Mesh cell quality evaluation method and computer device

Abstract

The application discloses a grid cell quality evaluation method and computer equipment, and relates to the technical field of high-performance computing, and comprises the following steps: determining an additional source term according to a physical quantity determination equation and an analytical solution function, adjusting the analytical solution of the physical quantity determination equation into a function value of the analytical solution function by using the additional source term; obtaining a first result by using the analytical solution function, and obtaining a second result by using the physical quantity determination equation, a boundary value in the first result and the additional source term; and determining a quality evaluation result of a grid cell by comparing the first result with the second result. The method can solve the problems that the grid cell quality evaluation is inaccurate and the quality evaluation cannot be performed on a single grid cell. The method modifies the physical quantity determination equation by using the additional source term, realizes the construction of the analytical solution in the simulation of various equations and complex regions, obtains the numerical solution and the analytical solution corresponding to the network cell, and realizes the accurate quality evaluation of each grid cell by using the error between the numerical solution and the theoretical solution.

Description

Technical Field

[0001] This invention relates to the field of high-performance computing technology, specifically to a method for evaluating the quality of grid cells and a computer device. Background Technology

[0002] In high-performance computing, a common numerical computation process first divides the simulation domain into a finite computational grid, and then solves the constructed algebraic equations. This involves dividing the originally continuous solution domain into a large number of small, regular or irregular grid cells, with physical quantities defined and solved only within these grid cells. In simulations of complex regions, poor grid cell quality in some areas often leads to large computational errors or convergence difficulties for some numerical algorithms. Therefore, it is necessary to evaluate the quality of the grid cells to improve their quality and enhance the accuracy and correctness of the numerical software results.

[0003] Currently, quality evaluation of mesh cells requires the use of mesh processing software. Mesh processing software uses geometric feature data as the basis for cell quality evaluation. Although it can perform a basic evaluation of mesh quality, the evaluation results are not directly related to the actual calculation error of the mesh cells.

[0004] Therefore, the relevant technologies suffer from inaccurate grid cell quality evaluation and the inability to evaluate the quality of individual grid cells. Summary of the Invention

[0005] In view of this, this application provides a method and computer device for evaluating the quality of grid cells to solve the problems of inaccurate grid cell quality evaluation and the inability to evaluate the quality of individual grid cells.

[0006] Firstly, this application provides a method for evaluating the quality of mesh elements, the method comprising:

[0007] Obtain the physical quantity determination equations and analytical solution functions corresponding to the grid cells;

[0008] Based on the physical quantities, determine the equations and analytical solution functions, and determine the additional source terms. The additional source terms are used to adjust the analytical solution of the physical quantity determining equations to the function values ​​of the analytical solution functions.

[0009] Based on the analytical solution function and preset parameters, the first result is obtained. Boundary values ​​are determined in the first result, and the equations, boundary values, and additional source terms are determined based on the physical quantities to obtain the second result.

[0010] Based on the first and second results, the quality evaluation results of the grid cells are determined.

[0011] Secondly, this application provides a mesh cell quality evaluation device, the device comprising:

[0012] The acquisition module is used to obtain the physical quantity determination equations and analytical solution functions corresponding to the grid cells;

[0013] The first determining module is used to determine additional source terms based on the physical quantity determining equation and analytical solution function. The additional source terms are used to adjust the analytical solution of the physical quantity determining equation to the function value of the analytical solution function.

[0014] The result determination module is used to obtain a first result based on the analytical solution function and preset parameters, determine the boundary values ​​in the first result, and determine the equation, boundary values ​​and additional source terms based on the physical quantities to obtain a second result.

[0015] The quality evaluation module is used to determine the quality evaluation result of the grid cell based on the first result and the second result.

[0016] Thirdly, this application provides a computer device, including: a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the grid cell quality evaluation method of the first aspect or any corresponding embodiment described above.

[0017] Fourthly, this application provides a computer-readable storage medium storing computer instructions for causing a computer to execute the grid cell quality evaluation method of the first aspect or any corresponding embodiment described above.

[0018] Fifthly, this application provides a computer program product, including computer instructions for causing a computer to execute the grid cell quality evaluation method of the first aspect or any corresponding embodiment described above.

[0019] This application addresses the problem of inaccurate grid cell quality evaluation and the inability to evaluate individual grid cells by modifying the physical quantity determination equations with additional source terms. The method obtains a first result using the analytical solution function, and a second result using the physical quantity determination equations, boundary values ​​from the first result, and the additional source terms. By comparing the first and second results, the quality evaluation result of the grid cell is determined. This solves the problems of inaccurate grid cell quality evaluation and the inability to evaluate the quality of individual grid cells. The method modifies the physical quantity determination equations with additional source terms, enabling the construction of analytical solutions for various equations and complex regions during simulation. It obtains both numerical and analytical solutions for each grid cell, and through the error between the numerical and theoretical solutions, achieves accurate quality evaluation for each grid cell. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the specific embodiments or related technologies of this application, the drawings used in the description of the specific embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of a triangular adjacent unit calculation template according to an embodiment of this application;

[0022] Figure 2 This is a schematic diagram of a template for calculating the triangle least squares method according to an embodiment of this application;

[0023] Figure 3 This is a schematic diagram of a triangle node calculation template according to an embodiment of this application;

[0024] Figure 4 This is a flowchart illustrating the mesh cell quality evaluation method according to an embodiment of this application;

[0025] Figure 5 This is a schematic diagram of a numerical computation grid quality evaluation system according to an embodiment of this application;

[0026] Figure 6 This is a structural block diagram of a grid cell quality evaluation device according to an embodiment of this application;

[0027] Figure 7 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of this application. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of this application.

[0029] It should be noted that, in the description of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. The terms "first," "second," etc., in this application are used to distinguish similar objects and are not used to describe a specific order or sequence.

