A flow field solving method and device, computer equipment and storage medium

Abstract

This application provides a flow field solution method, apparatus, computer equipment, and storage medium, including: first, retrieving a pre-trained model that can construct the mapping relationship between geometry, operating conditions, and flow field; inputting the geometry and operating condition information of the object to be solved; and generating the current round of overall flow field prediction field based on a discrete carrier. Next, selecting an evaluation location in the existing computational grid, calculating the prediction field residuals using physical equations, delineating the region to be refined based on the residuals, and implementing adaptive grid refinement to update the computational grid. Then, regenerating the prediction field using the pre-trained model and the updated grid as the basis for the next round of solution. The above process is iteratively repeated until a preset stopping condition is met, ultimately outputting a reliable flow field solution result. Using this method, the overall flow field solution efficiency, grid resource utilization efficiency, and accuracy of the flow field solution results can be effectively improved.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology of fluid mechanics, and more specifically, to a flow field solution method, apparatus, computer equipment, and storage medium. Background Technology

[0002] Numerical flow field analysis is a core foundational technique for fluid dynamics analysis in numerous engineering fields such as aerospace, energy, and transportation. It is primarily used to obtain the distribution patterns of fluid flow under different structural shapes and operating conditions. In practical engineering design and simulation verification, it is necessary not only to accurately reproduce complex and intricate flow characteristics such as shock waves, boundary layers, and flow separation to ensure that simulation results closely match real flow conditions, but also to have clear requirements for overall solution speed and batch simulation capabilities. Balancing solution accuracy and simulation efficiency has become a common goal pursued in the industry.

[0003] The most widely used method for solving flow fields is the traditional computational fluid dynamics global mesh refinement solution mode. This method first delineates the complete fluid computation domain and divides the overall computational mesh according to the shape characteristics of the simulation object. In order to accurately analyze the flow variation law of the high gradient flow region inside the flow field, the mesh in the entire computational domain is usually uniformly refined. Then, iterative calculations are carried out through discrete fluid control equations. The global flow field data is solved by long-term numerical iteration, thereby obtaining the complete distribution results of flow field parameters such as velocity, pressure, and density.

[0004] The solution method of global unified encryption has obvious drawbacks. Global mesh encryption will directly lead to a sharp increase in the number of overall mesh cells, resulting in a significant increase in the amount of data computation during the simulation. It will not only consume a lot of computer hardware computing resources, but also significantly prolong the numerical iteration calculation time. At the same time, global encryption will also perform fine meshing on ineffective areas with gentle flow changes, resulting in serious waste of mesh resources and low mesh utilization efficiency. It is difficult to adapt to the actual engineering needs of large-scale rapid simulation calculation under multiple geometric models and multiple working conditions. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a flow field solution method, apparatus, computer equipment and storage medium, which can effectively improve the overall flow field solution efficiency, grid resource utilization efficiency and the accuracy of flow field solution results.

[0006] In a first aspect, embodiments of this application provide a flow field solution method, the method comprising: Obtain a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field; The geometric and working condition information of the object to be solved is input into the pre-trained model to generate the overall prediction field of the current wheel on the discrete carrier; An evaluation location is selected on the computational grid of the current round, and at the evaluation location, the residual is calculated by substituting the physical equations based on the overall prediction field of the current round. The region to be encrypted is determined based on the residual, and adaptive mesh refinement is performed on the region to be encrypted to update the computational mesh; On the updated computational grid, the pre-trained model is used to regenerate the overall prediction field on the discrete carrier, and the regenerated prediction field is passed to the updated computational grid as the overall prediction field for the next round. Repeat the above steps until the stopping condition is met, and take the current round's overall predicted field when the stopping condition is met as the final flow field solution result; The step of calculating the residual at the evaluation location by substituting the overall prediction field of the current wheel into the physical equation includes: The coordinates of the evaluation location are mapped to the domain of the discrete carrier to obtain the mapped coordinates; Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation; Substituting the field values ​​and derivatives into the governing equations and boundary conditions, we obtain the internal field residuals and boundary residuals. The residual at the evaluation location is obtained by weighted summation of the interior field residual and the boundary residual.

[0007] Optionally, the discrete carrier is a regular grid; the pre-trained model is a neural operator model; the neural operator model is a physical information neural operator, a Fourier neural operator, or a geometric perception Fourier neural operator; the parameters of the pre-trained model remain unchanged during the iteration process; Selecting an evaluation location on the computation grid of the current round includes: The evaluation location is selected at the midpoint of the edge, the midpoint of the boundary edge, the cell center, the cell centroid, or the center of the circumcircle of the computational grid.

[0008] Optionally, determining the region to be encrypted based on the residual includes: The residuals at each of the aforementioned evaluation locations are sorted. The grid area corresponding to the top fixed percentage or fixed number of evaluation positions in the residual ranking is determined as the area to be encrypted.

[0009] Optionally, performing adaptive mesh refinement on the region to be encrypted to update the computational mesh includes: Insert a new node into the area to be encrypted; The computational mesh containing the new node is reconstructed using constrained Delaunay triangulation to obtain the reconstructed computational mesh; The reconstructed computational grid is subjected to grid quality constraints of minimum angle threshold and adjacent cell area ratio threshold to obtain the updated computational grid.

[0010] Optionally, the step of regenerating the overall prediction field on the discrete carrier using the pre-trained model on the updated computational grid, and transferring the regenerated prediction field to the updated computational grid as the overall prediction field for the next round, includes: Keeping the parameters of the pre-trained model unchanged, the geometric information and working condition information are input into the pre-trained model again; A single forward inference is performed on the discrete carrier to obtain the regenerated global prediction field. The regenerated global prediction field is mapped to the node or cell center of the updated computational grid by interpolation to obtain the global prediction field for the next round.

[0011] Optionally, the stopping condition is at least one of the following: The maximum residual value at all evaluation locations is below the first threshold; The average residual at all assessed locations is below the second threshold; The rate of change of the lift coefficient of the overall predicted field between two adjacent rounds is lower than the third threshold; The rate of change of the drag coefficient of the overall predicted field between two adjacent rounds is lower than the fourth threshold; The preset maximum number of iterations has been reached.

