A method for generating a three-dimensional body grid based on a conical surface grid radial growth

Abstract

The application relates to a generation method of a three-dimensional body grid based on radial growth of a conical surface grid, and belongs to the field of electromagnetic engineering.The generation method comprises the following steps: reading geometric parameters and discretization data of the conical surface grid, screening triangular surface units needing to be processed according to target material numbers, and generating a unit list to be processed; a local coordinate system C is established with a conical axis as a reference, vertex coordinates are converted to the local coordinate system C, and transformed coordinates are obtained; radial coordinate mapping is performed on the triangular surface units in the unit list to be processed, each mapping point is inversely transformed to a world coordinate system, and grown vertex coordinates are obtained; a three-prism body grid is generated by connecting original triangular surface units and the grown vertex coordinates, the three-prism body grid is decomposed into tetrahedron units, and a final body grid is output.The application realizes geometric self-adaptive deformation, ensures unit quality, controls the conical surface curvature error within 0.1%, and supports efficient generation of ten-million-level grids.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electromagnetic engineering, and in particular to a method for generating a three-dimensional body grid based on a radial growth of a conical surface grid. BACKGROUND

[0002] In the field of engineering simulation, the generation of body grids of conical structures has long been plagued by technical bottlenecks. Traditional methods such as global stretching, although simple and easy to use, cannot adapt to the nonlinear change of the conical radius with height, resulting in severe compression of the top cells. Actual measurement data shows that the temperature field calculation error in the simulation of a certain type of rocket nozzle due to this problem is as high as 12%. Delaunay triangulation can generate tetrahedral grids, but it is prone to produce "silver strip cells" in thin-walled structures, leading to calculation divergence. In a certain turbine blade analysis, the calculation failure rate due to this problem is as high as 37%. The sweep grid method has strict requirements for topological consistency and is not suitable for multi-material composite conical structures. Literature reports that its failure rate exceeds 40%. In recent years, improved techniques such as methods based on radial basis functions can maintain geometric features, but the O(N³) computational complexity makes the generation of million-level grids take more than 2 hours, and it cannot handle material interfaces. The adaptive octree subdivision method can control the cell density, but it produces step-like artifacts near the axis. IEEE Trans. data shows that the material boundary error is as high as 8.3%. In industrial practice, the demand for multi-materials in modern composite structures such as turbine blades is increasing. Commercial software such as ANSYS Meshing needs to spend 60% of the pre-processing time to manually mark the material interface. At the same time, high-fidelity simulation requires strict requirements, such as the length-width ratio of the wall surface cells of the conical vascular stent being less than 3:1. Traditional methods often require 3-5 times of grid reconstruction to meet the requirements. These technical defects seriously restrict the simulation accuracy and efficiency in the fields of aerospace, medical devices, etc., and there is an urgent need for a conical body grid generation method that can simultaneously ensure geometric fidelity, material adaptation, and computational efficiency. SUMMARY

[0003] The purpose of the present application is to overcome the shortcomings of the prior art and provide a method for generating a three-dimensional body grid based on the radial growth of a conical surface grid, which solves the problems existing in the prior art.

[0004] The purpose of the present application is achieved by the following technical solution: a method for generating a three-dimensional body grid based on the radial growth of a conical surface grid, the generation method comprising:

[0005] Step 1: Read the geometric parameters and discretization data of the conical surface grid, and select the triangular surface elements that need to be processed according to the target material number to generate a list of units to be processed;

[0006] Step 2: Establish a local coordinate system C with the conical axis as the reference, convert the vertex coordinates to the local coordinate system C, and obtain the transformed coordinates;

[0007] Step three, perform radial coordinate mapping on the triangular face unit vertex in the list of units to be processed, inverse transform each mapping point to the world coordinate system to obtain the grown vertex coordinates;

[0008] Step four, connect the original triangular face unit and the grown vertex coordinates to generate a triangular prism grid, and decompose it into tetrahedral units to output the final volume grid.

[0009] The step one specifically includes the following contents:

[0010] A1, read the geometric parameters and discretization data of the conical surface grid, including: bottom center point coordinates and axial unit vector , bottom radius and height , vertex list P, triangular face unit list E and material attribute list M;

[0011] A2, according to the target material number , filter the triangular face units to be processed to generate the list of units to be processed .

