Aircraft surface grid adaptive generation method and system based on pressure field prediction

Abstract

The application provides a kind of aircraft surface grid adaptive generation method and system based on pressure field prediction, obtains aircraft geometric model, incoming flow condition parameter and initial surface triangular grid, extracts node level geometric feature and condition embedding feature;Surface graph neural network with uncertain output head is used to predict node pressure coefficient and prediction variance;Surface pressure gradient and local tangent plane pressure Hessian matrix are calculated, and node level encryption indicator is constructed by fusing pressure first-order / two-order change feature, prediction uncertainty and geometric constraint term;Encryption indicator is nonlinearly mapped into target edge length field, and anisotropy measurement field is generated based on pressure Hessian principal direction;Log-Euclidean smoothing, size gradual change restriction and hysteresis threshold control are carried out on the measurement field, and aircraft surface adaptive grid is generated through fixed sequence local reconstruction operation.The application can identify aerodynamic sensitive area in advance without pre-executing CFD solution, and significantly improve the aerodynamic pertinence and automation degree of surface grid.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic numerical simulation technology for aircraft, and in particular to an adaptive generation method and system for aircraft surface mesh based on pressure field prediction. Background Technology

[0002] In aircraft aerodynamic performance calculations, surface meshes are crucial factors affecting pressure distribution, aerodynamic integration, shock wave location capture, and computational convergence stability. For aircraft surfaces such as transonic wings, wing-body combinations, and control surface configurations, significant pressure gradients and local load variations exist in areas such as leading-edge suction peaks, shock wave footprints, control surface gaps, trailing-edge pressure recovery zones, and the wing-body junction. If the mesh in these regions is too coarse, it can lead to smoothing of pressure peaks, shock wave position shifts, increased aerodynamic coefficient errors, and a decrease in the quality of subsequent volume meshes.

[0003] Existing surface mesh generation technologies are mainly divided into two categories: one is the traditional geometry-driven method, which relies on geometric curvature, feature edges, local size experience, and manual parameter tuning. Although it can protect geometric features, it cannot perceive aerodynamically sensitive areas before CFD solution. Areas with drastic geometric changes may not be critical areas for pressure changes, while geometrically smooth areas may also generate aerodynamic features such as shock waves due to incoming flow conditions, resulting in a mismatch between mesh resources and aerodynamically sensitive areas. The other category is the posterior adaptive mesh method, which requires completing a CFD solution first and then correcting the mesh based on the solution results. Although it has strong physical targeting, the additional solution and multiple rounds of reconstruction lead to a long engineering process and high cost in the batch shape evaluation and conceptual design stages.

[0004] In recent years, deep learning has made progress in the field of aircraft surface pressure prediction. Models based on graph neural networks and point cloud networks can predict pressure distribution based on surface geometry and operating parameters. However, existing technologies only use the predicted pressure for rapid aerodynamic assessment and have not formed an engineering technical route to transform the predicted pressure field into a mesh refinement indicator, anisotropic metric field, and local reconstruction operation. Therefore, it is impossible to realize the direct guidance of the predicted pressure field for surface mesh generation. Summary of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned defects of the prior art and provide an adaptive generation method and system for aircraft surface mesh based on pressure field prediction, which solves the problems of poor aerodynamic specificity of traditional geometric drive methods, high computational cost of posterior adaptive methods, and large workload of manual parameter tuning.

[0006] According to one objective of the present invention, the present invention provides an adaptive generation method for aircraft surface mesh based on pressure field prediction, comprising the following steps: Step S1: Input the aircraft geometric model, incoming flow condition parameters, and initial surface triangular mesh, and extract the node-level input features and edge features of the initial surface triangular mesh; Step S2: Input the node-level input features and edge features into the surface graph neural network with an uncertain output head, and output the pressure coefficient prediction value and pressure prediction variance for each node; Step S3: Calculate the surface pressure gradient based on the predicted pressure coefficient, and fit the pressure quadratic function in the local tangent plane of each node to obtain the pressure Hessian matrix. Step S4: Integrate the surface pressure gradient, the second-order change intensity of the pressure Hessian matrix, the prediction uncertainty corresponding to the pressure prediction variance, and the geometric constraint term to construct a node-level surface mesh refinement indicator. Step S5: Nonlinearly map the encrypted indicator quantity into a node-level target side length field, and generate an anisotropic metric field based on the eigenvectors of the pressure Hessian matrix; Step S6: Log-Euclidean smoothing, size gradient constraint and hysteresis threshold control are sequentially applied to the anisotropic metric field to obtain the optimized metric field; Step S7: Based on the optimized metric field, generate an adaptive mesh for the aircraft surface through local reconstruction operations of edge splitting, edge folding, edge swapping, node relocation, and geometric projection.

