A CFD boundary layer grid generation method and system based on mapping parameterization

Abstract

The application discloses a CFD boundary layer grid generation method and system based on mapping parameterization, which firstly constructs an initial boundary layer reference grid surface based on a Cartesian background grid, and optimizes the reference grid surface. Secondly, the optimized variational shape approximation algorithm is used for synchronous partitioning of the object surface and the reference grid surface, and a topologically corresponding partition pair is divided, each partition pair is projected to a two-dimensional parameter plane to obtain a plane grid, and a radial basis function is used for boundary alignment and internal coordinate interpolation to obtain an updated plane grid. Then, the updated plane grid is inversely mapped to a three-dimensional space to reconstruct a final reference grid surface. Finally, according to the distribution parameters, interlayer node interpolation is carried out between the object surface and the final reference grid surface to generate an overall boundary layer grid. The application ensures the ordered distribution of grid nodes in the physical space, eliminates the risk of mutual penetration of grid elements, and reduces the truncation error in numerical simulation.

Description

Technical Field

[0001] This invention belongs to the field of computational geometry processing and spatial discretization technology, and relates to computer-aided engineering (CAE) and boundary layer mesh topology construction technology for fine flow simulation of complex aircraft. Specifically, it relates to a boundary layer mesh generation method based on mapping parameterization. Background Technology

[0002] In computational fluid dynamics and aerodynamic numerical simulations, the boundary layer is a key region where fluid viscosity effects play a dominant role. When a real fluid flows over a solid surface, the fluid velocity close to the surface drops to zero due to viscous shear forces, and then rapidly recovers to the mainstream velocity within a very small normal distance. This region contains dramatic velocity gradients, pressure gradients, and energy exchange, directly determining the frictional drag, heat transfer coefficient, and flow separation characteristics of aircraft or underwater vehicles.

[0003] To accurately capture the physical phenomena within the boundary layer, high-resolution mesh cells must be arranged near the solid wall. Firstly, due to the high Reynolds number and extremely thin flow structure within the boundary layer, the mesh must have a very small initial height in the normal direction (typically requiring a dimensionless wall distance). First, the boundary layer mesh must meet certain requirements to accurately calculate the wall shear stress. Second, a high-quality boundary layer mesh must possess good orthogonality and a smooth growth rate, which is crucial for the convergence of the turbulence model. If the mesh is distorted or has a large aspect ratio, it will lead to increased numerical discretization errors and may even cause calculation divergence. Third, the boundary layer mesh must strictly conform to the complex geometry of the object surface. This ensures the accurate application of boundary conditions;

[0004] First, traditional Advancing Layer Methods and Normal Projection Methods, when dealing with narrow gaps, high-curvature concave angles, or close-range two-body structures, suffer from a lack of global topological awareness. Mesh cells stretched along the wall normal are prone to geometric self-intersection and physical compression, leading to negative mesh volumes and ultimately causing numerical computational failures. Second, in hybrid mesh systems where Cartesian meshes serve as the background field, topological mismatch often exists between the near-wall structured boundary layer mesh and the far-field Cartesian mesh, making it difficult to achieve a smooth transition in mesh scale and cell type. This not only increases data interpolation errors but also becomes a bottleneck restricting the efficiency of fully automated mesh generation. Furthermore, existing technologies generally lack effective parametric control methods, making it difficult to simultaneously maintain geometric features (such as sharp edges and corners) and optimize global mesh orthogonality in complex 3D spaces. Therefore, how to achieve deep coupling between the object's geometry and the background mesh in the parameter domain, and how to utilize mapping mechanisms to avoid mesh distortion caused by spatial stretching, has become a critical issue that urgently needs to be addressed in computational geometry processing and high-performance computational fluid dynamics (CFD). Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing boundary layer mesh generation techniques, such as mesh self-intersection, difficulty in topological matching with the external background mesh, and lack of effective parameterization control when handling complex topologies. This invention provides a CFD boundary layer mesh generation method and system based on mapping parameterization. By introducing a Cartesian background mesh as a reference datum and combining variational shape approximation partitioning and conformal mapping techniques, high-quality, highly orthogonal, and topologically compatible boundary layer meshes can be generated in complex three-dimensional spaces. This invention achieves high-quality, highly orthogonal boundary layer meshes on complex geometric surfaces by topologically associating the complex three-dimensional object surface mesh with the Cartesian background mesh and combining variational shape approximation partitioning and conformal mapping parameterization methods.

[0006] To achieve the above objectives, this invention provides a CFD boundary layer mesh generation method based on mapping parameterization, the technical solution of which is as follows:

[0007] Step 1: Construct the initial boundary layer reference mesh surface based on the Cartesian background mesh.

[0008] Step 2: The initial boundary layer reference mesh surface is optimized using a projection smoothing algorithm to obtain a geometrically continuous reference mesh surface.