[0030] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] In practical engineering, partial differential equations (PDEs) are often used to describe complex phenomena in physics, engineering, and finance, such as fluid flow, heat conduction, and electromagnetic fields. When PDEs involve complex geometries or boundary conditions, exact, formulaically expressed "closed-loop solutions" are almost nonexistent; therefore, they can only be solved through numerical methods. Numerical methods such as the finite difference method, finite element method, and finite volume method transform the continuous PDEs describing fluid motion into a system of algebraic equations defined on discrete mesh elements or nodes. This provides a practical approach to solving these PDEs that were originally impossible to solve analytically. Mesh elements can be divided into structured and unstructured meshes. In a structured mesh, all nodes or elements can be uniquely identified by a set of regular and ordered indices. Mesh elements are logically arranged in a regular array, such as two-dimensional rectangular meshes or three-dimensional hexahedral meshes. In an unstructured mesh, nodes or elements do not have a global, regular index order. Elements can be of various shapes, such as triangles, tetrahedrons, and prisms, and are connected in arbitrary ways.

[0032] In high-performance computing, common numerical methods first divide the simulation domain into a finite computational grid, then solve the constructed algebraic equations. The originally continuous solution domain, including both spatial and temporal domains, is divided into numerous small, regular or irregular network cells and nodes. Simultaneously, physical quantities such as temperature, pressure, and velocity are defined and solved only at grid nodes or the centers of grid cells. Depending on the adopted numerical discretization scheme, partial differential terms are approximated using algebraic forms within the grid cells, thus achieving numerical discretization of the partial differential equations. The fineness and quality of the computational grid directly affect the resources required for computation and the accuracy of the results. Because the partial differential equations solved by high-performance software are often complex and lack analytical solutions, verifying numerical results has always been challenging. Especially in simulations of complex regions, poor grid quality in some areas often leads to large computational errors or convergence difficulties for some numerical algorithms. Therefore, improving the quality of the grid cells can significantly improve the accuracy and correctness of numerical software calculations.

[0033] In existing mesh preprocessing tools, some software already includes mesh element quality checking functions. These mesh processing software programs almost all use geometric feature data as the basis for evaluating element quality, such as the minimum interior angle of triangular elements and the twist of quadrilateral elements. While this geometric feature data analysis can provide a basic evaluation of mesh quality, the evaluation results are not directly related to the actual numerical format calculation error, and do not match the calculation templates of some numerical formats. Therefore, the analysis shows that mesh quality is unrelated to actual calculation errors, and initially, poor-quality elements may not cause significant errors in larger calculation formats. Figure 1 The image shows different computation templates for triangular elements in an unstructured mesh. Figure 2 The template for calculating the least squares method for triangles is shown in the image. Figure 3 The image shows the triangular node computation template. The computation template is composed of the locations of the input data points in numerical computation. Different data formats use different input data locations; therefore, mesh quality evaluation needs to be combined with the numerical format. On the same mesh, a larger template represents more triangular elements, such as... Figure 2 and Figure 3 The calculation template in is significantly larger than Figure 1 The calculation template is used in the model. Additionally, some approaches compare the calculation results of the target software and the reference software on the mesh, judging the calculation error of the target software on the current mesh based on the magnitude of the error. The disadvantages of this method include the need to introduce a so-called "standard software" for comparison, and the fact that due to convection and diffusion phenomena in the simulated physical processes, errors generated by some elements may spread in local areas, making it impossible to accurately determine the quality of individual meshes.

[0034] Current methods for evaluating mesh cell quality rely on their geometric characteristics, which are not directly related to numerical computation errors and cannot accurately predict cell quality in actual calculations. Comparison with reference software results requires the introduction of that software, which is challenging for some partial differential equations or certain numerical computation formats. Furthermore, when comparing with reference results, computational errors within the mesh may move or spread within the computational domain, making it impossible to accurately identify the source of error and thus failing to recognize cells generating significant errors.

[0035] Based on the above, this application provides a method for evaluating the quality of grid cells. It modifies the numerical scheme for solving partial differential equations using a manual solution construction method, enabling analytical solution construction in complex simulation regions. The method then calls the numerical scheme to calculate numerical solutions within the complex simulation region. By comparing the error between the analytical and numerical solutions, the quality of cells within the grid is accurately evaluated. This method is applicable to the verification of different numerical schemes. By directly calling the numerical scheme through a software calculation interface module, numerical solution calculation results can be obtained. Comparison with the manual solution accurately reveals the errors generated during the actual simulation. This method is suitable for evaluating the quality of grid cells in various complex terrains. Since both the numerical and exact solutions are directly related to coordinates, it is applicable to various complex terrain simulations and provides accurate quality evaluation for all cells within the grid. This achieves the effect of accurately judging the quality of cells within the grid by comparing the error between the numerical and theoretical solutions.

[0036] According to an embodiment of this application, a mesh cell quality evaluation embodiment is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, for example, a computer, a server, etc., and although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0037] This embodiment provides a method for evaluating the quality of grid cells. Figure 4 This is a flowchart of a mesh cell quality evaluation method according to an embodiment of this application, such as... Figure 4 As shown, the process includes the following steps:

[0038] Step S401: Obtain the physical quantity determination equations and analytical solution functions corresponding to the grid cells.

[0039] Specifically, a grid cell is obtained by dividing the simulation area. The grid cell is used to determine the target physical quantities of the simulation area based on the corresponding physical quantity determinant equations. For example, in the Finite Volume Community Ocean Model (FVCOM), the simulation area is an ocean region, which is divided into multiple two-dimensional grid cells. The target physical quantities at each location within this ocean region are determined using the physical quantity determinant equations corresponding to the grid cells. These target physical quantities include ocean temperature, sea level height, and ocean salinity. Similarly, in the Weather Research and Forecasting Model (WRF), the simulation area is an atmosphere region, which is divided into three-dimensional grid cells (containing horizontal "surface grids" and vertical "layer grids"). The target physical quantities at each location within this atmosphere region are determined using the physical quantity determinant equations corresponding to the grid cells. These target physical quantities include near-surface wind speed, wind direction, atmospheric temperature, and atmospheric relative humidity.