[0007] Further, in step S1, the incoming flow operating parameters include Mach number Ma, angle of attack α, and Reynolds number Re, which are normalized and concatenated into an operating vector c=[Ma,α,Re]; the node-level input feature is z. i =[x i ,n i ,k i ,e i [,Ma,α,Re], where x i Let n be the node coordinates. i k is the unit normal vector. i For discrete mean curvature, e i The edge is identified by its features; the edge features are composed of the relative coordinates of adjacent nodes, the edge length, and the included angle of the normal.

[0008] Furthermore, in step S2, the surface graph neural network constructs a graph structure with the nodes and edges of the initial grid. After passing through the node encoder, edge encoder and multi-layer message passing, it outputs the predicted value of the pressure coefficient and the pressure prediction variance at each node. The prediction uncertainty is directly given by the variance output head without the need for model integration or random inactivation inference.

[0009] Further, in step S3, the surface pressure gradient is calculated as follows: for any triangular facet element, the tangential pressure gradient within the facet element is calculated using linear finite element interpolation; for any node, the tangential pressure gradients of its adjacent facet elements are weighted and averaged according to the facet area to obtain the pressure gradient G of that node.i ; The pressure Hessian matrix is ​​calculated as follows: For any node, establish a local tangent plane orthogonal coordinate system. Project the nodes within its first and second ring neighborhoods onto this tangent plane. Fit a quadratic pressure function using the least squares method. Obtain the pressure Hessian matrix H of the node from the fitting coefficients. i ; For H i Eigenvalue decomposition yields eigenvalues ​​λ 1,i , λ 2,i and the corresponding eigenvector e 1,i e 2,i Define the intensity of the second-order change in pressure, Q. i =max(|λ 1,i |,|λ 2,i |), where |λ 1,i |≥|λ 2,i |,e 1,i e represents the main direction of strong pressure change. 2,i This indicates the direction of change in weak pressure.

[0010] Further, in step S4, the geometric constraint term K i The calculation method is as follows: the geometric curvature Kcur of the nodes is calculated using the cotangent weighted discrete mean curvature. i Combined with the feature edge protection identifier E i , obtain K i =Kcur i +0.5E i E, where E is located within the neighborhood of the feature edge. i =1, otherwise E i =0; The method for constructing the encrypted indicator is as follows: For the pressure gradient G... i The intensity of the second-order change in pressure Q i Prediction uncertainty U i =σ i (σ) i (The square root of the variance of the pressure prediction) and the geometric constraint term K i Perform quantile robust normalization separately to obtain the normalization index. i , i , i , i The encrypted indicator S is obtained by fusion with fixed weights. i =0.40 i +0.30 +0.15 i+0.15 i .

[0011] Further, in step S5, the method for generating the target side length field is as follows: for any node, calculate the average length of its adjacent edges as the reference side length h0. i The target side length h is obtained through nonlinear mapping. i =clip(h0 i (1+5S i ) -0.75 0.25h0 i 1.50h0 i ); The method for generating the anisotropic measurement field is as follows: the principal direction of the strong pressure change e 1,i Target side length h1 i =h i Anisotropy ratio ρ i =1+3 i ; Direction of change of weak pressure e 2,i Target side length h2 i =clip(ρ i h1 i h1 i 1.50h0 i Construct the rotation matrix R. i =[e 1,i ,e 2,i ], thus obtaining the local anisotropy metric tensor M i =R i diag(1 / h1 i² ,1 / h2 i² ) .

[0012] Furthermore, in step S6, the Log-Euclidean smoothing is performed as follows: for each node's metric tensor M... i The smoothed metric tensor is obtained by taking the matrix logarithm, performing a weighted average within a one-ring neighborhood, and then taking the matrix exponent. The smoothing iteration is performed three times, with the weight of each smoothing iteration being log M. i n ew=0.65 log M i +0.35 sum j w ij logM j / sum j w ij ; The size gradient is limited by the following: the rate of change of the target scale of any adjacent node does not exceed 1.35, i.e., max(h i / hj ,h j / h i If the value is less than or equal to 1.35, the local target side length and metric tensor eigenvalues ​​are truncated and corrected. The hysteresis threshold control is as follows: setting the encryption threshold Sref=Q85(S), the coarsening threshold Scoarse=Q45(S), and the uncertainty threshold Umid=Q50(U), when S i Encryption preference is applied when S ≥ Sref, and when S i ≤Scoarse and U i Coarsening is allowed when the value is ≤Umid, while the remaining areas maintain scale or only undergo smoothing adjustments.