[0009] Step 3: Use the optimized variational shape approximation algorithm to synchronously partition the object surface and the reference mesh surface, and divide them into several topologically corresponding partition pairs.

[0010] Step 4: For each partition pair, project it onto the two-dimensional parametric plane through conformal mapping to obtain a planar mesh, and use radial basis functions to perform boundary alignment and internal coordinate interpolation to obtain an updated planar mesh.

[0011] Step 5: Based on the centroid coordinate interpolation, the updated planar mesh is inversely mapped to three-dimensional space to reconstruct the final reference mesh surface.

[0012] Step 6: Based on the preset distribution parameters, perform inter-layer node interpolation between the object surface and the final reference mesh surface to generate an overall boundary layer mesh.

[0013] In another aspect, the present invention also provides a CFD boundary layer mesh generation system based on mapping parameterization, comprising the following modules:

[0014] The reference mesh generation module constructs an initial boundary layer reference mesh based on a Cartesian background mesh. It then optimizes the initial boundary layer reference mesh using a projection smoothing algorithm to obtain a geometrically continuous reference mesh.

[0015] The topology partitioning module is used to synchronously partition the object surface and the reference mesh surface using an optimized variational shape approximation algorithm, thereby dividing the object surface into several topology-corresponding partitioning pairs.

[0016] The planar mesh update module is used to obtain a planar mesh for each partition pair by conformal mapping projection onto a two-dimensional parametric plane, and then use radial basis functions to perform boundary alignment and internal coordinate interpolation to obtain the updated planar mesh.

[0017] The final reference mesh reconstruction module reconstructs the final reference mesh by inverse mapping the updated planar mesh to three-dimensional space based on centroid coordinate interpolation.

[0018] The overall boundary layer mesh generation module is used to generate an overall boundary layer mesh by interpolating interlayer nodes between the object surface and the final reference mesh surface according to preset distribution parameters.

[0019] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0020] 1. Fundamentally avoids the problems of mesh self-intersection and overlap. Traditional algorithms often cause mesh self-intersection when dealing with high curvature geometry or narrow gap regions due to the intersection of normal stretching vectors. This invention transforms the three-dimensional stretching problem into a coordinate mapping and RBF interpolation problem in a two-dimensional parametric plane. By utilizing the topological order preservation property in the parameter domain, it ensures the orderly distribution of mesh nodes in physical space, eliminating the risk of mesh cells penetrating each other from the underlying logic of the algorithm.

[0021] 2. A high degree of compatibility between the boundary layer mesh and the background mesh is achieved. Because this invention uses a Cartesian background mesh to extract the initial reference surface, the generated boundary layer outer boundary naturally possesses a topological structure that matches the background mesh. This "outside-in" mapping design solves the problem of difficult docking between the boundary layer mesh and the far-field mesh in complex aerospace models, greatly improving the convergence speed and numerical stability of subsequent flow field calculations.

[0022] 3. Significantly improves the accuracy of capturing complex geometric features and the orthogonality of the mesh. By combining the optimized VSA partitioning algorithm and LSCM conformal mapping technology, this invention can automatically identify and lock singular points and feature lines on the object surface. Through boundary alignment and inverse mapping of barycentric coordinates in the parameter domain, the generated mesh not only closely fits the original object surface geometrically, but also maintains extremely high orthogonality and smoothness in the near-wall region, effectively reducing truncation errors in numerical simulations.

[0023] 4. Enhanced parametric control and robustness of mesh generation. Utilizing the global interpolation properties of radial basis functions (RBF), this invention requires only the adjustment of a small number of boundary control points to achieve precise driving of overall mesh deformation. Compared to traditional partial differential equation (PDE) smoothing methods, this scheme offers higher computational efficiency and good universality for various initial mesh forms, including unstructured and multi-block structured meshes, providing reliable technical support for automated mesh generation processes. Attached Figure Description

[0024] Figure 1 Flowchart of boundary layer generation technology based on mapping parameterization according to an embodiment of the present invention;

[0025] Figure 2 A schematic diagram of the generation of the Cartesian external field mesh according to an embodiment of the present invention;

[0026] Figure 3 Projection smoothing of the quadrilateral reference mesh in this embodiment of the invention;

[0027] Figure 4 The inner and outer grid partitioning results (left figure) of this invention embodiment are based on the corner boundary optimization results (right figure);

[0028] Figure 5 In this embodiment of the invention, the reference mesh topology is topologically aligned from the inside out, transforming quadrilaterals into triangles.

[0029] Figure 6 In this embodiment of the invention, the inner and outer mesh diagrams (top left) in the same partition of the three-dimensional space are conformally mapped to the same plane (top right) and the radial basis function boundaries are aligned (bottom left).

