Efficient Delaunay surface triangular mesh generation method

Abstract

The invention belongs to the technical field of three-dimensional fluid mechanics numerical solution, and relates to an efficient Delaunay surface triangular mesh generation method. The method comprises the following steps: firstly, acquiring information such as geometric surfaces, geometric edges and geometric vertexes of a to-be-processed model through a geometric modeling kernel; secondly, discretizing geometric edges of the model to construct a one-dimensional discrete grid; secondly, boundary discrete points are generated step by step based on the topological relation of the geometric surfaces and mapped to a parameter plane; then, an initial triangularized grid is generated by adopting a constraint Delaunay method, and internal points are inserted one by one, so that searching and multiple traversal on a base unit are avoided; according to the method, the grid generation efficiency can be remarkably improved, the calculation overhead is reduced, and the high-quality numerical simulation requirement of a complex geometrical shape is met.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical solution of three-dimensional fluid mechanics, and relates to an efficient Delaunay surface triangular mesh generation method. Background Art

[0002] Computational fluid dynamics (CFD) has been widely used in the fields of automobile manufacturing, civil engineering, environmental engineering, shipbuilding industry and aviation industry. It helps to explain and understand the results of theory and experiments, and is an indispensable method for fluid dynamics analysis. In the early stage, due to the limitation of computer level, CFD was limited to solving some simple problems. With the development of computer level, today's CFD can solve a large number of complex three-dimensional flow fields. Although it still requires a lot of manpower and computer resources, this solution method has been widely used in industrial equipment.

[0003] With the advancement of industrial technology, fluid dynamics has put forward higher requirements on the accuracy of numerical algorithms, so high-precision numerical simulation methods are needed. Grid generation is an important part of numerical calculation, especially in the field of computational fluid dynamics (CFD), where the requirements for grid generation speed are extremely strict. Most of the total time spent in CFD calculations is often concentrated in the grid generation link. As the starting point of CFD numerical simulation, grid generation is both the most basic step and a crucial step. The degree of automation and quality of grid generation directly affect the cycle, accuracy and efficiency of CFD calculations. With the continuous expansion of CFD application fields and the increase in problem complexity, the existing grid generation technology has become insufficient in dealing with high-quality numerical simulations of complex shapes. Therefore, how to develop highly automated and efficient grid generation technology has become a hot topic in current research.

[0004] At present, the mainstream Delaunay surface triangulated mesh generation serial procedure usually includes the following five steps: model input, boundary discretization, surface discretization, mesh optimization and mesh merging. Among them, surface discretization is the longest step. The traditional Delaunay surface triangulated mesh generation method usually adopts the method of using the current triangulation as the background mesh, batch generating internal points according to the requirements of the mesh discretization size, and inserting them one by one; this process is continuously cycled until the mesh density or geometric quality meets the convergence condition. Such a point generation and insertion algorithm inevitably needs to traverse the current triangulated mesh multiple times. In the process of internal point insertion, quadtree search algorithms and KD tree search algorithms are often used to accelerate the search for cavities. These algorithms locate the base unit containing the point to be inserted and use the adjacency relationship of the base unit triangle to find the cavity. However, due to the need for repeated iteration and search of base units, this process consumes a lot of computing resources, which restricts the engineering application of high-precision algorithms. Summary of the invention

[0005] In view of the above-mentioned problems or shortcomings, in order to solve the bottleneck of surface mesh generation efficiency and realize efficient Delaunay surface triangular mesh generation; the present invention provides an efficient Delaunay surface triangular mesh generation method, develops a more efficient internal point generation and insertion technology, reduces iterative cycles, and improves the mesh generation efficiency while ensuring high precision.

[0006] An efficient Delaunay surface triangular mesh generation method includes the following steps:

[0007] A. Carry out 3D solid modeling of the target structure and add it to the model list. Obtain the geometric face list, geometric edge list, geometric vertex list and the topological relationship between them of the target structure's outline through the geometric modeling kernel.

[0008] B. According to the size requirement of mesh discretization, all geometric edges in the geometric edge list obtained in step A are discretized, and a one-dimensional discrete mesh of the target model is generated based on the discretization information.