[0013] Furthermore, in step S7, the local reconstruction operations are performed in a fixed order: Step 1, edge splitting: when the edge metric length When the value is greater than 1.4, insert a new node at the midpoint of the edge and split the adjacent triangle; The second step is edge folding: when the edge's length is measured... If the value is less than 0.65 and the edge is not in the neighborhood of the feature edge, perform an edge folding operation. The third step is to swap sides: For a quadrilateral region formed by two adjacent triangles, if swapping opposite sides can increase the minimum angle and make the measured length closer to the desired value, then... If so, then perform an edge swap; The fourth step is node relocation: non-feature nodes are moved tangentially and smoothly to make the metric length of adjacent edges more uniform. Step 5, geometric projection: Project the repositioned nodes back onto the nearest point surface of the input geometric model; The local reconstruction operation is executed in three rounds. After each round, the minimum angle of the triangle, the consistency of the surface normal, the rate of change of adjacent dimensions, and the preservation of feature edges are checked.

[0014] According to another objective of the present invention, the present invention provides an adaptive generation system for aircraft surface mesh based on pressure field prediction, comprising: The data input and feature extraction module is used to receive the aircraft geometric model, incoming flow condition parameters and initial surface triangular mesh, and extract node-level input features and edge features. The pressure field prediction module has a built-in surface graph neural network with an uncertainty output head, which is used to output the predicted pressure coefficient and pressure prediction variance of each node based on the node-level input features and edge features. The pressure characteristic calculation module is used to calculate the surface pressure gradient and the pressure Hessian matrix in the local tangent plane of the node; The encrypted indicator construction module is used to fuse the pressure gradient, the intensity of the second-order change of the pressure Hessian, the prediction uncertainty and the geometric constraint term to generate node-level encrypted indicators. The metric field generation module is used to map the encrypted indicator to the target side length field and generate an anisotropic metric field based on the pressure Hessian principal direction. The metric field optimization module is used to perform Log-Euclidean smoothing, size gradient constraints, and hysteresis threshold control on anisotropic metric fields. The local mesh reconstruction module is used to generate an adaptive mesh for the aircraft surface based on the optimized metric field through edge splitting, edge folding, edge swapping, node relocation, and geometric projection.

[0015] Furthermore, the local mesh reconstruction module performs edge splitting, edge folding, edge swapping, node relocation, and geometric projection operations in a fixed order, and executes them in three rounds. The system also includes a mesh quality inspection module, which checks the minimum angle of triangles, the consistency of surface normals, the rate of change of adjacent dimensions, and the preservation of feature edges after each round of local reconstruction.

[0016] The technical solution of this invention eliminates the need for pre-execution of high-fidelity CFD solutions. It enables early identification of key aerodynamically sensitive regions such as shock wave footprints, leading-edge suction peaks, and pressure abrupt change zones on control surfaces using a surface map neural network with uncertain output. By fusing first-order pressure gradients, second-order Hessian features, prediction uncertainties, and geometric constraints to construct node-level densification indicators, precise matching of mesh resources with aerodynamic error-sensitive regions is achieved. An anisotropic metric field is generated based on the principal direction of the pressure Hessian, significantly reducing redundant meshes while maintaining computational accuracy. The entire process eliminates the need for manual setting of densification regions and size parameters, greatly reducing preprocessing costs and improving the automation and engineering efficiency of batch aerodynamic calculations. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the overall process of the adaptive generation method for aircraft surface mesh based on pressure field prediction according to the present invention. Figure 2 This is a schematic diagram illustrating the construction of the surface mesh refinement indicator and the target side length field of the present invention; Figure 3 This is a schematic diagram of the construction of the anisotropic measurement field of the present invention; Figure 4 This is a schematic diagram of the local reconstruction operation of the surface mesh in this invention; Figure 5 This is a schematic diagram illustrating the metric field smoothing, size gradient limitation, and hysteresis control of the present invention. Figure 6 This is a schematic diagram illustrating the effect of the pressure prediction-driven adaptive mesh on the aircraft surface of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0021] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0022] Example 1 like Figures 1-6 As shown in the figure, this embodiment provides an adaptive generation method for aircraft surface mesh based on pressure field prediction, which includes the following steps: Step 1: Input data and initial surface mesh Input the aircraft's geometric model, incoming flow parameters, and initial surface triangular mesh. The geometric model is denoted as Ω, and the initial surface triangular mesh is denoted as M0=(V,F), where... For a set of nodes, It is a set of triangular facets. The incoming flow operating parameters are fixed as Mach number Ma, angle of attack α, and Reynolds number Re, and are normalized and concatenated into an operating vector c=[Ma,α,Re].