[0030] Figure 7The boundary layer generation result of this embodiment of the invention. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] In one aspect, this invention provides a CFD boundary layer mesh generation method based on mapping parameterization, such as... Figure 1 As shown, the technical solution adopted is:

[0033] Step 1: Construct the initial boundary layer reference mesh surface based on the Cartesian background mesh. .

[0034] Step 2: Apply a projection smoothing algorithm to the initial boundary layer reference mesh surface. Optimization is performed to obtain a geometrically continuous reference mesh surface. .

[0035] Step 3: Use the optimized variational shape approximation algorithm to approximate the object surface. With the reference mesh surface Perform synchronized partitioning to create several partition pairs corresponding to the topology. , here This represents the partition number, and the same applies below.

[0036] Step 4: For each partition pair, project it onto a two-dimensional parametric plane using conformal mapping to obtain a planar mesh, and use radial basis functions to perform boundary alignment and internal coordinate interpolation to obtain an updated planar mesh. .

[0037] Step 5: Based on the barycenter coordinate interpolation, the updated planar mesh is... The final reference mesh surface is obtained by inverse mapping to three-dimensional space and reconstructing it.

[0038] Step 6: According to the preset distribution parameters, on the surface of the object... Inter-layer node interpolation is performed between the final reference mesh surface and the reference mesh surface to generate an overall boundary layer mesh.

[0039] Preferably, step 1 includes: obtaining a pre-generated coating that covers the original surface. The outer Cartesian background mesh; extracting the nearest unit surface of the original object surface from the Cartesian background mesh to obtain the initial boundary layer reference mesh surface composed of quadrilateral facets. .

[0040] As a preferred method, the Cartesian background mesh is generated within a spherical mesh that is twice the size of the minimum bounding box of the original object surface, and the final subdivision of the side length is made up to the average side length of the original object surface.

[0041] Preferably, step 2 includes: targeting the original surface The set of vertices is used to construct a kd-tree spatial index structure to achieve efficient spatial nearest neighbor search; the boundary layer reference mesh obtained in step 1 is traversed. All vertices on the surface, using the kd-Tree on the original surface Quickly find the corresponding vertex that is closest to the vertex set constructed by the kd-Tree. For the boundary layer reference mesh surface Previous vertex Obtain the original surface A set of vertices The position of the projected point is obtained through the average vertex set. According to the vertex With projection point Calculate the projection vector Based on the calculated projection vector pairs The vertex positions are directly added together to obtain the adjusted vertex coordinates, so that the reference mesh gradually converges geometrically towards the original object surface. To bring the mesh closer, a set number of iterations is set, with each iteration performing an additional Laplacian smoothing on the vertices. Through multiple iterations of the above search and projection process, the inherent stepped geometric features of the Cartesian background mesh are eliminated, ultimately resulting in a quadrilateral reference mesh surface that fits the shape and possesses geometric continuity. .

[0042] As a supplementary explanation to the Laplace smoothing in step 2:

[0043] Specifically, in order to further improve the mesh quality of the reference mesh surface and eliminate the local jaggedness that may be introduced during the projection process, Laplacian smoothing is performed on the adjusted vertices in each iteration.

[0044] The calculation principle is as follows: by calculating the positional relationship between the current vertex and its first-order adjacent vertices, the current vertex is moved towards the geometric center of its neighborhood to achieve a smooth mesh effect. The update formula is as follows:

[0045]

[0046] in, The Laplace operator is represented as:

[0047]

[0048] In the above formula: Indicates the current vertex coordinates before smoothing; This indicates the new coordinates of the current vertex after smoothing. Indicates the relationship with the current vertex The directly connected first The coordinates of the adjacent vertices; This represents the total number of adjacent vertices of the current vertex; This is the smoothing factor, used to control the intensity of smoothing; its value range is typically set to... .

[0049] By embedding the Laplacian smoothing step described above into the iterative projection loop, the present invention can ensure the reference mesh surface While closely conforming to the geometry of the original object surface, it significantly optimizes the side length ratio and interior angle distribution of the mesh cells, effectively avoiding local mesh distortion caused by uneven distribution of the Cartesian background mesh.

[0050] Preferably, step 3 includes: using the optimized variational shape approximation (VSA) algorithm to approximate the object surface. With reference mesh surface Perform synchronized partition processing.

[0051] The process first utilizes the principle of spectral feature clustering. It constructs a grid-like Laplacian matrix, performs eigenvalue decomposition on the Laplacian matrix, and then filters the decomposed eigenvalues ​​and eigenvectors, selecting the smallest non-zero eigenvalue and its corresponding vector. For vectors Traverse through the n dimensions to find the index corresponding to the minimum value. ,this This is the first seed facet we obtained during initialization.

[0052] Based on the initialization center, variational energy functionals are used to perform synchronous clustering of the object surface and the reference surface.