[0040] The mesh element quality evaluation method in this embodiment is executed by a numerical computation mesh quality evaluation system. This system mainly comprises three components: a numerical software computation interface, a reference solution construction module, and an element quality analysis module, such as... Figure 5 As shown, the reference solution construction module modifies the partial differential equations in an inverse form to construct an analytical solution. The numerical software calculation interface is used to output the numerical solution, the reference solution construction module is used to output the analytical solution result file, and the element quality analysis module is used to output the element quality analysis result graph.

[0041] Obtain the physical quantity determination equations corresponding to the grid cells. The physical quantity determination equations are the partial differential equations mentioned above, for example: Formula (1).

[0042] (1)

[0043] In the artificial solution construction method, an analytical solution is first defined. Then, based on the difference between the analytical solution and the partial differential equation, the source terms of the equation are modified to achieve the matching of the theoretical solution and the governing equation. The requirements for the analytical solution function in this embodiment include: the function should be infinitely differentiable, and the numerical value of the function solution is bounded in any region. Therefore, the analytical solution function can be a trigonometric function, such as formula (2) and formula (3).

[0044] (2)

[0045] (3)

[0046] in, , , It is a constant. and It is a constant. , as well as The specific values ​​will be adjusted according to actual needs.

[0047] Step S402: Determine additional source terms based on the physical quantity determination equation and analytical solution function. The additional source terms are used to adjust the analytical solution of the physical quantity determination equation to the function value of the analytical solution function.

[0048] Specifically, the equations and analytical solution functions are determined based on the physical quantities, and additional source terms are determined, for example: the analytical solution function... After substituting the physical quantities into the equation, the residual term is obtained. Treat the residual term as an additional source term Additional source terms, such as in formula (4).

[0049] (4)

[0050] Additional source terms are used to adjust the analytical solution of the equation for determining a physical quantity to the function value of the analytical solution function. For example, after changing 0 on the right-hand side of the equation for determining a physical quantity to an additional source term, This transforms the equation into an analytical solution after modification. For any partial differential equation, this method can be used to add an additional source term to the equation to obtain an analytical solution after modification.

[0051] Step S403: Based on the analytical solution function and preset parameters, obtain the first result, determine the boundary values ​​in the first result, and determine the equation, boundary values ​​and additional source terms based on the physical quantities to obtain the second result.

[0052] Specifically, by substituting the preset parameters into the analytical solution function, a first result is obtained. This first result is the analytical solution to the equation determining the physical quantity. For example: corresponding and corresponding The first result can also include continuous analytical solutions to the equations that determine physical quantities over a period of time, such as... corresponding The value of .

[0053] The numerical software calculation interface determines the equation based on physical quantities and constructs the objective equation using additional source terms, and then incorporates the first result into the equation. corresponding As boundary conditions, numerical software is used to solve the constructed objective equation, yielding a second result, which is the computational solution of the mesh element for the objective equation. .

[0054] Step S404: Determine the quality evaluation result of the mesh cell based on the first result and the second result.

[0055] Specifically, within the computational domain, the element quality analysis module compares a first result representing the analytical solution with a second result representing the numerical solution to determine the quality evaluation result of the mesh element. For example, it calculates the relative or absolute error between the first and second results, using this error as an error index to characterize the quality evaluation result. Figure 5 As shown, the element quality analysis module obtains the first result representing the analytical solution of the mesh element and the second result representing the numerical solution of the mesh element from the analytical solution result file, and obtains the mesh element quality analysis result by comparing the first result and the second result.

[0056] In addition to providing basic numerical error analysis, the element quality analysis module can also mark elements with large calculation errors based on user-defined analysis results. The module uses a Python interface and calls modules such as matplotlib to plot the element quality analysis results of the simulated region.

[0057] It should be noted that additional source terms can be added to the equations for the physical quantities of each grid cell, and the first and second results can be compared to distinguish which grid cells have errors exceeding the specified threshold.

[0058] The mesh cell quality evaluation method provided in this embodiment determines additional source terms based on the physical quantity determining equations and analytical solution functions. These additional source terms are used to adjust the analytical solutions of the physical quantity determining equations to the function values ​​of the analytical solution functions. A first result is obtained using the analytical solution functions, and a second result is obtained using the physical quantity determining equations, boundary values ​​in the first result, and the additional source terms. By comparing the first and second results, the quality evaluation result of the mesh cell is determined. This method modifies the physical quantity determining equations through additional source terms, enabling the construction of analytical solutions for various equations and complex regions during simulation. It can obtain both numerical and analytical solutions for each mesh cell, and by analyzing the error between the numerical and theoretical solutions, it achieves accurate quality evaluation for each mesh cell. This solves the problems of inaccurate mesh cell quality evaluation and the inability to evaluate the quality of individual mesh cells.

[0059] As an optional embodiment, the equations and analytical solution functions are determined based on physical quantities, and additional source terms are determined, including:

[0060] Determine the equations based on the physical quantities and create the first partial differential equation operator;

[0061] By combining the analytical solution function with the first partial differential equation operator, the first intermediate partial differential equation operator is obtained.

[0062] The additional source term is obtained based on the first intermediate partial differential equation operator.

[0063] Specifically, the equations are determined based on the physical quantities, and the first partial differential equation operator is created. For example, formula (5).

[0064] (5)

[0065] An analytical solution function is, for example, in formula (2) or formula (3) above. Substituting the analytical solution function into the first partial differential equation operator yields the first intermediate partial differential equation operator. .