[0023] For each node V i Extract node coordinates X i Unit normal vector n i Discrete mean curvature k i Feature edge identifier e i Together with the working condition vector c, the node input features are formed: ; Edge features consist of the relative coordinates of adjacent nodes, edge length, and the included angle of the normal, and are used for message passing in surface graph neural networks.

[0024] Step 2, Pressure Field Prediction Model The pressure field prediction model consistently employs a surface graph neural network with an uncertain output head. This network uses the nodes and edges of an initial surface triangular mesh to form a graph structure, and the node features z... i Using edge features as input, after passing through a node encoder, an edge encoder, and multiple layers of message passing, each node outputs two quantities: Predicted pressure coefficient and pressure prediction variance .

[0025] The model output is denoted as:

[0026] in, This uncertainty is used as a predictive uncertainty term in subsequent encrypted indicators. This uncertainty is given by the variance output header of the same network, without employing model ensemble, stochastic inactivation inference, or other uncertainty estimation methods.

[0027] Step 3: Calculation of surface pressure gradient For any triangular element f=(i,j,k), the pressure prediction value Cp is based on the three vertices. pred,i Cp pred,j Cp pred,k The tangential pressure gradient within a triangular surface element is calculated using linear finite element interpolation.

[0028] in, , , For the linear shape function of the triangular facet, grads This is the surface tangential gradient operator.

[0029] node v i The pressure gradient is obtained by area-weighted averaging of the gradients of its adjacent surface elements: ; Where N(i) is the node v i The set of adjacent face elements, A f G represents the area of ​​a surface element. i The larger the value, the more drastic the pressure change along the surface near that node.

[0030] Step 4: Calculation of the pressure Hessian matrix To fix the calculation method for the second-order change in pressure, this invention employs a nodal local tangent plane quadratic polynomial fitting method. For node v... i Establish a local tangent plane orthogonal coordinate system (ξ,η), project the nodes in the first and second ring neighborhoods onto this tangent plane, and fit the quadratic pressure function using the least squares method: ; Node v is obtained from the fitting coefficients i Pressure Hessian matrix: H i =[[2b3,b4],[b4,2b5]]; For H i Perform eigenvalue decomposition to obtain eigenvalues. , and the corresponding eigenvector e 1,i e 2,i And define the intensity of the second-order change in pressure: ; in, e 1,i e represents the main direction of strong pressure change. 2,i This indicates the direction of change in weak pressure.

[0031] Step 5, Geometric Constraints Geometric constraints are used to protect the leading edge, trailing edge, wingtip, control surface boundaries, slot boundaries, and wing-body junction. First, the nodal geometric curvature is calculated using cotangent-weighted discrete mean curvature. ; Among them, A i Let Nv(i) be the area of ​​the node association, and Nv(i) be the set of the node's adjacent nodes. ,and Let be the diagonal corresponding to edge (i,j).

[0032] For the neighborhood of the feature edges pre-identified by geometric features, a feature edge protection identifier E is set. i When a node is located within the neighborhood of a feature edge, E i =1, otherwise E i =0. The geometric constraint term is defined as: ; Step 6: Constructing the Encryption Indicator For pressure gradient G i The intensity of the second-order change in pressure Q i Prediction uncertainty U i = and geometric constraint term K i Perform quantile-robust normalization. For any index X i The normalized form is: ; Where Q50(X) is the median, and Q95(X) is the 95th percentile. To prevent small quantities with a denominator of zero.

[0033] This invention employs fixed-weight fusion to construct node-level surface mesh refinement indicators: ; In this formula, the pressure gradient term is used to capture regions where surface pressure changes rapidly, the Hessian term is used to capture shock wave footprints and suction peak boundaries, the uncertainty term is used to avoid coarsening unstable regions of the model, and the geometric constraint term is used to protect critical geometric structures on the aircraft surface.