[0053] To address the issue of jagged or blurred boundaries that clustering algorithms often produce in regions with complex features, this invention further implements a corner-based partition boundary optimization strategy. This strategy identifies singular points at the intersection of multiple partitions as feature corner points and reconstructs the topological boundaries between adjacent corner points using a shortest distance path algorithm, replacing the original discrete patch edges. This boundary constraint mechanism not only enhances the fit between partition boundaries and geometric feature lines but also ensures consistency between the object surface partition and the reference surface partition on the parameter domain boundary during subsequent parametric mapping, thereby effectively reducing interpolation distortion caused by topological differences.

[0054] Preferably, the initialization mechanism based on spectral feature clustering in step 3 is as follows: First, a Laplacian-Beltramian operator is constructed for the grid discrete manifold, and a discrete Laplacian matrix is ​​established based on the connectivity between patches and geometric weights. .in, For degree matrix, Let be the weight matrix. Then, based on the principle of solving the generalized eigenvalue problem, define the equation... Solve and The discrete Laplace matrix is ​​then obtained. A series of eigenvalues ​​and their corresponding eigenvectors form spectral features.

[0055] The purpose of using spectral features is to extract the eigenvector corresponding to the smallest non-zero eigenvalue (i.e., algebraic connectivity). This is also known as the Fiedler vector. Because the numerical distribution of this vector on the mesh surface reflects the geometric extension direction and topological density characteristics of the model, it can be used to... The components are divided into intervals, which can be done in the original grid. Fast global positioning The regions with the strongest geometric independence are selected as seed patches for the variational shape approximation algorithm. This spectral analysis-based selection method effectively avoids the slow clustering convergence and local optima problems caused by traditional random sampling, paving the way for subsequent utilization... Metrics-based precise partitioning and iteration lay the foundation for global topology.

[0056] Preferably, in step 3, the variational energy functional performs simultaneous clustering of the object surface and the reference surface as follows: The proxy partition facet is defined as the center facet of the already determined partition. After determining the initial seed facet, the partition boundary is updated by iteratively minimizing the geometric deviation between the facet and its proxy partition. This embodiment uses... Normal error, as a metric for energy functionals, is relevant for partitioning. Each facet in Its local geometric error is defined as:

[0057]

[0058] in, Represents a piece of dough On point The unit normal vector at that location, Indicates the first The average unit normal vector of each partition agent, Let be the differential area of ​​the patch. The core significance of this metric lies in clustering patches with similar geometric features (i.e., gentle curvature changes) into the same partition by measuring the consistency between the patch normal and the partition representative direction.

[0059] Preferably, the overall implementation process of step 4 is as follows: for each group of topologies divided in step 3, the corresponding three-dimensional partition pairs are... First, using the conformal mapping algorithm, while preserving local angle invariance and minimizing metric distortion, the 3D surface mesh is projected onto the 2D parametric domain complex plane, resulting in the object surface parametric mesh. With reference surface parameter mesh .

[0060] Due to the differences in 3D geometry during projection, the boundary shapes and vertex distributions of the two meshes in the parametric plane are not entirely consistent. Therefore, this step further introduces a radial basis function (RBF) interpolation mechanism: using the vertices on the partition boundary as control points, a displacement constraint equation is constructed, and the reference surface parametric mesh is then used. The boundary coordinates are precisely linearly transformed to the mesh of the object surface parameters. The boundary coordinates coincide. Subsequently, utilizing the global interpolation property of the RBF radial basis function, the parametric coordinates of all vertices within the partition are updated collaboratively based on the displacement vector at the boundary, thereby obtaining an updated planar mesh that achieves perfect boundary alignment with the object surface mesh and internal topological consistency within the parameter domain. This process lays the coordinate foundation for the subsequent high-fidelity inverse mapping of the two-dimensional optimization results back to three-dimensional space.

[0061] For the 3D surface sub-blocks after synchronization partitioning and This invention employs a least-squares conformal mapping (LSCM) scheme based on discrete conformal geometry theory, aiming to construct a low-distortion embedding from a 3D manifold to a 2D Euclidean plane. The core constraint of this mapping is to ensure that the tangent vector field in the parameter domain satisfies the discrete Cauchy-Riemann equations. At the discrete patch level, let the coordinates of the 3D vertex in the parameter plane be... , among them Represents two-dimensional spatial coordinates. Symbols for complex equations Satisfying linear operator relations:

[0062]

[0063] in, For gradient operators defined on triangular or quadrilateral elements, Counterclockwise rotation in the plane The operator. In order to approximate the above ideal conformal state in the least squares sense, this embodiment constructs a global energy functional. Used to measure the non-conformal distortion energy after mapping discrete patches:

[0064]

[0065] in, For parameterized mapping functions. By using the global energy functional Discretize into a weighted representation and construct a discrete Laplace matrix using cotangent weights:

[0066]

[0067] in, and Shared edge The corresponding geometric angle. Ultimately, the parameterization problem is transformed into solving a set of decoupled sparse linear equations:

[0068]

[0069] During the solution process, two vertices with large curvature extrema at the edge of the partition are selected as anchor points, and their initial parameter coordinates are fixed to eliminate the degrees of freedom of rigid body transformation, thereby obtaining the optimal distribution of vertices of each partition in the complex parameter plane. This method effectively preserves the local feature proportions of the original mesh and greatly reduces the energy compensation pressure in the subsequent RBF boundary alignment process.