[0009] C. According to step A, the geometric faces, geometric edges, geometric vertices and their topological relationships are obtained, and combined with the one-dimensional discrete grid obtained in step B, the discrete points of the geometric edges contained in a single geometric face are combined into the boundary discrete points of the geometric face, as well as the connection relationship between the boundary discrete points.

[0010] D. Combine the parameter domain information of the current geometric surface, construct a parameter plane, and map the boundary discrete points obtained in step C to the parameter plane to obtain the boundary discrete points and mapping relationship on the parameter plane of the current geometric surface.

[0011] E. Based on the boundary discrete points on the parameter plane of the current geometric surface obtained in step D, an incremental interpolation algorithm is used to insert the boundary points and perform boundary recovery to construct an initial triangulated mesh of the current geometric surface.

[0012] F. Based on the initial triangulated mesh of the current geometric surface obtained in step E, traverse the initial triangulated mesh, generate and insert internal points, and update the initial triangulated mesh to obtain a triangulated mesh of the current geometric surface that meets the mesh discrete size requirements.

[0013] G. Based on the triangular mesh of the single geometric surface generated in step F, perform mesh quality optimization to obtain an optimized triangular mesh of the single geometric surface.

[0014] H. Repeat steps C to G until all individual geometric faces in the geometric face list have been traversed, and obtain the triangular meshes of all individual geometric faces in the geometric face list.

[0015] I. Based on the topological relationship obtained in step A, the mapping relationship in step D and the triangular mesh obtained in step H, the triangular meshes of all individual geometric faces are reversely mapped from the parameter plane back to the three-dimensional real space to obtain the surface triangular mesh of the target structure contour.

[0016] The present invention first reads the CAD model to be meshed, obtains the faces, edges, and vertices of the model and establishes index relationships, then discretizes the edges, and then performs Delaunay triangulation on each surface, optimizes the quality, and finally merges them into an overall surface mesh.

[0017] In summary, in the process of generating a mesh on the parameter plane of a single geometric surface, the present invention generates insertion points one by one, and uses the triangles that generate the insertion points as the base units, thereby avoiding the search of base units and avoiding multiple traversals of the current triangulated mesh. In the process of generating a mesh on a single geometric surface, each triangular mesh is only traversed once during the traversal process. Therefore, a large amount of computational overhead is saved, and the efficiency of mesh generation is improved when the memory overhead is equivalent. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the present invention;

[0019] Figure 2 is the CAD model diagram constructed in step A of the embodiment;

[0020] Figure 3 This is a comparison chart of the computational performance of the embodiment and the MeshSim software of Simmetrix. DETAILED DESCRIPTION

[0021] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

[0022] An efficient method for generating triangular meshes of Delaunay surfaces, referring to Figure 1 , including the following steps:

[0023] A. Carry out 3D solid modeling of the target aircraft structure and add it to the model list. Obtain the geometric face list, geometric edge list, geometric vertex list and the topological relationship between them of the aircraft outline through the geometric modeling kernel.

[0024] In this embodiment, the ACIS geometry kernel is used to establish Figure 2 The X-51-like aircraft model is shown, and the X-51-like aircraft model is added to the model list through the API function. Then the geometric face list, geometric edge list, geometric vertex list and the topological relationship between them of the X-51-like aircraft outline in the model list are obtained through the geometric modeling kernel.

[0025] In step A, based on the information of geometric faces, geometric edges and geometric vertices in the geometric face list, geometric edge list and geometric vertex list, the ACIS geometric kernel is used to obtain the geometric edges and geometric vertices contained in each geometric face and the geometric vertices contained in each geometric edge.

[0026] B. According to the size requirement of mesh discretization, all geometric edges in the geometric edge list obtained in step A are discretized, and a one-dimensional discrete mesh of the target model is generated based on the discretization information.

[0027] Furthermore, based on the geometric edge list obtained in step A, for each geometric edge, based on the sampling size, a numerical integration algorithm is used to calculate the arc length and correct the sampling distance to obtain the distance from the sampling point to the starting point of the curve:

[0028]

[0029] where s i is the distance from the i-th sampling point to the starting point of the curve, u i is the parameter coordinate of the i-th sampling point, r(t) is the curve equation, m is the total number of sampling points, and l is the arc length of the curve.