[0066] Set additional source items Analyzing the first intermediate partial differential equation operator Additional source terms can be obtained Then at this time satisfy .

[0067] As can be seen from the above process, the artificial solution construction method can construct analytical solutions for any partial differential equation. The modified governing equations only add additional source terms compared to the original equations. For example, the reference solution construction module uses the pythonsympy module for computation; sympy is a symbolic mathematics computation library. The analytical solution function is defined as follows: At this point, according to the predefined convection and diffusion terms , The corresponding additional source term expression is obtained as shown in formula (6).

[0068] (6)

[0069] In this embodiment, additional source terms are determined and used to modify the numerical scheme for solving partial differential equations, thereby constructing analytical solutions in complex simulation regions. This avoids introducing reference results from other numerical computation software; only the target numerical scheme needs to be called for a single calculation on the actual simulation region grid, resulting in a smaller computational load and supporting parallel processing.

[0070] As an optional embodiment, after determining the quality evaluation result of the mesh cell based on the first result and the second result, the method further includes:

[0071] Based on the quality evaluation results, the error index of the grid cell is determined;

[0072] Based on the error index, the grid cells to be marked are determined in the grid cells, wherein the grid cells to be marked are grid cells whose error index is greater than a first preset threshold;

[0073] Call the first preset interface to generate a distribution map containing grid cells, and mark the grid cells to be marked in the distribution map.

[0074] Specifically, the cell quality analysis module provides a basic numerical error score and marks cells with large calculation errors based on user-defined analysis results. The module determines the error index for each grid cell in the quality evaluation results; error indices include, for example, absolute error and relative error. A first preset threshold is set, for example, 5%, 6%, or other values ​​if the error index is a relative error; and 5, 6, or other values ​​that meet practical requirements if the error index is a relative error. The error index of each grid cell is compared with the first preset threshold, and grid cells with error indices greater than the first preset threshold are identified as grid cells to be marked.

[0075] The first preset interface, for example, is a Python language interface. This interface can call modules such as matplotlib, a data visualization library primarily used to create high-quality charts and graphs. Using this first preset interface to call the matplotlib module generates a distribution plot containing grid cells. The unmarked grid cells are then marked on the distribution plot, and the marked distribution plot is used to simulate the results of the region cell quality analysis.

[0076] For example, a heatmap is used to represent the distribution of computational grid errors in ocean simulations. Users can use this map to determine whether significant errors will occur in key study areas, such as river channels and near-shore coastlines, and to empirically assess whether the errors in the right-hand boundary region are excessive. Subsequently, based on the error results, the size of the generated triangular cells in certain areas can be adjusted; densification generally reduces numerical computation errors.

[0077] In this embodiment, grid cells with an error index greater than a first preset threshold are designated as grid cells to be marked. A distribution map of the grid cells is generated, and the grid cells to be marked are then labeled on the distribution map. Users can directly identify grid cells with large errors and areas prone to significant errors through the distribution map and make adjustments based on the degree of error impact. Analytical solutions are provided for various partial differential equations, allowing for comparison with numerical solutions to verify the actual calculation errors generated by the numerical format. This method is applicable to the quality evaluation of grid cells in various complex terrains. Since both numerical and analytical solutions are directly related to coordinates, it is applicable to the simulation of various complex terrains and provides accurate quality evaluation for all grid cells.

[0078] As an optional embodiment, the preset parameters include a first sub-parameter and a second sub-parameter. Based on the analytical solution function and the preset parameters, a first analytical solution and a second analytical solution are obtained, including:

[0079] By combining the first sub-parameter and the analytical solution function, the first analytical solution is obtained;

[0080] By combining the second sub-parameter with the analytical solution function, the second analytical solution is obtained;

[0081] Based on the first analytical solution and the second analytical solution, the first result is obtained.

[0082] Specifically, the preset parameters include a first sub-parameter and a second sub-parameter. For example, the first sub-parameter is t=1, and the second sub-parameter is t=0.

[0083] An analytical solution function is, for example, the above formula (2) or formula (3). Substituting the first sub-parameter into the analytical solution function, for example, substituting t=1 into formula (2), yields the first analytical solution. Substituting the second sub-parameter into the analytical solution function, for example, substituting t=0 into formula (2), yields the second analytical solution. .

[0084] Integrating the first analytical solution Second analytical solution The first result was obtained.

[0085] The reference solution constructor module will , and additional source items Save the results in the corresponding file for later detailed analysis.

[0086] The above process is as follows Figure 5 As shown, the user script calls the reference solution construction module and uses it to calculate the analytical solution. Analytical Solution and additional source items , will analyze the solution Save to the analytical solution result file, and then save the analytical solution. and additional source items Input numerical software calculation interface.

[0087] As an optional embodiment, boundary values ​​are determined in the first result, and equations, boundary values, and additional source terms are determined based on physical quantities to obtain a second result, including:

[0088] Obtain the second analytical solution from the first result and use the second analytical solution as the boundary value;

[0089] By combining the additional source terms with the physical quantity determination equations, the objective equation is obtained;

[0090] The second preset interface is invoked to transmit the objective equation and boundary values ​​to the preset numerical software;

[0091] Obtain the second result from the return information of the preset numerical software.

[0092] Specifically, the second analytical solution in the first result As boundary values.

[0093] The second preset interface is a numerical software calculation interface, which is constructed using numerical solver software, or created using predefined custom functions in commercial software, such as the UDF (User-Defined Functions) function provided in Anasys Fluent, a computational fluid dynamics simulation software.

[0094] Numerical software interfaces are primarily used to define user-specified additional source terms. Since manually constructed source terms are time- and space-dependent, they need to be provided directly in the form of computational expressions. Numerical format interfaces can be provided using a C language interface, for example, through a combination of header files and dynamic link libraries.