[0070] Preferably, the RBF radial basis function mentioned in step 4, the core of this algorithm lies in constructing a globally smooth displacement mapping field. By establishing arbitrary parameter points within the reference plane With updated coordinates The functional relationship between them enables precise boundary alignment. Let the reference surface parameter mesh boundary be... The discrete vertices are a set of control points. The corresponding target position on the object surface is Then the mapping function expression is defined as .in, The radial basis kernel function reflects the deformation field as a function of the Euclidean distance. The energy decay characteristics. In this embodiment, a thin-plate spline kernel function with bending energy minimization characteristics is preferably used. ,and These are additional low-order polynomial operators used to describe the affine transformations such as global rotation, translation, and shearing in the deformable field.

[0071] To solve for the unknown coefficients of this interpolation system, this invention substitutes the forced alignment constraint condition of the boundary vertices. By combining the lateral equilibrium constraints of the polynomial part, a block-symmetric system of linear equations is constructed. This system can be represented in matrix form:

[0072]

[0073] In this system of equations The basis function evaluation matrix is ​​composed of elements determined by the kernel function. constitute; It is a polynomial constraint matrix containing the coordinates of control points and constant terms; and These are the kernel function weight matrix and the affine transformation coefficient matrix, respectively, to be solved. After obtaining the above coefficient matrices, for all non-boundary vertices within the partition, the mapping function is directly called. This propagates the displacement error at the boundary to the entire parameter domain in a smooth, continuous, and analytical manner.

[0074] Preferably, step 5 includes maintaining the linear consistency of local geometric relationships using barycentric coordinates. This process first determines the updated planar mesh by detecting the inclusion of points within the polygon. Vertex in In the original planar grid The triangular or quadrilateral unit in which it is located Let the original coordinates of the vertices of this element in the parametric plane be respectively... Then the updated vertex It can be uniquely represented as a linear combination of these vertex coordinates, i.e., satisfying:

[0075]

[0076] in, Let be the centroid coordinate coefficients to be solved, and they must satisfy the normalization constraints. For triangular elements, this coefficient can be obtained directly by solving a system of linear equations consisting of vertex coordinates; for quadrilateral elements, a set of smooth and positive definite weight coefficients is often obtained through mean value coordinates or bilinear interpolation.

[0077] After obtaining the barycenter coordinate coefficients, the topological equivalence before and after mapping is utilized to apply these coefficients to the corresponding 3D vertex coordinates. Let the vertex coordinates of the corresponding element in the original 3D mesh be... The reconstructed 3D reference plane vertex coordinates It can be calculated using the following formula:

[0078]

[0079] Based on the coordinates of all the reconstructed 3D reference surface vertices, the final reference mesh surface is obtained.

[0080] This inverse mapping mechanism is essentially an interpolation transformation based on a local coordinate system. It can accurately restore the topological distribution characteristics optimized by RBF in the parametric plane to the three-dimensional physical space. Since the barycentric coordinates are invariant under affine transformations, this method ensures that the reconstructed three-dimensional reference mesh surface maintains its alignment with the original object surface. While maintaining geometric similarity, it perfectly inherits the smoothness and orthogonality characteristics within the parameter domain, thereby constructing a high-quality reference surface for boundary layer stretching.

[0081] In another aspect, the present invention also provides a CFD boundary layer mesh generation system based on mapping parameterization, for implementing the aforementioned CFD boundary layer mesh generation method, including a reference mesh surface generation module, a topology partitioning module, a planar mesh update module, a final reference mesh surface reconstruction module, and a global boundary layer mesh generation module:

[0082] The reference mesh generation module constructs an initial boundary layer reference mesh based on a Cartesian background mesh, and optimizes the initial boundary layer reference mesh using a projection smoothing algorithm to obtain a geometrically continuous reference mesh.

[0083] The topology partitioning module is used to synchronously partition the object surface and the reference mesh surface using an optimized variational shape approximation algorithm, thereby dividing the object surface into several topology-corresponding partitioning pairs.

[0084] The planar mesh update module is used to obtain a planar mesh for each partition pair by conformal mapping projection onto a two-dimensional parameter plane, and to perform boundary alignment and internal coordinate interpolation using radial basis functions to obtain the updated planar mesh.