[0012] The step two specifically includes the following contents:

[0013] B1, establish a local coordinate system C with the conical axis as the reference: take as the origin, as the Z axis, calculate the radial unit vector through the circumferential point , calculate the tangential unit vector ;

[0014] B2, convert the vertex coordinates to the local coordinate system C to obtain the transformed coordinates .

[0015] The step three specifically includes the following contents:

[0016] C1, perform radial coordinate mapping on the triangular face unit vertex in E': calculate the radial distance , calculate the scaling factor according to the growth amount Δρ, generate the mapping point coordinates , , ;

[0017] C2, inverse transform each mapping point to the world coordinate system to obtain the grown vertex coordinates .

[0018] The step four specifically includes the following contents:

[0019] D1, connecting original triangular facet elements with growth post vertex generate a triangular prism grid;

[0020] D2, split each quadrilateral side of the triangular prism into two triangles along the diagonal;

[0021] D3, generate 3 tetrahedral elements with the center point of the triangular prism as the reference, each tetrahedral element contains one original triangular facet vertex, two growth post vertices and the center point, and finally output the final volume grid.

[0022] The A2 filters target elements by material matching, specifically comprising:

[0023] specifying the target material number ;

[0024] traverse the element list E, filter out elements that meet to form the to-be-processed element list E';

[0025] record the number N of elements obtained by filtering.

[0026] The present application has the following advantages: a method for generating a three-dimensional volume grid based on the radial growth of a conical surface grid, by parameterizing the growth function , realize geometric self-adaptive deformation, ensure element quality (Jacobian > 0.8); based on the quadratic mapping technology of local coordinate system C, the conical surface curvature error is controlled within 0.1%; material sensitive parallel processing architecture, support efficient generation of ten million level grid (<10 minutes). BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is the flowchart of the present application;

[0028] Figure 2 is a schematic diagram of a conical model;

[0029] Figure 3 is a conical surface grid model diagram;

[0030] Figure 4 is a model diagram after material number matching ;

[0031] Figure 5 is a conical surface coordinate mapping diagram;

[0032] Figure 6 is a schematic diagram of a triangular prism grid. DETAILED DESCRIPTION

[0033] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in combination with the drawings is not intended to limit the protection scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present application. The present application will be further described below in combination with the drawings.

[0034] One of the embodiments of the present application specifically relates to a method for generating a three-dimensional body grid based on a conical surface grid radial growth, which provides a parameterized modeling solution for engineering simulation. Through the radial growth technology of geometric feature preservation, high-quality body grid generation of conical structures can be realized, which provides technical support for simulation calculation in the field of electromagnetic engineering.

[0035] As shown in Figures 1-3 , specifically includes device data input module, material screening module, local coordinate system construction module, coordinate transformation module, radial mapping module, inverse transformation module and body grid generation module.

[0036] The data input module performs the following content:

[0037] S101, read the conical geometric parameters: the coordinates of the center point of the base surface, the axial unit vector ŵ, the base surface radius and the conical height. , wherein the i-th point is expressed as ;

[0038] S102, import the discretized surface grid data: vertex list P, triangular facet list E and material attribute list M.

[0039] As shown in Figure 4 , the material screening module performs the following content:

[0040] S201, material matching condition setting: define the target material number M0 as the screening reference value, establish the element selection criterion: M [j] ≡ M0, the elements satisfying this condition are the target element set E', wherein j ∈ [0, n) is the element index number, and n represents the total number of elements in the grid.

[0041] Further, the local coordinate system construction module performs the following content: ​​

[0042] S301, select the bottom surface circumferential point P d ;

[0043] S302, calculate the orthogonal basis vector , , , which respectively represent the local coordinate system radial, tangential, axial unit vector.

[0044] Further, the coordinate transformation module performs the following:

[0045] S401, convert the vertex coordinates to local coordinates , including:

[0046] ,

[0047] ,

[0048] ,

[0049] wherein, , , is the local coordinate x, y, z direction coordinate value. , , is the radial unit vector x, y, z component, is the tangential unit vector x, y, z component, , is the axial unit vector x, y, z component. , the bottom surface origin x, y, z coordinates. , represent any point x, y, z coordinates.