[0030] Solve the integral of formula (1) to obtain the parameter coordinates of the sampling points (set the sampling points), and then discretize the geometric edges in the one-dimensional parameter space according to the size information of the sampling points to obtain the one-dimensional parameter coordinates of the discrete points.

[0031] Then, through the geometric modeling kernel, based on the one-dimensional parameter coordinates of the discrete points and the information of the geometric edges, the three-dimensional real space coordinates of the discrete points are obtained through the ACIS geometric kernel.

[0032] After all geometric edges are discretized, a one-dimensional grid is generated according to the three-dimensional real space coordinates of the discrete points of all geometric edges, so as to obtain the connection relationship between the discrete points of all geometric edges and obtain a one-dimensional discrete grid.

[0033] C. According to step A, the geometric faces, geometric edges, geometric vertices and their topological relationships are obtained, and combined with the one-dimensional discrete grid obtained in step B, the discrete points of the geometric edges contained in a single geometric face are combined into the boundary discrete points of the geometric face, as well as the connection relationship between the boundary discrete points.

[0034] D. Combine the parameter domain information of the current geometric surface, construct a parameter plane, and map the boundary discrete points obtained in step C to the parameter plane to obtain the boundary discrete points and mapping relationship on the parameter plane of the current geometric surface.

[0035] Furthermore, according to the parameter domain information of a single geometric surface, the parameter range of the parameter domain of the geometric surface is obtained through the ACIS geometric kernel, and the parameter plane is constructed. Then, according to the boundary discrete points and geometric surface information of the single geometric surface obtained in step C, the boundary discrete points of the single geometric surface are mapped to the parameter plane through the ACIS geometric kernel, and at the same time, it is recorded which boundary discrete points on the parameter plane are mapped from, and the boundary discrete points on the parameter plane of the single geometric surface and the mapping relationship are obtained.

[0036] E. Based on the boundary discrete points on the parameter plane of the current geometric surface obtained in step D, the constrained Delaunay method is used to construct the initial triangulated mesh of the current geometric surface.

[0037] Furthermore, a super triangle containing all the boundary discrete points on the parameter plane of a single geometric face is constructed based on the parameter plane constructed in step D. The super triangle is used as the initial triangulation, and the boundary discrete points on the parameter plane of a single geometric face are inserted one by one using the Bowyer-Watson incremental interpolation algorithm. Then, the boundary is restored based on the connection relationship between the discrete points obtained in step B to obtain a triangulated mesh containing external units.

[0038] Based on the triangulated mesh containing external cells, search for a triangle containing the vertices of a super triangle, and set the attributes of the triangle to invalid. Using this triangle as the starting point, set the attributes of the surrounding triangles according to the triangle adjacency relationship: if the two vertices of the common edge of the two triangles are both boundary discrete points on the parameter plane and they are connected, the attributes are reversed; otherwise, they are the same. After setting the valid attributes of all triangles in the triangulated mesh containing external cells, delete the triangles with invalid attributes to obtain the initial triangulated mesh of a single geometric face.

[0039] F. Based on the initial triangulated mesh of the current geometric surface obtained in step E, traverse the initial triangulated mesh, generate and insert internal points, and update the initial triangulated mesh to obtain a triangulated mesh of the current geometric surface that meets the mesh discrete size requirements.

[0040] Furthermore, according to the initial triangulated mesh of a single geometric face obtained in step E, the triangles in the initial triangulated mesh are traversed to determine whether the current triangle meets the requirements of the mesh discrete size. If not, the parameter coordinates of the point P to be inserted are calculated according to the parameter coordinates of the three vertices of the current triangle and the Riemann metric of the three vertices:

[0041] (P u ,P v )(2)

[0042] P u =(size 1u ×P1u +size 2u ×P 2u +size 3u ×P 3u ) / (size 1u +size 2u +size 3u ) (3)

[0043] P v =(size 1v ×P 1v +size 2v ×P 2v +size 3v ×P 3v ) / (size 1v +size 2v +size 3v ) (4)

[0044] Where P u is the u-direction coordinate of the insertion point P, where P v is the v direction coordinate of the insertion point P, P 1u ,P 2u ,P 3u , are the u-direction coordinates of the three vertices, P 1v ,P 2v ,P 3v , respectively, the v-direction coordinates of the three vertices, size 1u size 2u ,size 3u The discrete size of the mesh in the u direction of the three vertices of the current triangle, size 1v ,size 2v ,size 3v They are the discrete sizes of the mesh in the v direction of the three vertices of the current triangle.