[0012] Secondly, embodiments of this application provide a flow field solving apparatus, the apparatus comprising: The pre-trained model acquisition module is used to acquire a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field; The overall prediction field generation module is used to input the geometric information and working condition information of the object to be solved into the pre-trained model and generate the overall prediction field of the current round on the discrete carrier. The residual calculation module is used to select an evaluation position on the computational grid of the current round, and at the evaluation position, calculate the residual by substituting the physical equation into the overall prediction field of the current round. The computational grid update module is used to determine the region to be encrypted based on the residual, and to perform adaptive grid refinement on the region to be encrypted in order to update the computational grid; The overall prediction field update module is used to regenerate the overall prediction field on the discrete carrier through the pre-trained model on the updated computing grid, and then pass the regenerated prediction field to the updated computing grid as the overall prediction field for the next round. The flow field solution result determination module is used to repeat the above steps until the stopping condition is met, and the overall predicted field of the current round when the stopping condition is met is taken as the final flow field solution result. The step of calculating the residual at the evaluation location by substituting the overall prediction field of the current wheel into the physical equation includes: The coordinates of the evaluation location are mapped to the domain of the discrete carrier to obtain the mapped coordinates; Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation; Substituting the field values ​​and derivatives into the governing equations and boundary conditions, we obtain the internal field residuals and boundary residuals. The residual at the evaluation location is obtained by weighted summation of the interior field residual and the boundary residual.

[0013] Optionally, the discrete carrier is a regular grid; the pre-trained model is a neural operator model; the neural operator model is a physical information neural operator, a Fourier neural operator, or a geometric perception Fourier neural operator; the parameters of the pre-trained model remain unchanged during the iteration process; Selecting an evaluation location on the computation grid of the current round includes: The evaluation location is selected at the midpoint of the edge, the midpoint of the boundary edge, the cell center, the cell centroid, or the center of the circumcircle of the computational grid.

[0014] Optionally, determining the region to be encrypted based on the residual includes: The residuals at each of the aforementioned evaluation locations are sorted. The grid area corresponding to the top fixed percentage or fixed number of evaluation positions in the residual ranking is determined as the area to be encrypted.

[0015] Optionally, performing adaptive mesh refinement on the region to be encrypted to update the computational mesh includes: Insert a new node into the area to be encrypted; The computational mesh containing the new node is reconstructed using constrained Delaunay triangulation to obtain the reconstructed computational mesh; The reconstructed computational grid is subjected to grid quality constraints of minimum angle threshold and adjacent cell area ratio threshold to obtain the updated computational grid.

[0016] Optionally, the step of regenerating the overall prediction field on the discrete carrier using the pre-trained model on the updated computational grid, and transferring the regenerated prediction field to the updated computational grid as the overall prediction field for the next round, includes: Keeping the parameters of the pre-trained model unchanged, the geometric information and working condition information are input into the pre-trained model again; A single forward inference is performed on the discrete carrier to obtain the regenerated global prediction field. The regenerated global prediction field is mapped to the node or cell center of the updated computational grid by interpolation to obtain the global prediction field for the next round.

[0017] Optionally, the stopping condition is at least one of the following: The maximum residual value at all evaluation locations is below the first threshold; The average residual at all assessed locations is below the second threshold; The rate of change of the lift coefficient of the overall predicted field between two adjacent rounds is lower than the third threshold; The rate of change of the drag coefficient of the overall predicted field between two adjacent rounds is lower than the fourth threshold; The preset maximum number of iterations has been reached.

[0018] Thirdly, embodiments of this application provide a computer device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, the steps of the flow field solving method described in any of the optional embodiments of the first aspect are performed.

[0019] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the flow field solution method described in any of the optional embodiments of the first aspect.

[0020] The technical solution provided in this application includes, but is not limited to, the following beneficial effects: By acquiring a pre-trained model, a stable mapping relationship is established between geometric parameters, operating conditions, and flow field distribution results. This allows for the pre-establishment of the basic logic for flow field solving, eliminating the tedious on-site setup of the corresponding relationships and laying a solid foundation for subsequent rapid flow field simulation.

[0021] By inputting the geometric and working condition information of the object to be solved into the pre-trained model, and generating the overall prediction field for the corresponding rounds based on a fixed discrete carrier, the preliminary deduction of the global flow field can be completed quickly within a unified carrier range, and the complete preliminary distribution data of the flow field can be obtained at one time. This effectively simplifies the initial flow field solution process and improves the output efficiency of the preliminary flow field results.

[0022] By selecting the corresponding evaluation location within the existing computational grid and performing residual calculations on the overall prediction field in conjunction with physical equations, it is possible to strictly determine the deviations in the prediction results according to the actual fluid flow laws, accurately locate the specific location of errors in the flow field data, clearly quantify the magnitude of the deviations, and provide accurate and reliable judgment basis for subsequent grid optimization and adjustment.

[0023] Based on the calculated residual data, the area to be refined is delineated, and the mesh is adaptively refined and the overall computational mesh is updated in a targeted manner. Mesh optimization and adjustment can be performed only on the areas where the flow field deviation is concentrated, without the need to perform uniform mesh refinement on the entire solution area, and the overall mesh layout can be reasonably optimized.

[0024] On top of the updated computational grid, a new overall prediction field is generated again using the pre-trained model. This prediction field is then used as the basis for the next round of solution calculations. This allows for the correction of deficiencies in the previous flow field predictions by combining the optimized grid conditions, thereby achieving gradual optimization and improvement of the flow field solution results.

[0025] The solution process continuously executes various solution operations until the preset stopping conditions are met, at which point the final flow field solution result is determined. Through multiple iterations, the flow field prediction deviation can be continuously reduced, and the fit of the flow field data can be gradually improved to ensure that the final output flow field result can meet the accuracy standards required for actual use.

[0026] In summary, this application completes the overall solution of the flow field according to the defined steps, simplifies the flow field deduction process by relying on the pre-trained model, accurately controls data deviation by relying on residual judgment, optimizes the solution conditions by cooperating with adaptive mesh adjustment, and steadily improves the solution accuracy through iterative calculation. The overall solution process is simple and orderly, and can reasonably optimize the overall solution rhythm while ensuring the accuracy of the flow field solution results, taking into account both the practicality and efficiency of the flow field solution.