[0085] The final reference mesh reconstruction module reconstructs the final reference mesh by inversely mapping the updated planar mesh to three-dimensional space based on centroid coordinate interpolation.

[0086] The overall boundary layer mesh generation module is used to perform inter-layer node interpolation between the object surface and the final reference mesh surface according to preset distribution parameters to generate an overall boundary layer mesh.

[0087] Example:

[0088] This embodiment uses the generation of boundary layer meshes for an aircraft model as an example to demonstrate the specific execution process of the present invention.

[0089] 1. Construct the initial boundary layer reference mesh surface based on the Cartesian background mesh.

[0090] First, obtain the surface covering the wing. The outermost pre-defined Cartesian background mesh. In the computational environment, an Inside-out mapping mechanism is used to extract a layer of quadrilateral cells adjacent to the wing surface, constructing the initial reference mesh surface. For aircraft models, Figure 2 The image shows the construction of the Cartesian background grid. Figure 3 The left image shows the extraction of a Cartesian grid layer from the surface of the aircraft.

[0091] 2. The initial boundary layer reference mesh surface is smoothed using a projection smoothing algorithm. Optimization is performed to obtain a geometrically continuous reference mesh surface. .

[0092] To address the stepped topological features of the initial surface, this embodiment constructs a kd-Tree spatial index structure. Quick search and The set of nearest neighbors of a vertex.

[0093] Subsequently, projection iterative optimization is performed. In each iteration, based on the vertex displacement... Update coordinates and embed smoothing factor. Laplace smoothing, the formula is: After approximately 10-20 iterations, a reference surface was obtained that both closely matches the wing geometry and exhibits good continuity. .

[0094] For aircraft models Figure 3 The left image shows the structural quadrilateral mesh before smoothing, and the right image shows the structural quadrilateral mesh after projection smoothing. It is highly similar in shape to the original aircraft model.

[0095] 3. Utilize the optimized variational shape approximation algorithm to approximate the object surface. With the reference mesh surface Perform synchronized partitioning to create several partition pairs corresponding to the topology. .

[0096] To handle the high curvature region at the leading edge and the sharp features at the trailing edge of the wing, an optimized VSA algorithm is used for partitioning. First, the Laplace-Beltramm matrix of the wing mesh is solved, and its Fiedler vectors are extracted. The algorithm automatically determines 8-12 initial cluster centers based on the numerical gradient distribution of the vector. During the iteration process, it utilizes... Normal error measurement The partition boundaries are continuously optimized. Finally, by identifying feature points at the wingtip and root as corner points, the boundaries are reconstructed using Dijkstra's algorithm to ensure a strict one-to-one topological correspondence between the object plane partitions and the reference plane partitions. For the aircraft model, Figure 4 The left-middle image shows the result after VSA partitioning but without corner optimization. Figure 4 The rightmost image shows the result with corner-based shortest path optimization. It can be seen that this significantly reduces jagged edges in the shape, making the partition boundaries smoother. Figure 5 A schematic diagram of the reference mesh topology alignment from the inside out to the triangle in an embodiment of the present invention.

[0097] 4. For each partition pair, project it onto a two-dimensional parametric plane using conformal mapping to obtain a planar mesh, and then use radial basis functions for boundary alignment and internal coordinate interpolation to obtain an updated planar mesh. .

[0098] For the extracted wing surface partition pairs, conformal projection is performed using the LSCM algorithm. This is achieved by minimizing the energy functional. The three-dimensional bending partition is unfolded onto a two-dimensional complex parametric plane. Since the leading edge of the wing may exhibit localized stretching differences after projection, this embodiment uses the common boundary vertices of the partition pairs as control points to construct a thin-plate spline function-based system. The RBF interpolation system is described. By solving a system of linear equations containing affine transformation terms, the boundary of the reference surface parameter mesh is forced to align with the boundary of the object surface parameter mesh, and the displacement field is smoothly transferred to the inner field vertices, eliminating geometric mismatches in the parameter domain.

[0099] For aircraft models Figure 6 The top left image represents the same partition, the original grid. With reference grid Correspondence in three-dimensional space; Figure 6 The top right image represents the grid correspondence after projection transformation to the same space; Figure 6 The lower figure shows the result obtained after boundary alignment and RBF fitting of the center point;

[0100] 5. Based on barycenter coordinate interpolation, the updated planar mesh is... The inverse mapping is performed to three-dimensional space to reconstruct the final reference mesh surface. Then, according to preset distribution parameters, the mesh is applied to the object surface. Inter-layer node interpolation is performed between the final reference mesh surface and the reference mesh to generate an overall boundary layer mesh.