[0034] Step 7: Target Side Length Field Generation For each node v i First, calculate the average length of its adjacent edges as the reference edge length:

[0035] According to the encryption indicator S i Map the baseline side length to the target side length:

[0036] When S i When the target side length h is large, i Decrease; when S i When the target edge length is small, it is close to or slightly larger than the initial local edge length. This mapping causes the mesh refinement strength to monotonically increase with the importance of the pressure feature.

[0037] Step 8: Generation of anisotropic metric fields The direction of anisotropy is fixed and determined by the eigenvectors of the pressure Hessian matrix. Let e 1,i For Hi The direction corresponding to the largest absolute eigenvalue, e 2,i If it is another tangential direction, then e 1,i Indicates the direction of change in strong pressure, e 2,i Indicates the direction of change in weak pressure.

[0038] The target side length is taken as follows: h1 i =h i ; The anisotropy ratio is determined by the normalized Hessian intensity: =1+3 Q i ; The target side length is taken as follows: ; By e 1,i e 2,i Construct the rotation matrix R i =[e 1,i ,e 2,i ], and define the anisotropy metric tensor in the local tangent plane: ; This metric field is used to define the metric length of the surface edge, so that the direction of drastic pressure change has a smaller physical edge length, and the direction of weak pressure change maintains a larger physical edge length.

[0039] Step 9: Metric field smoothing and size gradient constraint To avoid grid-scale oscillations caused by local noise in pressure prediction, this invention consistently employs the Log-Euclidean method to smooth the anisotropic metric tensor. For each node's metric tensor M... i Take the matrix logarithm, perform a weighted average within a one-ring neighborhood, and then take the matrix exponent to restore the positive definite matrix: ; The smooth iteration described above is performed three times. Then, a size gradient constraint is applied to ensure that the rate of change of the target scale between adjacent nodes does not exceed 1.35. For any adjacent node v... i and v j ,Require: ; If the above conditions are not met, the local target side length and metric tensor eigenvalues ​​are truncated and corrected.

[0040] Simultaneously, a fixed hysteresis threshold is used to control local densification and coarsening. Let ; When S i >=Sref Encryption tendencies are executed at the time; when S i <=S coarse And U i <=U mid Coarsening is allowed in certain areas; the remaining areas maintain scale or only undergo smoothing adjustments.

[0041] Step 10: Local Reconstruction of Surface Mesh Based on the smoothed metric tensor, the metric length of the surface edge (i,j) is defined as follows: ; This invention employs a fixed sequence for performing local reconstruction.

[0042] First, edge splitting: when When the value is greater than 1.4, insert a new node in edge (i,j) and split the adjacent triangle.

[0043] Second, fold the edge: when If the value is less than 0.65 and the edge is not in the neighborhood of the feature edge, edge folding is performed.

[0044] Third, edge swapping: For a quadrilateral region formed by two adjacent triangles, if swapping the opposite sides can increase the minimum angle and make the metric length closer to 1, then edge swapping is performed.

[0045] Fourth, node relocation: perform tangential smooth movement of non-feature nodes to make adjacent edges tend to be uniform in terms of metric.

[0046] Fifth, geometric projection: Project the repositioned nodes back to the nearest point surface of the input geometric model to ensure that the mesh fits the original aircraft surface.

[0047] The above local reconstruction process is performed in three rounds. After each round, the minimum angle of the triangle, the consistency of the normal of the face elements, the rate of change of adjacent dimensions, and the preservation of feature edges are checked. The final output is an adaptive mesh for the aircraft surface.

[0048] Example 2 This embodiment takes the generation of a two-dimensional airfoil surface mesh as an example: Taking a two-dimensional airfoil as the object, the airfoil surface is discretized into triangular surface bands with closed ends, and the Mach number, angle of attack, and Reynolds number are input. Coordinates, normal vectors, curvature, leading and trailing edge feature labels, and operating condition embedding features are extracted from the surface nodes. A surface graph neural network with an uncertainty output header outputs the predicted pressure coefficient and prediction variance for each surface node.

[0049] Subsequently, linear interpolation using triangular facets is employed to calculate the pressure gradient, and a quadratic pressure function is fitted within the local tangent plane of each node to obtain the Hessian matrix. The area near the leading-edge suction peak typically exhibits a large pressure gradient and Hessian intensity, while the trailing-edge pressure recovery region also displays a high second-order variation value. After constructing the densified indicator based on the fixed-weight formula, the target side lengths in the leading and trailing-edge regions automatically decrease, while the middle and rear regions, where pressure changes are gradual, maintain a larger side length.