[0027] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A flowchart of a flow field solution method provided in Embodiment 1 of this application is shown; Figure 2This illustration shows a schematic diagram of a candidate point provided in Embodiment 1 of this application; Figure 3 The diagram shows a mesh before and after refinement of a neural operator according to Embodiment 1 of this application; Figure 4 This illustration shows a schematic diagram of a high residual value region and a local encryption location of a neural operator provided in Embodiment 1 of this application; Figure 5 A flowchart of a method for determining the residual of an evaluation location provided in Embodiment 1 of this application is shown; Figure 6 A flowchart of a method for determining a region to be encrypted, provided in Embodiment 1 of this application, is shown; Figure 7 A flowchart of a computational grid update method provided in Embodiment 1 of this application is shown; Figure 8 A flowchart of a global prediction field update method provided in Embodiment 1 of this application is shown; Figure 9 A general flowchart of a flow field solution method provided in Embodiment 1 of this application is shown; Figure 10 This illustration shows a schematic diagram of a velocity field in the x-direction optimized by a neural operator, as provided in Embodiment 1 of this application. Figure 11 This illustration shows a schematic diagram of a y-direction velocity field optimized by a neural operator according to Embodiment 1 of this application; Figure 12 A schematic diagram of a pressure field optimized by a neural operator is shown in Embodiment 1 of this application; Figure 13 This illustration shows a schematic diagram of a density field optimized by a neural operator according to Embodiment 1 of this application; Figure 14 This shows a schematic diagram of the structure of a flow field solving device provided in Embodiment 2 of this application; Figure 15 A schematic diagram of the structure of a computer device provided in Embodiment 3 of this application is shown. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, 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. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0031] Example 1 This application provides a flow field solution method that can be adapted to continuous medium field problems controlled by PDEs (Partial Differential Equations), such as aerodynamic flow fields, internal flow fields, and thermal-fluid coupled flow fields. It is particularly suitable for flow field simulation of aerodynamic shapes such as two-dimensional airfoils, three-dimensional wings, and blades. Through iterative coordination of model inference, residual evaluation, and mesh refinement, the computational cost is significantly reduced while ensuring solution accuracy.

[0032] To facilitate understanding of this application, the following is combined with... Figure 1 The flowchart of the flow field solving method provided in Embodiment 1 of this application illustrates Embodiment 1 in detail.

[0033] See Figure 1 As shown, Figure 1 A flowchart of a flow field solving method provided in Embodiment 1 of this application is shown, wherein the method includes steps S101 to S106: S101: Obtain a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field.

[0034] Specifically, the pre-trained model is a neural operator model, with FNO (Fourier Neural Operator) or PINO (Physics-Informed Neural Operator) as the backbone structure. The network width is preferably 64, the number of Fourier modes is preferably 8 or 12, the number of network layers is preferably 4, and the activation function is preferably GeLU (Gaussian Error Linear Unit). The model parameters can be flexibly adjusted according to the specific PDE type, background grid resolution, and target accuracy.

[0035] The Adam optimizer is preferred for model training, with an initial learning rate set to 10. -3 The learning rate adopts a phased decay strategy; the training objective is composed of data loss, PDE residual loss, and boundary loss.

[0036] The training samples contain multi-geometry and multi-condition data, with condition parameters including incoming Mach number, angle of attack, Reynolds number, far-field pressure, and far-field temperature. After the model training is completed, the parameters are frozen to form an operator mapping that can be directly called.

[0037] S102: Input the geometric information and working condition information of the object to be solved into the pre-trained model to generate the overall prediction field of the current wheel on the discrete carrier.

[0038] Specifically, geometric information is encoded as a symbolic distance function, occupancy mask, wall marker, and boundary type marker; working condition information is encoded as a normalized parameter channel.

[0039] The discrete carrier is a background regular grid, which is a rectangular tensor product Cartesian grid. Preset resolutions such as 128×128, 128×256, and 256×256 can be selected. This grid is a standard inference carrier adapted to neural operators and supports fast spatial operations and feature extraction.

[0040] The model directly outputs the complete flow field prediction results on the background regular grid. The overall prediction field expression is:

[0041] in: : Predicted flow field vector on the background regular grid; : The x-coordinate of the background grid; : The y-coordinate of the background grid; Fluid density; Momentum density in the x-direction; : Momentum density in the y-direction; Total energy per unit volume.

[0042] S103: Select an evaluation position on the computational grid of the current round, and at the evaluation position, calculate the residual by substituting the physical equation into the overall prediction field of the current round.

[0043] Specifically, the current round of computation uses a triangular unstructured grid to adapt to the boundary fitting requirements of complex geometries; the evaluation location is not limited to the cell center, but covers the relevant locations of the grid edge, boundary, and cell core, which can accurately capture the characteristics of local high gradient and high rate of change regions in the flow field.

[0044] Residual calculation is based on the continuous flow field prediction field output by the model. It achieves a more refined error assessment by substituting the continuous prediction field into the fluid control equations and boundary conditions, rather than relying on discrete grid solutions obtained through traditional numerical methods.

[0045] See Figure 2 As shown, Figure 2 This diagram illustrates a candidate point distribution for an airfoil NACA (National Advisory Committee for Aeronautics) 6334-18, as provided in Embodiment 1 of this application. Blue dots represent original mesh nodes, and red dots represent candidate points generated from the original mesh edges. These candidate points are evaluation points for continuous PDE residual evaluation. This diagram visually demonstrates the PDE residual evaluation implementation method based on mesh edge-generated evaluation points, providing fundamental data support for subsequent selection of the refinement area and mesh refinement.

[0046] S104: Determine the region to be encrypted based on the residual, and perform adaptive mesh refinement on the region to be encrypted to update the computational mesh.

[0047] Specifically, the larger the residual value, the greater the deviation between the predicted flow field and the physical equation at the corresponding evaluation location. This location usually corresponds to regions with significant flow field physical characteristics such as shock waves, leading edge, trailing edge, and boundary layer. The area to be refined should prioritize covering such high residual regions to avoid redundant calculations caused by global mesh refinement.

[0048] The mesh refinement adopts a local refinement method, inserting new nodes and reconstructing the mesh only in the area to be refined, while maintaining the original mesh topology and density in the unrefined area. While focusing on the analytical accuracy of key flow field areas, the overall number of mesh cells is strictly controlled.