[0101] Using barycentric coordinate interpolation, the linear weight coefficients of the updated parameter vertices within the original cells are calculated. Through the formula The two-dimensional optimization results are restored to the three-dimensional physical space to reconstruct the final high-quality reference mesh surface.

[0102] Finally, the height of the first-layer mesh is set between the wing object surface and the final reference surface. The average chord length is 1.2, the growth rate is 1.2, and the total number of layers is 25. Node distribution interpolation is performed along the linearly corresponding direction between the two surfaces to generate the final boundary layer mesh. Experimental results show that the mesh orthogonality is maintained in narrow regions such as the wing trailing edge. The above points were observed, and no form of unit self-crossing was detected.

[0103] For aircraft models Figure 7 The top left image represents the segmentation diagram generated by the boundary layer, showing excellent global orthogonality. Figure 7 The above figure represents the boundary layer between the generated outer and inner meshes; Figure 7 The image below shows a magnified view of the boundary layer, demonstrating excellent orthogonality between different boundary layers.

[0104] The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A CFD boundary layer mesh generation method based on mapping parameterization, characterized in that, Includes the following steps: Step 1: Construct the initial boundary layer reference mesh surface based on the Cartesian background mesh; Step 2: Optimize the initial boundary layer reference mesh surface using a projection smoothing algorithm to obtain a geometrically continuous reference mesh surface. Specifically, this includes: optimizing the original object surface... Construct a kd-Tree spatial index structure from the vertex set, and traverse the boundary layer reference mesh obtained in step 1. All vertices on the surface are plotted using a kd-tree on the original surface. Quickly find the corresponding vertex that is closest to the vertex set constructed by the kd-Tree. For the boundary layer reference mesh surface Previous vertex Obtain the original surface A set of vertices The position of the projected point is obtained through the average vertex set. According to the projection point vertex The projection vector is obtained by subtraction. Based on the calculated projection vector pair The vertex positions are directly added together to obtain the adjusted vertex coordinates, so that the reference mesh gradually converges geometrically towards the original object surface. Approach; set the number of iterations, and perform Laplacian smoothing on the vertices in each iteration; through multiple iterations of the above search and projection process, a quadrilateral reference mesh surface with a fitted shape and geometric continuity is finally obtained. ; Step 3: Use the optimized variational shape approximation algorithm to synchronously partition the object surface and the reference mesh surface, and divide them into several topologically corresponding partition pairs; Step 4: For each partition pair, project it onto the two-dimensional parametric plane through conformal mapping to obtain a planar mesh, and use radial basis functions to perform boundary alignment and internal coordinate interpolation to obtain the updated planar mesh; Step 5: Based on the barycenter coordinate interpolation, the updated planar mesh is inversely mapped to three-dimensional space to reconstruct the final reference mesh surface; Step 6: Based on the preset distribution parameters, perform inter-layer node interpolation between the object surface and the final reference mesh surface to generate the overall boundary layer mesh.

2. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 1, characterized in that, Step 1 includes: obtaining a pre-generated object covering the original surface. The outer Cartesian background mesh; extract the nearest unit surface from the Cartesian background mesh to obtain the initial boundary layer reference mesh surface composed of quadrilateral patches. ; The Cartesian background mesh is generated within a spherical mesh that is twice the size of the minimum bounding box of the original object surface, and the edge length is finally subdivided to the average edge length of the original object surface.

3. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 2, characterized in that, Step 3 includes using an optimized variational shape approximation algorithm to approximate the object surface. With reference mesh surface Perform synchronized partition processing: First, spectral feature clustering is used. This involves constructing a grid-like Laplacian matrix, performing eigenvalue decomposition on the Laplacian matrix, and then filtering the decomposed eigenvalues ​​and eigenvectors to select the smallest non-zero eigenvalue and its corresponding vector. For vectors Traverse through the n dimensions to find the index corresponding to the minimum value. ,this It is the first seed facet obtained after initialization; Variational energy functionals are used to simultaneously cluster the object surface and the reference surface to complete the partitioning; After partitioning, a corner-based partition boundary optimization strategy is introduced. This strategy identifies singular points at the intersection of multiple partitions as feature corner points and reconstructs the topological boundary between adjacent corner points using a shortest distance path algorithm, replacing the original discrete patch edges; thus, several topologically corresponding partition pairs are divided. , This represents the partition number.

4. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 3, characterized in that, The initialization mechanism for the spectral feature clustering is as follows: First, a Laplacian-Beltramian operator is constructed for the grid discrete manifold, and then a discrete Laplacian matrix is ​​established based on the connectivity between patches and the geometric weights. Then, based on the principle of solving generalized eigenvalue problems, the equation is defined. Solve and The discrete Laplace matrix is ​​then obtained. A series of eigenvalues ​​and their corresponding eigenvectors form spectral features.

5. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 4, characterized in that, The variational energy functional performs synchronous clustering of the object surface and the reference surface as follows: the Proxy partition to which the object belongs is defined as the center patch of the determined partition. After determining the initial seed patch, the partition boundary is updated by iteratively minimizing the geometric deviation between the patch and the Proxy partition to which the object belongs. The normal error metric is used as the standard for measuring the energy functional.

6. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 5, characterized in that, Step 4 is specifically implemented as follows: for each group of topologies divided in step 3, the corresponding three-dimensional partitions are... First, using a conformal mapping algorithm, the three-dimensional surface mesh is projected onto the two-dimensional parametric domain complex plane to obtain the object surface parametric mesh. With reference surface parameter mesh ; Introducing a radial basis function interpolation mechanism: using vertices on the partition boundary as control points, constructing displacement constraint equations, and incorporating the reference surface parameter mesh. The boundary coordinates are linearly transformed to the object surface parameter mesh. The boundary coordinates coincide; Subsequently, utilizing the global interpolation property of the RBF radial basis function, the parametric coordinates of all vertices within the partition are updated collaboratively based on the displacement vectors at the boundary, resulting in an updated planar mesh that is aligned with the object surface mesh at the boundary and has internal topological consistency within the parameter domain. .

7. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 6, characterized in that, The conformal mapping algorithm specifically refers to: for synchronized partitions... and A least-squares conformal mapping scheme based on discrete conformal geometry theory is employed to construct a low-distortion embedding from a 3D manifold to a 2D Euclidean plane. The core constraint of this mapping is to ensure that the tangent vector field in the parameter domain satisfies the discrete Cauchy-Riemann equations. At the discrete patch level, let the coordinates of the 3D vertices in the parameter plane be... , among them Represents two-dimensional spatial coordinates. Symbols for complex equations Satisfying linear operator relations ,in For gradient operators defined on triangular or quadrilateral elements, Counterclockwise rotation in the plane Operators; based on Constructing a global energy functional It is used to measure the non-conformal distortion energy after mapping discrete patches, by using a global energy functional Discretization is performed in a weighted form, and a discrete Laplace matrix is ​​constructed using the cotangent weight coefficients. The parameterization problem is transformed into solving a set of decoupled sparse linear equations: ; In the solution process, by selecting two vertices with larger curvature extrema at the edge of the partition as anchor points, the degrees of freedom of rigid body transformation are eliminated by fixing the initial parameter coordinates, and the optimal distribution of each partition vertex in the complex parameter plane is obtained.

8. The CFD boundary layer mesh generation method based on mapping parameterization according to claim 7, characterized in that, Step 5 includes: maintaining the linear consistency of local geometric relationships using barycentric coordinates, firstly by determining the updated planar mesh through inclusion detection of points within the polygon. Vertex in In the original planar grid The triangular or quadrilateral unit in which it is located Let the original coordinates of the vertices of this element in the parametric plane be respectively... Then the updated vertex It can be uniquely represented as a linear combination of these vertex coordinates, satisfying ,in, Let be the centroid coordinate coefficients to be solved, and they must satisfy the normalization constraints. For triangular units, this coefficient The weights are obtained directly by solving a system of linear equations consisting of vertex coordinates; for quadrilateral elements, a set of smooth and positive definite weight coefficients are obtained by mean coordinates or bilinear interpolation. Obtain the centroid coordinate coefficients Then, using the topological equivalence before and after the mapping, the coefficient is... It acts on the corresponding 3D vertex coordinates; let the vertex coordinates of the corresponding element in the original 3D mesh be... The reconstructed 3D reference plane vertex coordinates Based on the vertex coordinates of all reconstructed 3D reference surfaces, the final reference mesh surface is obtained.

9. A CFD boundary layer mesh generation system based on mapping parameterization, used to implement the CFD boundary layer mesh generation method according to any one of claims 1 to 8, characterized in that, Includes the following modules: The reference mesh generation module constructs an initial boundary layer reference mesh based on a Cartesian background mesh, and optimizes the initial boundary layer reference mesh using a projection smoothing algorithm to obtain a geometrically continuous reference mesh. The topology partitioning module is used to synchronously partition the object surface and the reference mesh surface using an optimized variational shape approximation algorithm, dividing the object surface into several topology-corresponding partitioning pairs. The planar mesh update module is used to obtain a planar mesh for each partition pair by projecting it onto a two-dimensional parametric plane through conformal mapping, and then using radial basis functions to perform boundary alignment and internal coordinate interpolation to obtain the updated planar mesh. The final reference mesh reconstruction module reconstructs the final reference mesh by inverse mapping the updated planar mesh to three-dimensional space based on barycentric coordinate interpolation. The overall boundary layer mesh generation module is used to generate an overall boundary layer mesh by interpolating interlayer nodes between the object surface and the final reference mesh surface according to preset distribution parameters.

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