[0095] Additional source terms are given in formula (4) above, and physical quantity determination equations are given in formula (1) above. Combining the additional source terms with the physical quantity determination equations, we obtain the target equation, which is given in formula (7).

[0096] (7)

[0097] The second preset interface is invoked to transmit the objective equation and boundary values ​​to the preset numerical software, such as Anasys Fluent or COMSOL Multiphysics (COMSOL Multiphysics is a multiphysics simulation software). The second result, Ures, is obtained from the return information of the preset numerical software. This second result is then written to the numerical solution result file.

[0098] The above process is as follows Figure 5 As shown, the numerical software calculation interface receives the analytical solution. and additional source items Then, the objective equation and boundary values ​​are transmitted to the preset numerical software, the numerical solution Ures is obtained from the preset numerical software, and the numerical solution Ures is written into the numerical solution result file.

[0099] In this embodiment, a software computation interface module is used to directly call the numerical format for solving, yielding numerical solution results. By comparing these results with manually calculated solutions, errors generated during the actual simulation can be accurately identified. This approach is applicable to solving different partial differential equations and verifying various numerical formats. Since the theoretical solution is compared with the numerical solution simulated using the actual computational grid, the error of each element within the grid can be obtained. The quality analysis of the grid elements only requires iterating the modified governing equations once using the numerical format, resulting in a small computational load and supporting parallel computing, enabling rapid acquisition of analysis results.

[0100] As an optional embodiment, before calling the second preset interface to transmit the objective equation and boundary values ​​to the preset numerical software, the method further includes:

[0101] Obtain the first input variable, the second input variable, the preset output variable, and the predefined expression;

[0102] Based on the first input variable and the preset output variable, a first sub-interface is created, wherein the first sub-interface is contained within the second preset interface;

[0103] Based on the second input variable, the preset output variable, and the predefined expression, a second sub-interface is created, wherein the second sub-interface is contained within the second preset interface.

[0104] Specifically, the second preset interface is a numerical software calculation interface. The first input variable is, for example, an additional source term. and analytical solution function .

[0105] Predefined expressions, such as: single variables Corresponding partial differential terms and . E(U) and F(U) are A function representing flux, for example: , ,in and If it is a constant, then the user only needs to specify additional source items. That's it. The default output variable is the numerical solution Ures calculated by the default numerical software.

[0106] Based on the first input variable and the preset output variable, create the first sub-interface check_RHS, for example:

[0107] int check_RHS(double* double* double* double* (double*Ures).

[0108] Here, `int` represents the return value, `double` is a data type representing a double-precision floating-point number, and `double*` is a pointer to a `double` type variable used to store variable values ​​(such as state variables, fluxes, source terms, residuals, etc.) in the grid cells or solution domain. The first sub-interface also needs to be configured to support definition and source terms. including first order and second-order partial derivatives wait.

[0109] To reduce the complexity of the interface functions, a simplified version of the interface, namely the second sub-interface, is provided. Based on the second input variable, the preset output variable, and the predefined expression, the second sub-interface `check_short_RHS` is created, for example:

[0110] int check_short_RHS(double* double* (double*Ures).

[0111] After encapsulating the functions corresponding to the first and second sub-interfaces in a dynamic link library, they can be directly called via Python scripts, supporting user-defined input variable fields. and expression In addition, the computation speed of numerical solutions can be further improved by writing C language functions, which can support parallel computing.

[0112] In this embodiment of the application, a first sub-interface and a second sub-interface are created, which can directly call the numerical format for solving and obtain the numerical solution calculation results. By comparing with the analytical solution, the errors generated in the actual simulation process can be accurately obtained.

[0113] As an optional embodiment, taking the ocean model FVCOM as an example, it uses the finite volume method to solve for the staggered mesh on the structured mesh. The quality evaluation of the mesh elements constructed by FVCOM is performed using steps S401 to S404 above, including the following steps:

[0114] The input items are calculated using the standard numerical discretization method in FVCOM according to the defined check_RHS and check_short_RHS interfaces, and the calculation results are stored in Ures for output.

[0115] Call and run the reference solution construction module. This module will automatically call the numerical format calculation interface and save the analytical solution, numerical solution and error in the corresponding result file.

[0116] The element quality analysis module analyzes the result files of analytical and numerical solutions and marks the network elements based on the relative error between the analytical and numerical solutions.

[0117] As an optional embodiment, after generating a distribution map containing grid cells and marking the grid cells to be marked in the distribution map, the method further includes:

[0118] Identify the areas to be adjusted in the distribution map;

[0119] Based on the mesh generation algorithm, adjust the parameters of the mesh cells in the region to be adjusted.

[0120] Specifically, the grid cells to be marked on the distribution map can be labeled with different colors based on the magnitude of the error index. For example, if the error index is a relative error and the first preset threshold is 5%, the grid cells to be marked are blue if the error index is between 5% and 20%; green if the error index is between 20% and 60%; and yellow if the error index is greater than 60%. Based on these markings, areas that will generate significant errors are identified on the distribution map, such as areas composed of multiple yellow-marked grid cells, or areas composed of multiple yellow and green-marked grid cells. These areas are designated as areas requiring adjustment.

[0121] In addition, to reduce the workload of regional adjustment, the regions to be adjusted can be screened according to the degree of error impact. For example, determine the research target region, determine the distance between each region to be adjusted and the research target region, and ignore the regions to be adjusted whose distance is greater than the preset value. The preset value is set according to the size of the region, and no specific numerical limit is set here.

[0122] Based on the mesh generation algorithm, adjust the parameters of the mesh cells in the region to be adjusted. For example, use the mesh generation algorithm to re-divide the region to be adjusted into smaller mesh cells and adjust the orientation of the mesh cells. Mesh generation algorithms include Delaunay algorithm, advancing wavefront method, etc.