[0049] See Figure 3 As shown, Figure 3 The diagram illustrates the mesh before and after refinement using a neural operator according to Embodiment 1 of this application. The upper diagram shows the initial mesh before refinement, and the lower diagram shows the mesh after refinement using the method described in this application. This visually demonstrates the local mesh refinement effect in key areas of the flow field. This diagram, through before-and-after comparison, showcases the mesh optimization effect of this application and verifies the technical advantage of achieving local refinement only in key areas of the flow field.

[0050] Taking the NACA6334-18 main example, the hierarchical scale of the mesh refinement process is as follows: the initial mesh has 4511 nodes and 8657 elements; after the first round of refinement, the number of nodes is approximately 6000 and the number of elements is approximately 12000; after the second round of refinement, the number of nodes is approximately 8000 and the number of elements is approximately 16000; after the third round of refinement, the number of nodes is approximately 10000 and the number of elements is approximately 20000; after the fourth round of refinement, the number of nodes is approximately 14000 and the number of elements is approximately 28000.

[0051] Compared with the adaptive refinement method of traditional commercial CFD software, the mesh size control effect of this method is significant: In the same example, the commercial software has a mesh size of about 788,402 elements after 5 rounds of adaptive refinement, while this method only has about 20,000 elements after the 3rd round of refinement, and can achieve a lift-drag convergence trend close to that of high-density adaptive refinement. This shows that this method does not rely on finer meshes, but rather concentrates refinement resources on key flow field regions through residual guidance, which greatly reduces the mesh size and computational cost.

[0052] See Figure 4 As shown, Figure 4 This diagram illustrates a high residual value region and the local refinement location of the neural operator provided in Embodiment 1 of this application. The high residual value region is concentrated at the leading and trailing edges of the airfoil and near the shock wave, indicating that the candidate interpolation point residual evaluation can effectively locate the key physical regions, rather than relying solely on the element center error marker. This diagram corresponds to the PDE residual calculation and region selection steps of this application, verifying that the residual evaluation method of this application can accurately capture the key physical regions of the flow field, solving the deficiency of traditional element center error markers in identifying boundary surface errors, and providing a reliable basis for mesh refinement.

[0053] S105: On the updated computational grid, the overall prediction field is regenerated on the discrete carrier using the pre-trained model, and the regenerated prediction field is passed to the updated computational grid as the overall prediction field for the next round.

[0054] Specifically, all parameters of the pre-trained model remain fixed during the iteration process, eliminating the need to retrain the model for the updated grid and avoiding the high computational overhead and time cost of repeated training. The model can be repeatedly called to perform inference tasks.

[0055] Each inference by the model is performed on a fixed background regular grid, outputting a new round of complete continuous flow field prediction. Then, the prediction field on the regular grid is mapped to the topology-updated unstructured grid through interpolation, adapting to the node distribution of the current computing grid, without needing to adjust the model inference carrier.

[0056] S106: Repeat the above steps until the stopping condition is met, and take the current overall predicted field of the current wheel when the stopping condition is met as the final flow field solution result.

[0057] Specifically, the iterative process forms a closed-loop execution logic. Each round sequentially completes model inference to generate the prediction field, evaluates the position residual calculation, determines the region to be encrypted, refines and updates the mesh, and regenerates and maps the prediction field, thereby gradually improving the accuracy of the flow field solution.

[0058] The number of iterations can be flexibly set according to the required solution accuracy. In normal scenarios, 4 to 5 iterations are sufficient to achieve convergence. In the later stages of iteration, a high-precision CFD solver can be switched to verify the results and further improve the reliability of the final results.

[0059] To avoid confusion between hierarchical meshes and sensitivity analysis meshes, the mesh correspondences in the examples are as follows: the initial mesh to the 4th round of refinement is a 5-layer hierarchical mesh formed by 4 rounds of refinement, used to demonstrate the refinement process round by round; the target mesh is the 3rd round of refinement mesh, which is the optimal mesh for the main example; the coarser contrast mesh is a reduced-density contrast mesh constructed around the target mesh, and is not by default equivalent to the 2nd round of refinement mesh; the finer contrast mesh is a denser contrast mesh constructed around the target mesh, and is not by default equivalent to the 4th round of refinement mesh.

[0060] Taking the NACA6334-18 main example, the lift and drag of the target mesh and its coarser and finer comparison meshes are compared. The results show that the difference in lift and drag between the target mesh and the finer comparison mesh is less than 1%, and the difference in lift and drag between the target mesh and the coarser comparison mesh is about 10%. This indicates that the third round of mesh refinement has entered the effective convergence range, and it is not simply a matter of the finer the mesh.

[0061] When NACA0010-65 is used as an auxiliary verification object, a similar convergence trend can be obtained: the optimal mesh is located around the first round of refinement mesh, the difference in lift and drag between the target mesh and the finer comparison mesh is less than 0.1%, and the difference between the target mesh and the coarser comparison mesh is about 2%, which verifies the effectiveness of this method in different examples.

[0062] See Figure 5 As shown, Figure 5 The flowchart illustrates a residual determination method for evaluating a location provided in Embodiment 1 of this application, wherein determining the region to be encrypted based on the residual includes steps S501-S504: S501: Map the coordinates of the evaluation location to the domain of the discrete carrier to obtain the mapped coordinates.

[0063] Specifically, the evaluation location is located in a triangular unstructured grid with arbitrary spatial coordinates. These coordinates need to be mapped to the spatial region corresponding to the background regular grid, and the grid cell containing the evaluation location in the regular grid needs to be located to establish a spatial relationship between the evaluation location in the unstructured grid and the inference domain in the regular grid.

[0064] No. The two-dimensional coordinate vector expression for each evaluation location is:

[0065] in: : No. Two-dimensional coordinate vectors of each evaluation location; : No. x-axis coordinate components of each evaluation location; : No. The y-axis coordinate components of each evaluation location; : Evaluation location number.

[0066] S502: Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation.

[0067] Specifically, the interpolation adopts the bilinear interpolation method. Based on the flow field prediction values ​​of the background regular grid nodes, the interpolation calculation calculates the field value information such as density, velocity, and total energy at the evaluation location, ensuring the continuity and accuracy of the field value interpolation.

[0068] The field derivative can be obtained in two ways: one is to use the Fourier space derivative or automatic differentiation function inside the neural operator to directly output the spatial derivative of the predicted field; the other is to use methods such as finite difference and local polynomial reconstruction to calculate the derivative based on the interpolated field value, thereby reducing numerical calculation errors.