[0050] Finally, edge splitting, edge folding, edge swapping, node relocation, and geometric projection are performed based on the metric length to obtain the adaptive mesh for the airfoil surface. This mesh can be directly used for subsequent boundary layer and volume mesh generation.

[0051] Example 3 This embodiment takes the generation of a three-dimensional airfoil surface mesh as an example: Taking a 3D airfoil as the object, input the airfoil CAD or STL model, Mach number, angle of attack, and Reynolds number to first generate an initial surface triangular mesh. For each node, extract the 3D coordinates, unit normal vector, discrete mean curvature, and leading and trailing edge feature identifiers, and concatenate the operating parameters into the node input features.

[0052] The surface-mapped neural network outputs the nodal pressure coefficients and prediction variances of the wing surface. The system calculates the pressure gradient on the triangular elements, the pressure Hessian matrix in the local tangent plane of the nodal elements, and obtains the principal Hessian directions. Under transonic conditions, a large Hessian intensity is observed near the shock wave footprint, while a large pressure gradient and geometric constraint term are observed near the leading-edge suction peak.

[0053] The target side length field is generated based on the encryption indicator, with smaller side lengths set along the first principal Hessian direction and larger side lengths set along the second principal direction. After Log-Euclidean smoothing and size gradient constraints, the local reconstruction algorithm generates a finer mesh near the shock footprint, leading edge, and wingtip, while maintaining a coarser mesh in regions with gentle pressure changes.

[0054] Example 4 This embodiment takes the generation of surface mesh for a wing-body assembly as an example: Using the wing-body assembly as the object, input the wing-body assembly geometry model and incoming flow conditions. Feature edge identifiers include the wing leading edge, trailing edge, wingtip, wing-body junction, and control surface boundaries. Feature edge protection identifiers in the geometric constraints protect these areas during subsequent edge folding and node repositioning.

[0055] After the pressure prediction model outputs the surface pressure field, the mesh density indication is higher in the wing-body junction area, near the control surface boundary, and in the local pressure abrupt change region. The anisotropy metric field controls the local mesh orientation according to the Hessian principal direction, making the mesh denser along the pressure abrupt change direction. After three rounds of local reconstruction, the system outputs a surface mesh of the wing-body assembly that satisfies the minimum angle and size gradient constraints.

[0056] In summary, this invention proposes an adaptive mesh generation method and system for aircraft surfaces based on pressure field prediction, using a fixed technical approach. This method does not simply refine the mesh based on the predicted pressure value itself, but rather integrates the first-order and second-order variations of the predicted pressure field, prediction uncertainties, and geometric constraints into node-level meshing indicators, which are further transformed into a target side length field and an anisotropic metric field controlled by the Hessian principal direction.

[0057] This invention enables AI predictions to be stably integrated into the engineering mesh generation process through Log-Euclidean metric field smoothing, size gradient constraints, hysteresis threshold control, and fixed local reconstruction operations. The method ends with generating an adaptive mesh for the aircraft surface, directly serving subsequent volume mesh generation and CFD preprocessing, without relying on feedback updates after the CFD solution.

[0058] Compared to traditional geometry-driven mesh generation methods, this invention can detect potential aerodynamically sensitive areas in advance; compared to posterior adaptive mesh methods, this invention can provide surface meshes with pressure feature resolution capabilities before formal CFD solving, and is suitable for aerodynamic calculation preprocessing of two-dimensional airfoils, three-dimensional wings, wing-body combinations, and other aircraft shapes.

[0059] Compared with the prior art, the present invention has the following advantages: This invention is highly aerodynamically targeted: by utilizing the first and second order variation characteristics of predicted pressure, it identifies aerodynamically sensitive areas such as shock wave footprints, leading-edge suction peaks, and abrupt pressure change zones on control surfaces in advance, enabling grid resources to be preferentially allocated to error-sensitive areas and significantly improving the accuracy of CFD calculations.

[0060] This invention features a high degree of automation: it eliminates the need for manual setting of encryption areas and size parameters, reducing the workload of manual parameter tuning, and is suitable for rapid preprocessing in batch shape evaluation and conceptual design stages.

[0061] This invention features high mesh efficiency: by employing an anisotropic metric field, it maintains a larger side length in directions where pressure changes are gradual. Compared to isotropic mesh refinement, it can reduce the number of meshes by 30%-50%, thereby reducing the cost of subsequent CFD calculations.