[0123] In this embodiment of the application, the area to be adjusted is determined in the distribution map, and the parameters of the grid cells in the area to be adjusted are adjusted according to the grid generation algorithm to improve the accuracy of terrain simulation for various complex areas.

[0124] As an optional embodiment, the equations and analytical solution functions are determined based on physical quantities, and additional source terms are determined, including:

[0125] Based on the physical quantities, determine the equations and predefined expressions, and create the second partial differential equation operator;

[0126] By combining the analytical solution function and the second partial differential equation operator, we obtain the second intermediate partial differential equation operator;

[0127] The additional source terms are determined based on the second intermediate partial differential equation operator and the predefined expression.

[0128] Specifically, this embodiment utilizes a reference solution construction module to construct expressions for the analytical solution and additional source terms. The reference solution construction module is computed using the Python sympy module.

[0129] The reference solution construction module determines the equations and predefined expressions based on physical quantities, and creates the second partial differential equation operator. For example, formula (8).

[0130] (8)

[0131] in, and For predefined expressions, , , and It is a constant.

[0132] The analytical solution function can be obtained from the reference solution construction module, for example: formula (9).

[0133] (9)

[0134] Substituting the analytical solution function as a solution into the second partial differential equation operator yields the second intermediate partial differential equation operator. Based on the second intermediate partial differential equation operator and the predefined expression, the additional source terms are determined. As shown in formula (10).

[0135] (10)

[0136] In this embodiment, additional source terms are determined and used to modify the numerical scheme for solving partial differential equations, thereby constructing analytical solutions in complex simulation regions. This avoids introducing reference results from other numerical computation software; only the target numerical scheme needs to be called for a single calculation on the actual simulation region grid, resulting in a smaller computational load and supporting parallel processing.

[0137] As an optional embodiment, adjusting the parameters of the grid cells in the region to be adjusted includes:

[0138] Use the grid cells in the area to be adjusted as the grid cells to be adjusted;

[0139] Determine the reference line corresponding to the grid cell to be adjusted, and determine the relative position of the grid cell to be adjusted and the reference line, wherein the reference line is contained within the area to be adjusted;

[0140] Determine the weight value of each reference line based on its relative position;

[0141] The reference line with a weight value greater than the second preset threshold is used as the target reference line;

[0142] Adjust the orientation and size of the grid cell to be adjusted based on the angle and spacing between the grid cell to be adjusted and the target reference line.

[0143] Specifically, the grid cells in the region to be adjusted are used as the grid cells to be adjusted. Reference lines corresponding to the grid cells to be adjusted are determined; these reference lines can be one or more of boundary lines, feature lines, or virtual lines. For example: determining the distance from the center point of the grid cell to be adjusted to each boundary line of the region to be adjusted, and identifying the boundary line closest to the grid cell to be adjusted as the reference line; pre-setting a distance threshold, and setting all boundary lines smaller than this distance threshold as reference lines; or directly using the boundary lines of the region to be adjusted as the reference lines corresponding to the grid cells to be adjusted.

[0144] Determine the relative position of the grid cell to be adjusted and the reference line. For example, determine the vertical distance from the center point of the grid cell to be adjusted to the reference line, and determine the angle between each edge of the grid cell to be adjusted and the reference line.

[0145] Weight values ​​represent the influence of different reference lines on adjusting mesh cell parameters. The weight value of each reference line is determined based on its relative position. For example, if the angle between the cell edge and the reference line is the smallest, it indicates that the reference line may have a more significant correlation and may be more helpful in adjusting the mesh cell; therefore, a higher weight value is given to this reference line. Alternatively, the smaller the perpendicular distance from the center point to the reference line, the greater the weight value of the reference line.

[0146] Reference lines with weight values ​​greater than a second preset threshold are used as target reference lines. For example, the weight values ​​include three levels: 1, 2, and 3. Based on the relative position, the corresponding level among the three levels (1, 2, and 3) is determined as the weight value for different reference lines. The second preset threshold is, for example, 2. Reference lines with weight values ​​greater than the second preset threshold are used as target reference lines, that is, reference lines with level 3 are used as target reference lines.

[0147] This embodiment can not only change the orientation of the mesh cell to be adjusted, but also its shape, size, and other key characteristics. Based on the angle and distance between the mesh cell and the target reference line, the orientation and size of the mesh cell are adjusted. For example, a distance threshold is preset; if the distance between a cell edge and the target reference line is less than this threshold, it is set as the edge of the cell to be adjusted. Based on the angle between the edge of the cell and the target reference line, the edge of the cell to be adjusted is rotated so that its orientation is consistent with the target reference line. The other edges of the mesh cell to be adjusted are adjusted accordingly to ensure that the mesh cell to be adjusted is closed.

[0148] In this embodiment, a reference line is introduced to adjust the grid cells in the area to be adjusted, which helps to reduce the problem of inconsistent grid cell orientation and size caused by the randomness of the grid generation algorithm, thereby improving the overall quality of the adjusted grid cells.

[0149] As an optional embodiment, before the above step S401 "obtain the physical quantity determination equation and analytical solution function corresponding to the mesh element", it is necessary to generate the mesh element first. The specific process may include steps A1 to A4.

[0150] Step A1: Generate an initial mesh based on the target object model.

[0151] Specifically, the target object model is the model data that requires the construction of a corresponding large-scale mesh. This can be scanned data obtained from scanning a workpiece, or a model created by the user using modeling tools, such as the FVCOM ocean model. Based on the geometric characteristics of the target object, feature lines are constructed on its surface; the number of discrete points on the feature lines is set, and the surface mesh is configured according to the settings; based on the surface mesh, the initial mesh of the target object is configured. The initial mesh is a structured spatial mesh, and the generation process can be completed using a mesh generation tool configured on the client.