[0069] S503: Substitute the field values ​​and derivatives into the governing equations and boundary conditions to obtain the internal field residuals and boundary residuals.

[0070] Specifically, the flow field governing equations adopt the two-dimensional steady-state Euler equations, and their conservative variable form is as follows:

[0071] in: : Conservative variable vectors of the flow field; Vector transpose operation.

[0072] The static pressure of the fluid is calculated based on the flow field density, velocity, and total energy. The formula for calculating the pressure is:

[0073] in: Hydrostatic pressure; Specific heat ratio; : Velocity component in the x-direction; : The velocity component in the y-direction.

[0074] Substituting the field values ​​and derivatives into Euler's equations, we can calculate the internal field residuals corresponding to the continuity equation, the momentum equation in the x-direction, the momentum equation in the y-direction, and the energy equation: 1. Residuals of the continuity equation:

[0075] 2. Residual of momentum equation in the x-direction:

[0076] 3. Residual of momentum equation in the y-direction:

[0077] 4. Energy equation residuals:

[0078] in: : No. The continuous equation residuals at each evaluation location; : No. The residuals of the momentum equation in the x-direction at each evaluation location; : No. The residuals of the momentum equation in the y-direction at each evaluation location; : No. Energy equation residuals at each evaluation location; : The partial derivative with respect to the x-coordinate of the background grid; : The partial derivative with respect to the y-coordinate of the background grid.

[0079] For the evaluation location located at the solid wall boundary, calculate the boundary residual, which characterizes the deviation between the predicted field and the solid wall normal velocity constraint. The expression for the solid wall boundary residual is:

[0080] in: : No. Boundary residuals at each evaluation location; : The x-component of the normal vector outside the boundary; : The y-component of the outer normal direction; S504: The weighted sum of the inner field residual and the boundary residual is used to obtain the residual of the evaluation position.

[0081] Specifically, based on the importance of physical constraints at different locations in the flow field, weights are assigned to each internal field residual component and the boundary residual, and the weighted sum is used to obtain the comprehensive residual. The expression for the total residual at each evaluation location is:

[0082] in: : No. Total residuals at each assessment location; : Residual weights for continuous equations; : Residual weights of the momentum equation in the x-direction; : Residual weights of the momentum equation in the y-direction; Energy equation residual weights; Boundary residual weights.

[0083] The weights can be adjusted according to actual needs; the boundary residual weights can be adjusted based on the location of the indoor assessment. Setting it to 0, only considering the residuals of the internal field equations; the boundary evaluation location increases. Weights highlight the impact of boundary constraint deviations and are tailored to the physical characteristics of different locations.

[0084] In an alternative implementation, the discrete carrier is a regular grid.

[0085] Specifically, the regular grid is a rectangular tensor product Cartesian grid with grid nodes distributed in a regular array. It has spatial regularity and computational efficiency, and is compatible with the core operations of neural operators such as Fourier transform and spatial convolution, which can significantly improve the inference speed and stability of the model.

[0086] The pre-trained model is a neural operator model.

[0087] Specifically, the neural operator model is a dedicated machine learning model for solving partial differential equations. Unlike traditional neural networks, its core capability is to learn the solution operators of partial differential equations. It can directly establish the mapping from input (geometry, working conditions) to output (flow field solution) and has the characteristics of cross-grid resolution inference and adaptation to parameterized equation families.

[0088] The neural operator model is a physical information neural operator, a Fourier neural operator, or a geometric perception Fourier neural operator.

[0089] Specifically, the physical information neural operator integrates flow field data with physical equation constraints during training, which can improve the physical consistency of the model's prediction results; the Fourier neural operator excels at high-precision inference of regular domain flow fields and is suitable for conventional aerodynamic shape simulation; the geometric perception Fourier neural operator can adapt to unconventional inputs such as point clouds, unstructured meshes, and complex geometric domains through geometric deformation mapping, thus expanding the applicable scenarios of the model.

[0090] The parameters of the pre-trained model remain unchanged during the iteration process.

[0091] Specifically, the model parameters are fixed to the values ​​that are solidified after training. During the iteration process, only forward inference operations are performed, without backpropagation, parameter updates, or other training operations. This design can significantly reduce the computational load of the iteration process, shorten the overall solution cycle, and ensure the stability of the model inference results.

[0092] Selecting an evaluation location on the computation grid of the current round includes: The evaluation location is selected at the midpoint of the edge, the midpoint of the boundary edge, the cell center, the cell centroid, or the center of the circumcircle of the computational grid.

[0093] Specifically, in a two-dimensional triangular mesh scenario, the midpoints of the inner edge and the boundary edge are selected as the core evaluation locations to accurately capture the flow field gradient changes at the mesh boundary surface; the cell center, cell centroid, and circumcircle center are used as supplementary evaluation locations to adapt to different mesh topologies and flow field distribution scenarios, thus improving the residual evaluation system.

[0094] The evaluation location is selected to cover key locations of the grid, breaking through the traditional single evaluation method that only relies on the cell center. It captures flow field deviations from multiple points and dimensions, improving the comprehensiveness and accuracy of residual evaluation.

[0095] In an optional implementation, see Figure 6 As shown, Figure 6 The flowchart illustrates a method for determining a region to be encrypted according to Embodiment 1 of this application, wherein determining the region to be encrypted based on the residual includes steps S601-S602: S601: Sort the residuals at each of the evaluation locations.

[0096] Specifically, the total residuals corresponding to all assessment locations Arranged in descending order of numerical values, the larger the residual value, the greater the flow field prediction deviation at that location, and the more urgent the need for grid refinement.

[0097] S602: The grid area corresponding to the evaluation positions with the highest residual ranking by a fixed percentage or a fixed number is determined as the area to be encrypted.

[0098] Specifically, three screening methods can be used: first, select the top 15% of evaluation positions based on residuals; second, select a fixed number (e.g., 2000) of high residual evaluation positions; and third, set a residual threshold. Select the one that satisfies The evaluation location and the filtering criteria expression are as follows:

[0099] in: : The preset residual threshold.

[0100] After screening, a neighborhood expansion strategy can be combined to include adjacent grids around the high residual evaluation location into the area to be refined, forming a continuous refinement zone. This adapts to the refinement requirements of continuous high gradient flow field regions such as shock waves and avoids fragmentation of the refinement area.