[0050] As Figure 5 shown, the radial mapping module specifically performs the following:

[0051] S501, for each face element in E', the k vertex (k=0,1,2) is calculated: ;

[0052] S502, calculate the growth coefficient: , wherein , wherein α is a user-defined scaling factor, is the height coordinate of the vertex in the local coordinate system;

[0053] S503, perform mapping: , and .

[0054] Further, the inverse module specifically performs the following:

[0055] S601, for each mapping point , calculate the global coordinates , wherein

[0056] ,

[0057] ,

[0058] .

[0059] As Figure 6 shown, the volume mesh generation module specifically performs the following:

[0060] S701, collect and , k=0,1,2, get the three-prism mesh composed of 6 points generated by the radial of j cells;

[0061] S702, decompose the three-prism into 3 tetrahedrons;

[0062] S703, loop the steps of S701-S702, traverse all triangular cells , get the final tetrahedron volume mesh and three-prism mesh, and complete the radial growth of the conical surface mesh to the three-prism mesh or tetrahedron volume mesh.

[0063] Further, the target cell is screened by material matching, specifically including:

[0064] specify the target material number ;

[0065] traverse the cell list E, filter out the cells that meet , to form the to-be-processed cell list E';

[0066] record the number of cells obtained by screening N.

[0067] The above only describes the preferred embodiments of the present application, and it should be understood that the present application is not limited to the forms disclosed herein, and should not be considered as excluding other embodiments, but can be used in various other combinations, modifications and improvements, and can be modified within the scope of the concepts described herein, by the above teachings or related art or knowledge. The modifications and changes made by those skilled in the art without departing from the spirit and scope of the present application shall be within the scope of protection of the appended claims of the present application.

Claims

1. A method for generating a grid of three-dimensional bodies based on the radial growth of a grid of conical surfaces, characterized in that: The generating method comprises: Step one, reading the geometric parameters and discretization data of the conical surface grid, and screening the triangular surface elements to be processed according to the target material number to generate a list of elements to be processed; Step two, establishing a local coordinate system C with the conical axis as the reference, converting the vertex coordinates to the local coordinate system C to obtain the transformed coordinates; Step three, performing radial coordinate mapping on the triangular surface elements in the list of elements to be processed, inversely transforming each mapping point to the world coordinate system to obtain the grown vertex coordinates; Step four, connecting the original triangular surface elements and the grown vertex coordinates to generate a triangular prism grid, and decomposing the triangular prism grid into tetrahedral elements to output the final volume grid; The step three specifically comprises the following contents: C1. Perform radial coordinate mapping on the triangular facet element vertices in E' : compute radial distances , compute scaling factor from growth amount Δρ , generate mapped point coordinates 、 、 , E' represents the list of elements to be processed; C2. Transform each mapping point inverse transform to world coordinate system, get post-growth vertex coordinates .

2. The method of claim 1, wherein the method further comprises: generating a three-dimensional body mesh based on the conic surface mesh. The step one specifically comprises the following contents: A1, read the geometric parameters and discretization data of the conical surface grid, including: the coordinates of the bottom surface center point and the axial unit vector , the bottom surface radius and the height , the vertex list P, the triangular surface element list E and the material attribute list M; A2. According to the target material number Screening the triangular surface elements to be processed, generating a list of elements to be processed .

3. The method of claim 2, wherein the method further comprises: generating a three-dimensional body mesh based on the conic surface mesh. The step two specifically comprises the following contents: B1. Establish a local coordinate system C with the conical axis as the reference: with the origin, Z axis, through the circumferential point Calculate the radial unit vector Calculate the tangential unit vector ; B2, convert the vertex coordinates to a local coordinate system C to obtain transformed coordinates =( , ).

4. The method of claim 1, wherein: The step four specifically comprises the following contents: D1, connect original triangular facets with the growing apex generate a triangular prism mesh; D2, each quadrilateral side of the triangular prism is divided into two triangles along the diagonal; D3, taking the center point of the triangular prism as the reference, generating 3 tetrahedral elements, each tetrahedral element containing one original triangular surface vertex, two grown vertices and the center point, and finally outputting the final volume grid.

5. The method of claim 2, wherein: The A2 screens the target elements by material matching, specifically comprising: Designated target material number ; Traverse the unit list E, filter out the units satisfying == to form the to-be-processed unit list E'; Recording the number N of elements obtained by screening.

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