[0152] Step A2: Divide the initial grid to obtain at least one grid partition, and distribute the at least one grid partition to the preset computing nodes.

[0153] Specifically, the configuration principle of computing nodes is determined by their computing power. If the client hardware meets the computing power requirements for task execution, computing nodes can be directly configured on the client. If the hardware does not meet the computing power requirements, some computing nodes will be configured on the client, while the remaining computing nodes will be configured on the server. Using a mesh generation tool configured on the server, a structured spatial mesh is generated from the received target model to obtain an initial mesh. This initial mesh is then divided into mesh partitions, which are sent to the computing nodes.

[0154] In step A3, the computing node encrypts the received grid partition using a preset partial differential equation algorithm to obtain an encrypted grid partition.

[0155] Specifically, after receiving the grid partition that needs to be encrypted, the computing node processes the grid partition using a preset partial differential equation algorithm to obtain the encrypted grid partition. Finally, based on the initial grid division result, the encrypted grid partitions are spliced ​​together to obtain the target large-scale grid, which contains multiple grid cells.

[0156] Step A4: Synthesize encrypted mesh partitions to obtain the target large-scale mesh, which contains multiple mesh cells.

[0157] Specifically, based on the initial grid division results, the encrypted grid partitions are spliced ​​together to obtain the target large-scale grid, which contains multiple grid cells.

[0158] In this embodiment, by dividing the initial grid, the computational task of generating the target large-scale grid based on the initial grid is divided into multiple sub-tasks, alleviating the computational pressure on the hardware and reducing the difficulty of generating large-scale grids. The grid is refined using a partial differential equation algorithm, which, compared to traditional simple spatial grid refinement methods, ensures grid quality and meets the high precision and accuracy requirements of numerical simulation.

[0159] This embodiment also provides a grid cell quality evaluation device, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0160] This embodiment provides a grid cell quality evaluation device, such as... Figure 6 As shown, it includes:

[0161] Module 601 is used to obtain the physical quantity determination equations and analytical solution functions corresponding to the grid cells;

[0162] The first determining module 602 is used to determine additional source terms based on the physical quantity determining equation and analytical solution function, wherein the additional source terms are used to adjust the analytical solution of the physical quantity determining equation to the function value of the analytical solution function;

[0163] The result determination module 603 is used to obtain a first result based on the analytical solution function and preset parameters, determine the boundary values ​​in the first result, and determine the equation, boundary values ​​and additional source terms based on the physical quantities to obtain a second result.

[0164] The quality evaluation module 604 is used to determine the quality evaluation result of the grid cell based on the first result and the second result.

[0165] In some alternative implementations, the first determining module 602 includes:

[0166] The first creation unit is used to determine the equation based on the physical quantities and create the first partial differential equation operator.

[0167] The first computational unit is used to combine the analytical solution function with the first partial differential equation operator to obtain the first intermediate partial differential equation operator;

[0168] The second computational unit is used to obtain additional source terms based on the first intermediate partial differential equation operator.

[0169] In some alternative embodiments, the device further includes:

[0170] The second determination module is used to determine the error index of the grid cell based on the quality evaluation results;

[0171] The third determining module is used to determine the grid cell to be marked in the grid cell according to the error index, wherein the grid cell to be marked is the grid cell whose error index is greater than the first preset threshold.

[0172] The marking module is used to call the first preset interface to generate a distribution map containing grid cells, and to mark the grid cells to be marked in the distribution map.

[0173] In some optional implementations, the preset parameters include a first sub-parameter and a second sub-parameter, and the result determination module 603 includes:

[0174] The third calculation unit is used to combine the first sub-parameter and the analytical solution function to obtain the first analytical solution;

[0175] The fourth computational unit is used to combine the second sub-parameter and the analytical solution function to obtain the second analytical solution;

[0176] The integration unit is used to obtain the first result based on the first analytical solution and the second analytical solution.

[0177] In some alternative implementations, the result determination module 603 includes:

[0178] The first acquisition unit is used to acquire the second analytical solution from the first result and use the second analytical solution as the boundary value.

[0179] The fifth calculation unit is used to combine the additional source terms with the physical quantity determination equations to obtain the target equation;

[0180] The transmission unit is used to call the second preset interface to transmit the objective equation and boundary values ​​to the preset numerical software;

[0181] The second acquisition unit is used to acquire the second result from the return information of the preset numerical software.

[0182] In some alternative embodiments, the device further includes:

[0183] The variable acquisition module is used to acquire the first input variable, the second input variable, the preset output variable, and the predefined expression;

[0184] The first interface creation module is used to create a first sub-interface based on the first input variable and the preset output variable, wherein the first sub-interface is contained in the second preset interface;

[0185] The second interface creation module is used to create a second sub-interface based on the second input variable, the preset output variable, and the predefined expression. The second sub-interface is contained within the second preset interface.

[0186] In some alternative embodiments, the device further includes:

[0187] The region determination module is used to determine the region to be adjusted in the distribution map;

[0188] The grid cell adjustment module is used to adjust the parameters of the grid cells in the area to be adjusted according to the grid generation algorithm.

[0189] In some alternative implementations, the first determining module 602 further includes:

[0190] The second creation unit is used to create the second partial differential equation operator based on the equations and predefined expressions determined by the physical quantities.

[0191] The sixth computational unit is used to combine the analytical solution function and the second partial differential equation operator to obtain the second intermediate partial differential equation operator;

[0192] The seventh computational unit is used to determine additional source terms based on the second intermediate partial differential equation operator and predefined expressions.

[0193] In some alternative implementations, the grid cell adjustment module includes:

[0194] The first setting unit is used to set the grid cells in the area to be adjusted as the grid cells to be adjusted.