[0101] In an optional implementation, see Figure 7 As shown, Figure 7 The flowchart of a computational grid update method provided in Embodiment 1 of this application is shown, wherein the step of performing adaptive grid refinement on the region to be refined to update the computational grid includes steps S701 to S703: S701: Insert a new node in the area to be encrypted.

[0102] Specifically, new nodes are candidate insertion points corresponding to the high residual evaluation positions obtained through screening; the midpoints of the boundary edges are inserted sequentially in the order of arc length parameterization to ensure that the boundary node sequence is monotonically ordered and fits the geometric boundary; high residual points are inserted only in the area to be encrypted in the inner field to accurately match the flow field feature distribution.

[0103] S702: The computational grid containing the new nodes is reconstructed using constrained Delaunay triangulation to obtain the reconstructed computational grid.

[0104] Specifically, during reconstruction, hole points are set to mark the internal regions of the entity, preventing the generation of mesh cells inside the entity and avoiding mesh penetration of geometric boundaries; the constraint Delaunay triangulation tool is called to regenerate triangular mesh cells based on new nodes and existing mesh nodes, ensuring that the mesh boundaries strictly fit the geometric shape.

[0105] S703: Apply mesh quality constraints of minimum angle threshold and adjacent cell area ratio threshold to the reconstructed computational mesh to obtain the updated computational mesh.

[0106] Specifically, mesh quality constraints are used to eliminate malformed mesh cells. The minimum angle threshold is set to 20° to avoid triangular cells with excessively small angles. The area ratio threshold between adjacent cells is set to 2 to control the size difference between adjacent mesh cells, ensure a smooth transition in mesh size, reduce the accumulation of errors during the numerical solution process, and improve the overall uniformity of the mesh and the stability of the solution.

[0107] In an optional implementation, see Figure 8 As shown, Figure 8 The flowchart illustrates a global prediction field update method provided in Embodiment 1 of this application, wherein the steps of regenerating the global prediction field on the discrete carrier using the pre-trained model on the updated computational grid, and transferring the regenerated prediction field to the updated computational grid as the global prediction field for the next round, include steps S801-S803: S801: Keeping the parameters of the pre-trained model unchanged, input the geometric information and working condition information back into the pre-trained model.

[0108] Specifically, the geometry, boundary conditions, and operating parameters of the object to be solved remain unchanged during the iteration process, without the need for recoding; the model parameters are fixed throughout the process, and the model that has been trained initially can be reused directly. Only the input-output inference process is repeated, which simplifies the iteration operation and reduces the computational cost.

[0109] S802: Perform a single forward inference on the discrete carrier to obtain the regenerated global prediction field.

[0110] Specifically, single forward inference serves as the basic operation of the model, requiring only one feature extraction and mapping calculation. It eliminates the need for iterative solutions or backpropagation, resulting in short computation time, high efficiency, and the ability to quickly output a new round of complete continuous flow field prediction, thus shortening the iteration cycle.

[0111] S803: The regenerated global prediction field is mapped to the node or cell center of the updated computational grid by interpolation to obtain the global prediction field for the next round.

[0112] Specifically, the interpolation method is consistent with S502, using bilinear interpolation to accurately map the continuous predicted field on the background regular grid to the node or cell center position of the updated unstructured grid; the mapped flow field data serves as the basis for the next round of residual calculation, ensuring the continuity and consistency of the flow field data during the iteration process, and forming a stable closed-loop iterative link.

[0113] In an optional implementation, the stopping condition is at least one of the following: Specifically, the stopping conditions are set from three dimensions: residual convergence, flow field parameter stability, and iteration efficiency, taking into account both solution accuracy and computational cost, avoiding excessive iteration that would waste resources, and ensuring the reliability of the final flow field results.

[0114] The maximum residual value at all evaluation locations is below the first threshold.

[0115] Specifically, the first threshold is a preset residual convergence critical value. When the maximum value of the total residual at all evaluation locations is lower than this threshold, it indicates that the maximum deviation between the overall flow field prediction and the physical equation has met the accuracy requirements, and the overall flow field deviation is within a controllable range.

[0116] The average residual at all evaluation locations is below the second threshold.

[0117] Specifically, the second threshold is the critical value of the average level of the residuals across the entire field. It is used to measure the overall prediction accuracy of the flow field, avoid situations where local residuals meet the standard but the overall deviation of the entire field is large, and ensure the overall uniformity of the flow field solution.

[0118] The rate of change of the lift coefficient of the overall predicted field between two adjacent rounds is lower than the third threshold.

[0119] Specifically, the lift coefficient is the core performance parameter for solving the flow field of aerodynamic shapes such as airfoils and wings. After two consecutive iterations, the rate of change of the lift coefficient is lower than the threshold, indicating that the aerodynamic lift characteristics of the flow field have become stable and there is no need to continue iterating.

[0120] The rate of change of the drag coefficient of the overall predicted field between two adjacent wheels is lower than the fourth threshold.

[0121] Specifically, the drag coefficient and lift coefficient together characterize the overall aerodynamic performance of the aerodynamic shape. The synchronous stability of the two is an important indicator of flow field convergence. The rate of change is below the threshold and can be used as a reliable convergence criterion, which is suitable for solving aerodynamic shapes such as transonic airfoils.

[0122] The preset maximum number of iterations has been reached.

[0123] Specifically, the maximum number of iteration rounds is set to 4 to 5 rounds to prevent the residuals or flow field parameters from falling into infinite iterations when they do not converge for a long time. This balances solution efficiency and time cost while ensuring basic solution accuracy, making it suitable for most conventional flow field simulation scenarios.

[0124] To further clarify the technical process, solution results, and flow field characteristics of this application, a complete explanation of all text, annotations, and graphic information in the accompanying drawings is provided.