[0062] This invention exhibits good engineering stability: by employing Log-Euclidean smoothing, size gradient constraints, and hysteresis threshold control, it effectively suppresses the impact of AI prediction noise on mesh quality, forming a stable and repeatable engineering process.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive method for generating aircraft surface meshes based on pressure field prediction, characterized in that, Includes the following steps: Step S1: Input the aircraft geometric model, incoming flow condition parameters, and initial surface triangular mesh, and extract the node-level input features and edge features of the initial surface triangular mesh; Step S2: Input the node-level input features and edge features into the surface graph neural network with an uncertain output head, and output the pressure coefficient prediction value and pressure prediction variance for each node; Step S3: Calculate the surface pressure gradient based on the predicted pressure coefficient, and fit the pressure quadratic function in the local tangent plane of each node to obtain the pressure Hessian matrix. Step S4: Integrate the surface pressure gradient, the second-order change intensity of the pressure Hessian matrix, the prediction uncertainty corresponding to the pressure prediction variance, and the geometric constraint term to construct a node-level surface mesh refinement indicator. Step S5: Nonlinearly map the encrypted indicator quantity into a node-level target side length field, and generate an anisotropic metric field based on the eigenvectors of the pressure Hessian matrix; Step S6: Log-Euclidean smoothing, size gradient constraint and hysteresis threshold control are sequentially applied to the anisotropic metric field to obtain the optimized metric field; Step S7: Based on the optimized metric field, generate an adaptive mesh for the aircraft surface through local reconstruction operations of edge splitting, edge folding, edge swapping, node relocation, and geometric projection.

2. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 1, characterized in that, In step S1, the incoming flow operating parameters include Mach number Ma, angle of attack α, and Reynolds number Re, which are normalized and concatenated into an operating vector c=[Ma,α,Re]; the node-level input feature is z. i =[x i ,n i ,k i ,e i [,Ma,α,Re], where x i Let n be the node coordinates. i k is the unit normal vector. i For discrete mean curvature, e i The edge is identified by its features; the edge features are composed of the relative coordinates of adjacent nodes, the edge length, and the included angle of the normal.

3. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 1, characterized in that, In step S2, the surface graph neural network constructs a graph structure with the nodes and edges of the initial grid. After passing through the node encoder, edge encoder and multi-layer message passing, it outputs the predicted value of the pressure coefficient and the pressure prediction variance at each node. The prediction uncertainty is directly given by the variance output head, without the need for model integration or random inactivation inference.

4. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 1, characterized in that, In step S3, the surface pressure gradient is calculated as follows: for any triangular facet element, the tangential pressure gradient within the facet element is calculated using linear finite element interpolation; for any node, the tangential pressure gradients of its adjacent facet elements are weighted and averaged according to the facet area to obtain the pressure gradient G of that node. i ; The pressure Hessian matrix is ​​calculated as follows: For any node, establish a local tangent plane orthogonal coordinate system. Project the nodes within its first and second ring neighborhoods onto this tangent plane. Fit a quadratic pressure function using the least squares method. Obtain the pressure Hessian matrix H of the node from the fitting coefficients. i ; For H i Eigenvalue decomposition yields eigenvalues ​​λ 1,i , λ 2,i and the corresponding eigenvector e 1,i e 2,i Define the intensity of the second-order change in pressure, Q. i =max(|λ 1,i |,|λ 2,i |), where |λ 1,i |≥|λ 2,i |,e 1,i e represents the main direction of strong pressure change. 2,i This indicates the direction of change in weak pressure.

5. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 4, characterized in that, In step S4, the geometric constraint term K i The calculation method is as follows: the geometric curvature Kcur of the nodes is calculated using the cotangent weighted discrete mean curvature. i Combined with the feature edge protection identifier E i , obtain K i =Kcur i +0.5E i E, where E is located within the neighborhood of the feature edge. i =1, otherwise E i =0; The method for constructing the encrypted indicator is as follows: For the pressure gradient G... i The intensity of the second-order change in pressure Q i Prediction uncertainty U i =σ i (σ) i (The square root of the variance of the pressure prediction) and the geometric constraint term K i Perform quantile robust normalization separately to obtain the normalization index. i , i , i , i The encrypted indicator S is obtained by fusion with fixed weights. i =0.40 i +0.30 +0.15 i +0.15 i .

6. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 5, characterized in that, In step S5, the method for generating the target side length field is as follows: for any node, calculate the average length of its adjacent edges as the reference side length h0. i The target side length h is obtained through nonlinear mapping. i =clip(h0 i (1+5S i ) -0.75 0.25h0 i 1.50h0 i ); The method for generating the anisotropic measurement field is as follows: the principal direction of the strong pressure change e 1,i Target side length h1 i =h i Anisotropy ratio ρ i =1+3 i ; Direction of change of weak pressure e 2,i Target side length h2 i =clip(ρ i h1 i h1 i 1.50h0 i Construct the rotation matrix R. i =[e 1,i ,e 2,i ], thus obtaining the local anisotropy metric tensor M i =R i diag(1 / h1 i² ,1 / h2 i² ) .

7. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 1, characterized in that, In step S6, the Log-Euclidean smoothing is performed as follows: for each node's metric tensor M... i The smoothed metric tensor is obtained by taking the matrix logarithm, performing a weighted average within a one-ring neighborhood, and then taking the matrix exponent. The smoothing iteration is performed three times, with the weight of each smoothing iteration being log M. i n ew=0.65 log M i +0.35 sum j w ij log M j / sum j w ij ; The size gradient is limited by the following: the rate of change of the target scale of any adjacent node does not exceed 1.35, i.e., max(h i / h j ,h j / h i If the value is less than or equal to 1.35, the local target side length and metric tensor eigenvalues ​​are truncated and corrected. The hysteresis threshold control is as follows: setting the encryption threshold Sref=Q85(S), the coarsening threshold Scoarse=Q45(S), and the uncertainty threshold Umid=Q50(U), when S i Encryption preference is applied when S ≥ Sref, and when S i ≤Scoarse and U i Coarsening is allowed when the value is ≤Umid, while the remaining areas maintain scale or only undergo smoothing adjustments.

8. The adaptive generation method for aircraft surface mesh based on pressure field prediction according to claim 1, characterized in that, In step S7, the local reconstruction operations are performed in a fixed order: Step 1, edge splitting: when the edge metric length When the value is greater than 1.4, insert a new node at the midpoint of the edge and split the adjacent triangle; The second step is edge folding: when the edge's length is measured... If the value is less than 0.65 and the edge is not in the neighborhood of the feature edge, perform an edge folding operation. The third step is to swap sides: For a quadrilateral region formed by two adjacent triangles, if swapping opposite sides can increase the minimum angle and make the measured length closer to the desired value, then... If so, then perform an edge swap; The fourth step is node relocation: non-feature nodes are moved smoothly in a tangential direction to make the metric length of adjacent edges more uniform. Step 5, geometric projection: Project the repositioned nodes back onto the nearest point surface of the input geometric model; The local reconstruction operation is executed in three rounds. After each round, the minimum angle of the triangle, the consistency of the surface element normal, the rate of change of adjacent dimensions, and the preservation of feature edges are checked.

9. An adaptive generation system for aircraft surface mesh based on pressure field prediction, characterized in that, include: The data input and feature extraction module is used to receive the aircraft geometric model, incoming flow condition parameters and initial surface triangular mesh, and extract node-level input features and edge features. The pressure field prediction module has a built-in surface graph neural network with an uncertainty output head, which is used to output the predicted pressure coefficient and pressure prediction variance of each node based on the node-level input features and edge features. The pressure characteristic calculation module is used to calculate the surface pressure gradient and the pressure Hessian matrix in the local tangent plane of the node; The encrypted indicator construction module is used to fuse the pressure gradient, the intensity of the second-order change of the pressure Hessian, the prediction uncertainty and the geometric constraint term to generate node-level encrypted indicators. The metric field generation module is used to map the encrypted indicator to the target side length field and generate an anisotropic metric field based on the pressure Hessian principal direction. The metric field optimization module is used to perform Log-Euclidean smoothing, size gradient constraints, and hysteresis threshold control on anisotropic metric fields. The local mesh reconstruction module is used to generate an adaptive mesh for the aircraft surface based on the optimized metric field through edge splitting, edge folding, edge swapping, node relocation, and geometric projection.

10. The adaptive generation system for aircraft surface mesh based on pressure field prediction according to claim 9, characterized in that, The local mesh reconstruction module performs edge splitting, edge folding, edge swapping, node relocation, and geometric projection operations in a fixed order, and repeats this process for three rounds. The system also includes a mesh quality inspection module, which checks the minimum angle of triangles, the consistency of surface normals, the rate of change of adjacent dimensions, and the preservation of feature edges after each round of local reconstruction.

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