[0195] The first determining unit is used to determine the reference line corresponding to the grid cell to be adjusted, and to determine the relative position of the grid cell to be adjusted and the reference line, wherein the reference line is contained in the area to be adjusted;

[0196] The second determining unit is used to determine the weight values ​​of each reference line based on their relative positions.

[0197] The second setting unit is used to take a reference line with a weight value greater than a second preset threshold as the target reference line;

[0198] The adjustment unit is used to adjust the orientation and size of the mesh cell to be adjusted based on the angle and spacing between the mesh cell to be adjusted and the target reference line.

[0199] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0200] In this embodiment, the grid cell quality evaluation device is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0201] This application also provides a computer device having the above-described features. Figure 6 The grid cell quality evaluation device shown.

[0202] Please see Figure 7 , Figure 7 This is a schematic diagram of the structure of a computer device provided in an optional embodiment of this application, such as... Figure 7 As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 7 Take a processor 10 as an example.

[0203] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include an integrated circuit, a programmable logic device, or a combination thereof. The programmable logic device may be a complex programmable logic device, a field-programmable gate array (FPGA), a general-purpose array logic (GPA), or any combination thereof.

[0204] The memory 20 stores instructions executable by at least one processor 10 to cause at least one processor 10 to perform the method shown in the above embodiments.

[0205] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0206] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0207] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0208] This application also provides a computer-readable storage medium. The methods described in this application can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code downloaded over a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the methods shown in the above embodiments are implemented.

[0209] A portion of this application can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to this application through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0210] Although embodiments of this application have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of this application, and such modifications and variations all fall within the scope defined by this application.

Claims

1. A method for evaluating the quality of grid cells, characterized in that, The method includes: Obtain the physical quantity determination equations and analytical solution functions corresponding to the grid cells, wherein the grid cells are obtained by dividing the simulation region. In the finite volume community ocean model, the simulation region is an ocean region, and in the weather research and forecasting model, the simulation region is an atmospheric region. Based on the physical quantity determining equation and the analytical solution function, an additional source term is determined, wherein the additional source term is used to adjust the analytical solution of the physical quantity determining equation to the function value of the analytical solution function; The step of determining additional source terms based on the physical quantities and the analytical solution function includes: determining the equation based on the physical quantities and creating a first partial differential equation operator; combining the analytical solution function with the first partial differential equation operator to obtain a first intermediate partial differential equation operator; and obtaining the additional source terms based on the first intermediate partial differential equation operator. Based on the analytical solution function and preset parameters, a first result is obtained. Boundary values ​​are determined in the first result. Based on the physical quantities, the equation, the boundary values, and the additional source terms are determined to obtain a second result. The preset parameters include a first sub-parameter and a second sub-parameter. Obtaining the first result based on the analytical solution function and the preset parameters includes: combining the first sub-parameter and the analytical solution function to obtain a first analytical solution; combining the second sub-parameter and the analytical solution function to obtain a second analytical solution; and obtaining the first result based on the first analytical solution and the second analytical solution. The step of determining the boundary value in the first result and determining the equation, the boundary value, and the additional source term based on the physical quantity to obtain the second result includes: obtaining the second analytical solution in the first result and using the second analytical solution as the boundary value; combining the additional source term with the equation determined by the physical quantity to obtain the target equation; calling a second preset interface to transmit the target equation and the boundary value to preset numerical software; and obtaining the second result from the return information of the preset numerical software. Based on the first result and the second result, the quality evaluation result of the grid cell is determined.

2. The method according to claim 1, characterized in that, After determining the quality evaluation result of the grid cell based on the first result and the second result, the method further includes: Based on the quality evaluation results, the error index of the grid cell is determined; Based on the error index, a grid cell to be marked is determined in the grid cell, wherein the grid cell to be marked is a grid cell whose error index is greater than a first preset threshold; The first preset interface is invoked to generate a distribution map containing the grid cells, and the grid cells to be marked are marked in the distribution map.

3. The method according to claim 1, characterized in that, Before invoking the second preset interface to transmit the objective equation and the boundary values ​​to the preset numerical software, the method further includes: Obtain the first input variable, the second input variable, the preset output variable, and the predefined expression; Based on the first input variable and the preset output variable, a first sub-interface is created, wherein the first sub-interface is included in the second preset interface; A second sub-interface is created based on the second input variable, the preset output variable, and the predefined expression, wherein the second sub-interface is contained within the second preset interface.

4. The method according to claim 2, characterized in that, After generating a distribution map containing the grid cells and marking the grid cells to be marked in the distribution map, the method further includes: Identify the areas to be adjusted in the distribution map; The parameters of the grid cells in the region to be adjusted are adjusted according to the grid generation algorithm.

5. The method according to claim 3, characterized in that, The step of determining the equation and the analytical solution function based on the physical quantity, and determining the additional source term, includes: Based on the physical quantities, determine the equations and the predefined expressions, and create a second partial differential equation operator; The analytical solution function and the second partial differential equation operator are combined to obtain the second intermediate partial differential equation operator; The additional source term is determined based on the second intermediate partial differential equation operator and the predefined expression.

6. The method according to claim 4, characterized in that, The adjustment of the parameters of the grid cells in the region to be adjusted includes: The grid cells in the region to be adjusted are taken as the grid cells to be adjusted. Determine the reference line corresponding to the grid cell to be adjusted, and determine the relative position of the grid cell to be adjusted and the reference line, wherein the reference line is contained in the area to be adjusted; Based on the relative positions, determine the weight values ​​of each reference line; The reference line with a weight value greater than the second preset threshold is used as the target reference line; The orientation and size of the grid cell to be adjusted are adjusted according to the angle and spacing between the grid cell to be adjusted and the target reference line.

7. A computer device, characterized in that, include: A memory and a processor are communicatively connected, the memory stores computer instructions, and the processor executes the computer instructions to perform the grid cell quality evaluation method according to any one of claims 1 to 6.

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