[0125] See Figure 9 As shown, Figure 9This diagram illustrates the overall flowchart of a flow field solution method provided in Embodiment 1 of this application. The diagram clearly delineates two main execution modules: the model preparation stage and the online usage stage, comprehensively covering the entire execution logic of the method from model training to iterative solution. The model preparation phase is completed sequentially according to the technical execution order: construction of multiple geometries and working conditions samples, encoding of geometric information, boundary conditions and working conditions, mapping of background regular mesh or latent regular domain, joint construction of training data and physical constraints, training of neural operator prior models, and finally generating a pre-trained neural operator prior model. After the model preparation is completed, the online usage phase is entered, which sequentially executes the following steps: input of new geometry and new working conditions, overall prediction of background regular mesh or latent regular domain, construction of candidate insertion point evaluation points, calculation of PDE (Partial Differential Equations) residuals, selection of regions to be refined or insertion points, boundary update and constraint Delaunay (Delaunay mesh partitioning algorithm) reconstruction, and overall re-inference after refinement. CFD (Computational Fluid Dynamics) high-precision verification can be selectively performed according to accuracy requirements. After completing a single iteration, it is determined whether the termination condition is met. If the termination condition is not met, the iteration process is repeated from the candidate insertion point evaluation point construction step. If the termination condition is met, the final flow field result and the optimal mesh are output.

[0126] See Figure 10 As shown, Figure 10 This diagram illustrates a velocity field in the x-direction optimized by a neural operator, as provided in Embodiment 1 of this application. It shows the final velocity field in the x-direction optimized by the neural operator, and clearly demonstrates the distinct shock wave characteristics appearing in the flow field. The dimensions verified that the method in this application can effectively capture key physical features such as shock waves in transonic flow fields and achieve high-precision flow field solutions.

[0127] See Figure 11 As shown, Figure 11 This diagram illustrates a y-direction velocity field optimized by a neural operator according to Embodiment 1 of this application. It shows the final y-direction velocity field optimized by the neural operator, and clearly demonstrates the distinct shock wave characteristics appearing in the flow field. The dimensions further validated the ability of the proposed method to capture key physical features of flow field components in different directions.

[0128] See Figure 12 As shown, Figure 12This diagram illustrates a pressure field optimized by a neural operator according to Embodiment 1 of this application. It shows the final pressure field optimized by the neural operator, and the obvious shock wave characteristics appearing in the flow field are clearly visible in the figure. The dimensions verified the accuracy of the flow field solution of the proposed method, demonstrating its ability to accurately reproduce the pressure abrupt change before and after the shock wave.

[0129] See Figure 13 As shown, Figure 13 This diagram illustrates a density field optimized by a neural operator according to Embodiment 1 of this application. It shows the final density field optimized by the neural operator, and the obvious shock wave characteristics appearing in the flow field can be clearly observed in the figure. The dimensions verified the ability of the proposed method to capture key physical features of transonic flow fields and fully presented the density changes before and after the shock wave.

[0130] Example 2 See Figure 14 As shown, Figure 14 This illustration shows a schematic diagram of a flow field solving device provided in Embodiment 2 of this application, wherein the device includes: The pre-trained model acquisition module 1401 is used to acquire a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field. The overall prediction field generation module 1402 is used to input the geometric information and working condition information of the object to be solved into the pre-trained model and generate the overall prediction field of the current wheel on the discrete carrier. The residual calculation module 1403 is used to select an evaluation position on the computation grid of the current round, and at the evaluation position, calculate the residual by substituting the physical equation into the overall prediction field of the current round. The computational grid update module 1404 is used to determine the region to be encrypted based on the residual, and to perform adaptive grid refinement on the region to be encrypted in order to update the computational grid; The overall prediction field update module 1405 is used to regenerate the overall prediction field on the discrete carrier through the pre-trained model on the updated computing grid, and to pass the regenerated prediction field to the updated computing grid as the overall prediction field for the next round. The flow field solution result determination module 1406 is used to repeat the above steps until the stopping condition is met, and the overall predicted field of the current round when the stopping condition is met is taken as the final flow field solution result. The step of calculating the residual at the evaluation location by substituting the overall prediction field of the current wheel into the physical equation includes: The coordinates of the evaluation location are mapped to the domain of the discrete carrier to obtain the mapped coordinates; Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation; Substituting the field values ​​and derivatives into the governing equations and boundary conditions, we obtain the internal field residuals and boundary residuals. The residual at the evaluation location is obtained by weighted summation of the interior field residual and the boundary residual.

[0131] In one optional implementation, the discrete carrier is a regular grid; the pre-trained model is a neural operator model; the neural operator model is a physical information neural operator, a Fourier neural operator, or a geometric perception Fourier neural operator; the parameters of the pre-trained model remain unchanged during the iteration process; Selecting an evaluation location on the computation grid of the current round includes: The evaluation location is selected at the midpoint of the edge, the midpoint of the boundary edge, the cell center, the cell centroid, or the center of the circumcircle of the computational grid.

[0132] In an optional implementation, determining the region to be encrypted based on the residual includes: The residuals at each of the aforementioned evaluation locations are sorted. The grid area corresponding to the top fixed percentage or fixed number of evaluation positions in the residual ranking is determined as the area to be encrypted.

[0133] In an optional implementation, performing adaptive mesh refinement on the region to be encrypted to update the computational mesh includes: Insert a new node into the area to be encrypted; The computational mesh containing the new node is reconstructed using constrained Delaunay triangulation to obtain the reconstructed computational mesh; The reconstructed computational grid is subjected to grid quality constraints of minimum angle threshold and adjacent cell area ratio threshold to obtain the updated computational grid.

[0134] In an optional implementation, the step of regenerating the overall prediction field on the discrete carrier using the pre-trained model on the updated computational grid, and passing the regenerated prediction field to the updated computational grid as the overall prediction field for the next round, includes: Keeping the parameters of the pre-trained model unchanged, the geometric information and working condition information are input into the pre-trained model again; A single forward inference is performed on the discrete carrier to obtain the regenerated global prediction field. The regenerated global prediction field is mapped to the node or cell center of the updated computational grid by interpolation to obtain the global prediction field for the next round.

[0135] In an optional implementation, the stopping condition is at least one of the following: The maximum residual value at all evaluation locations is below the first threshold; The average residual at all assessed locations is below the second threshold; The rate of change of the lift coefficient of the overall predicted field between two adjacent rounds is lower than the third threshold; The rate of change of the drag coefficient of the overall predicted field between two adjacent rounds is lower than the fourth threshold; The preset maximum number of iterations has been reached.

