range, grid scale, nesting method, parameterization scheme configuration, monitoring point locations and monitoring variables for the mesoscale WRF simulation; S14, perform mesoscale numerical simulation of wind fields over complex terrain and analyze the results.

3. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 2 is characterized in that: In step S13, the calculation domain range is determined according to the reference point position and the target wind field size; the grid scale and time scale of each nested domain are determined according to the complexity of the underlying surface terrain; The nesting method uses bidirectional nesting; the parameterization scheme includes microphysical processes, shortwave and longwave radiation, surface and land surface processes, urban and ocean models, planetary boundary layer schemes and cumulus cloud parameterization processes; The monitoring location is the wind tower location, and the monitored variables include wind speed, pressure and potential temperature.

4. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 1 is characterized in that: In step S1, the process of judging the accuracy of the mesoscale numerical simulation of the complex terrain wind field includes: Obtain field observation data, which include the latitude and longitude and altitude of the observation location, as well as the wind speed, wind direction, temperature, humidity and air pressure variables of each observation location; use the observation data to verify whether the accuracy of the mesoscale numerical simulation of the complex terrain wind field meets the first preset accuracy requirement.

5. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 1 is characterized in that: In step S2, the accuracy of mesoscale numerical simulation of wind fields in complex terrain is improved based on the four-dimensional variational assimilation method. The data assimilation expression is: ； Where i is the index of the observation data, x, y, z are the spatial coordinates, t is the simulation time, q is the assimilated physical quantity, μ is the dry air static pressure, q0 is the observed value of the physical quantity, and q m (x i ,y i ,z i ,t) is the predicted value of the WRF model, G q is the assimilation intensity of q, N is the total number of observations, W q is a weighted function based on the distance between the grid cell and the observation point; W t 、W z and W xy Describes the assimilation strength of time and space; W xy and W z is the assimilation spatial weight function, W t is the time weight function; ； ； Where R is the maximum horizontal influence radius, D is the horizontal distance between the grid point and the observation point, t0 is the observation time point, and t is the model time. is the time window length of the observation data; W t The value range is 0 to 1.

6. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 1 is characterized in that: Step S3 further comprises: S31: Establish a meso-microscale coupled simulation framework based on WRF-CFD model coupling, and use the boundary coupling method for WRF-CFD data transfer. Specifically, the spatiotemporal series of wind speed, temperature, and turbulent kinetic energy parameters corresponding to the microscale computational domain boundary are extracted from the WRF simulation results, and the extracted data are imported into the CFD simulation domain boundary through time and space interpolation for microscale calculations. S32, perform high-fidelity CFD numerical simulation of the target wind farm; S33, verify the WRF-CFD numerical simulation results based on field measured data.

7. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 6 is characterized in that: In step S31, the process of establishing the coupling boundary includes the following steps: S311, determining the latitude, longitude and coordinates of a reference point, where the reference point is located at the center of the mesoscale computational domain and the microscale computational domain; S312, determining the boundary of the microscale computational domain according to the height of the mountain and the thickness of the atmospheric boundary layer; S313, extracting the boundary coordinates of the microscale computational domain; S314, extracting wind speed, turbulent kinetic energy, temperature, and pressure information corresponding to the boundary coordinates from the mesoscale numerical simulation results, and performing spatial interpolation and temporal interpolation on the extracted boundary variables, respectively. The interpolated boundary variables meet the requirements of the microscale grid in space and the requirements of the microscale simulation time step in time; S315, adding the derived boundary variables to the microscale computational domain boundary to complete the CFD numerical simulation.

8. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 1 is characterized in that: Step S4 further comprises: S41, add the source term F and the modified velocity field U to the momentum equation and modify the momentum equation to: ； Where: is the velocity component, subscript Represents flow direction, horizontal direction and vertical direction respectively. are coordinate components, For time, is the fluid density, is the static pressure, Indicates the position temperature, Representation is averaged in the horizontal plane; is the acceleration due to gravity, is the reference potential temperature, represents the Coriolis force coefficient, is the average angular velocity of the Earth's rotation, is the local latitude, 、 represent the directional and lateral components of the geostrophic wind, respectively; is the Dirac function, j=1, 2, 3, when hour, , 0 in other cases; is stress, is the source term for velocity correction; S42, adjusting the flow field velocity to the target wind speed profile by updating the source term F.

9. The real-time assimilation method for multi-scale numerical simulation of complex terrain wind fields by integrating field measurement data according to claim 8, characterized in that: Step S42 further includes: S421, calculate the weighted average wind speed within the specified grid volume at the target location: ； Where, represents the wind speed vector in the i-th grid cell corresponding to the j-th assimilation point, represents the volume within the i-th grid cell corresponding to the j-th assimilation point, j is a point to be assimilated, and m is the number of grids within the specified volume; after removing the vertical component, we get: ； Where, Represents the unit normal vector in the vertical direction; S422, read the wind speed vector of the target position at the nearest time point from the wind speed time series ; S423: Calculate the wind speed adjustment value ds based on the difference between the target wind speed and the current average wind speed, and perform normalization: ； ； ； Where α is the relaxation factor, is the volume-weighted average of the inverse of the momentum equation diagonal matrix rAU; S424, calculate and obtain the spatial and temporal weight functions; wherein the horizontal weight is: ； Where r xy is the maximum horizontal influence radius, d xy is the horizontal distance between the grid point and the observation point; The vertical weight is: ； Where r z is the maximum vertical influence range, d z is the vertical distance between the grid point and the observation point; The time weight is: ； Where t0 is the observation time point, t is the simulation time, is the time window length of the observation data; The total weight is: ; Where, 、 、 They represent the assimilation space weight function and time weight function of the j-th assimilation point respectively; S425, distribute the adjustment amount to the grid according to the weight, and update F and velocity field U as follows: ； ； The synchronously updated flux field φ is: ； Where n is the number of grids in the computational domain, The surface interpolation field of rAU, the inverse of the momentum equation diagonal matrix, is used to construct the pressure correction equation to ensure the numerical stability of velocity-pressure coupling. fvc represents finite volume convection, and interpolate represents the interpolation function, which is used to interpolate the physical quantity at the center of the grid cell to the grid interface. The area vector representing the mesh interface.

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