[0136] Example 3 Based on the same application concept, see [link / reference] Figure 15 As shown, Figure 15 This illustration shows a structural schematic diagram of a computer device provided in Embodiment 3 of this application, wherein, as shown... Figure 15 As shown, the computer device 1500 provided in Embodiment 3 of this application includes: The computer device 1500 includes a processor 1501, a memory 1502, and a bus 1503. The memory 1502 stores machine-readable instructions that can be executed by the processor 1501. When the computer device 1500 is running, the processor 1501 and the memory 1502 communicate through the bus 1503. When the machine-readable instructions are executed by the processor 1501, the steps of the flow field solution method shown in Embodiment 1 are performed.

[0137] Example 4 Based on the same concept, this application also provides a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the flow field solution method described in any of the above embodiments.

[0138] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and apparatus described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0139] The computer program product for solving flow fields provided in this application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation details, please refer to the method embodiments, which will not be repeated here.

[0140] The flow field solving device provided in this application embodiment can be specific hardware on a device or software or firmware installed on the device. The implementation principle and technical effects of the device provided in this application embodiment are the same as those in the foregoing method embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the foregoing method embodiments. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can all be referred to the corresponding processes in the above method embodiments, and will not be repeated here.

[0141] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0142] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0143] In addition, the functional units in the embodiments provided in this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0144] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0145] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0146] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application. All should be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A method for solving flow fields, characterized in that, The method includes: Obtain a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field; The geometric and working condition information of the object to be solved is input into the pre-trained model to generate the overall prediction field of the current wheel on the discrete carrier; An evaluation location is selected on the computational grid of the current round, and at the evaluation location, the residual is calculated by substituting the physical equations based on the overall prediction field of the current round. The region to be encrypted is determined based on the residual, and adaptive mesh refinement is performed on the region to be encrypted to update the computational mesh; On the updated computational grid, the pre-trained model is used to regenerate the overall prediction field on the discrete carrier, and the regenerated prediction field is passed to the updated computational grid as the overall prediction field for the next round. Repeat the above steps until the stopping condition is met, and take the current round's overall predicted field when the stopping condition is met as the final flow field solution result; The step of calculating the residual at the evaluation location by substituting the overall prediction field of the current wheel into the physical equation includes: The coordinates of the evaluation location are mapped to the domain of the discrete carrier to obtain the mapped coordinates; Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation; Substituting the field values ​​and derivatives into the governing equations and boundary conditions, we obtain the internal field residuals and boundary residuals. The residual at the evaluation location is obtained by weighted summation of the interior field residual and the boundary residual.

2. The method according to claim 1, characterized in that, The discrete carrier is a regular grid; the pre-trained model is a neural operator model; the neural operator model is a physical information neural operator, a Fourier neural operator, or a geometric perception Fourier neural operator; The parameters of the pre-trained model remain unchanged during the iteration process; Selecting an evaluation location on the computation grid of the current round includes: The evaluation location is selected at the midpoint of the edge, the midpoint of the boundary edge, the cell center, the cell centroid, or the center of the circumcircle of the computational grid.

3. The method according to claim 1, characterized in that, The step of determining the region to be encrypted based on the residual includes: The residuals at each of the aforementioned evaluation locations are sorted. The grid area corresponding to the top fixed percentage or fixed number of evaluation positions in the residual ranking is determined as the area to be encrypted.

4. The method according to claim 1, characterized in that, The step of performing adaptive mesh refinement on the region to be encrypted to update the computational mesh includes: Insert a new node into the area to be encrypted; The computational mesh containing the new node is reconstructed using constrained Delaunay triangulation to obtain the reconstructed computational mesh; The reconstructed computational grid is subjected to grid quality constraints of minimum angle threshold and adjacent cell area ratio threshold to obtain the updated computational grid.

5. The method according to claim 1, characterized in that, The step of regenerating the overall prediction field on the discrete carrier using the pre-trained model on the updated computational grid, and then transferring the regenerated prediction field to the updated computational grid as the overall prediction field for the next round, includes: Keeping the parameters of the pre-trained model unchanged, the geometric information and working condition information are input into the pre-trained model again; A single forward inference is performed on the discrete carrier to obtain the regenerated global prediction field. The regenerated global prediction field is mapped to the node or cell center of the updated computational grid by interpolation to obtain the global prediction field for the next round.

6. The method according to claim 1, characterized in that, The stopping condition is at least one of the following: The maximum residual value at all evaluation locations is below the first threshold; The average residual at all assessed locations is below the second threshold; The rate of change of the lift coefficient of the overall predicted field between two adjacent rounds is lower than the third threshold; The rate of change of the drag coefficient of the overall predicted field between two adjacent rounds is lower than the fourth threshold; The preset maximum number of iterations has been reached.

7. A flow field solving device, characterized in that, The device includes: The pre-trained model acquisition module is used to acquire a pre-trained model, which is used to establish the mapping relationship between geometry, working conditions and flow field; The overall prediction field generation module is used to input the geometric information and working condition information of the object to be solved into the pre-trained model and generate the overall prediction field of the current round on the discrete carrier. The residual calculation module is used to select an evaluation position on the computational grid of the current round, and at the evaluation position, calculate the residual by substituting the physical equation into the overall prediction field of the current round. The computational grid update module is used to determine the region to be encrypted based on the residual, and to perform adaptive grid refinement on the region to be encrypted in order to update the computational grid; The overall prediction field update module is used to regenerate the overall prediction field on the discrete carrier through the pre-trained model on the updated computing grid, and then pass the regenerated prediction field to the updated computing grid as the overall prediction field for the next round. The flow field solution result determination module is used to repeat the above steps until the stopping condition is met, and the overall predicted field of the current round when the stopping condition is met is taken as the final flow field solution result. The step of calculating the residual at the evaluation location by substituting the overall prediction field of the current wheel into the physical equation includes: The coordinates of the evaluation location are mapped to the domain of the discrete carrier to obtain the mapped coordinates; Based on the mapped coordinates, the field value and derivative of the overall predicted field of the current wheel at the evaluation position are obtained by interpolation; Substituting the field values ​​and derivatives into the governing equations and boundary conditions, we obtain the internal field residuals and boundary residuals. The residual at the evaluation location is obtained by weighted summation of the interior field residual and the boundary residual.

8. A computer device, characterized in that, include: The system includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the flow field solution method as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the flow field solution method as described in any one of claims 1 to 7.

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