[0045] According to the combined Delaunay criterion for parametric planes:

[0046]

[0047] where α p is the Delaunay metric of the insertion point, α vi The three vertices v of the current triangle 1 ,v 2 ,v 3 The Delaunay metric of .

[0048] Taking the current triangle as the base unit and combining the adjacency relationship of the triangle, search for all triangles containing the insertion point, form a cavity and insert the point to be inserted, and generate a new triangle; the properties of the destroyed triangle are set to invalid, and the current triangulated mesh and the adjacency relationship of the internal triangles are updated.

[0049] The updated new triangles are traversed to determine whether they meet the requirements of the mesh discrete size. If not, the internal points are generated and inserted until the current triangulated mesh is traversed and meets the requirements of the mesh discrete size, and all triangles with invalid attributes are deleted.

[0050] In the above process, after the traversal is completed, it can be ensured that all triangles meet the mesh discrete size requirements. Therefore, the triangulated mesh at this time is the triangulated mesh of a single geometric face that meets the mesh discrete size requirements.

[0051] G. Based on the triangular mesh of the single geometric surface finally generated in step F, the gradient descent method is used to optimize the mesh quality to obtain the optimized triangular mesh of the single geometric surface.

[0052] Furthermore, according to the triangular mesh of a single geometric face generated in step F, the square of the difference between the actual mesh side length and the ideal mesh side length required by the mesh discrete size is used as the energy function:

[0053]

[0054] Where E is the energy function, N is the total number of edges of the triangulated mesh of a single geometric face generated in step F, and L i is the length of the ith side, L i0 is the ideal mesh edge length required by the mesh discretization size of the i-th edge.

[0055] The gradient of the energy function to the actual mesh edge length is calculated, and the mesh points except the discrete points on the boundary are moved in the gradient direction until the energy function meets the set convergence conditions, and the optimized triangular mesh of a single geometric surface is obtained.

[0056] H. Repeat steps C to G until all individual geometric faces in the geometric face list have been traversed, and obtain the triangular meshes of all individual geometric faces in the geometric face list.

[0057] I. Based on the topological relationship obtained in step A, the mapping relationship in step D and the triangular mesh obtained in step H, the triangular meshes of all individual geometric faces are de-mapped from the parameter plane back to the three-dimensional real space to obtain the surface triangular mesh of the target structure's outline.

[0058] Based on the topological relationship obtained in step A and the triangular mesh obtained in step H, the internal vertex parameter coordinates of the triangular mesh of a single geometric face generated on the parameter plane are mapped into three-dimensional real space coordinates through the ACIS geometry kernel. The boundary discrete points of the triangular mesh are inversely mapped into three-dimensional real space coordinates using the mapping relationship in step D to obtain the triangular mesh of the aircraft contour surface.

[0059] Figure 3 The time consumption comparison of generating the same number of meshes between this embodiment and the comparative example is shown, and the results show that the present invention can greatly improve the efficiency of mesh generation.

[0060] It can be seen from the above embodiments and comparative examples that the present invention generates insertion points one by one, uses the triangles generated by the insertion points as base units, avoids searching for base units, and traverses the triangulated mesh of the current geometric surface multiple times, thereby ensuring that the mesh meets the size requirements and the quality of the mesh, and at the same time, improves the efficiency of Delaunay surface triangulated mesh generation. The present invention provides a basis for the high-precision algorithm engineering application of computational fluid dynamics and computational electromagnetics in the fields of automobile manufacturing, civil engineering, environmental engineering, shipbuilding industry, and aviation industry, and helps the explanation, understanding of theory, experiment, and design of related industries.

Claims

1. An efficient Delaunay surface triangular mesh generation method, characterized in that: The following steps are involved: A. Carry out 3D solid modeling of the target structure and add it to the model list. Obtain the geometric face list, geometric edge list, geometric vertex list and the topological relationship between them of the target structure's outline through the geometric modeling kernel; B. According to the size requirement of mesh discretization, all geometric edges in the geometric edge list obtained in step A are discretized, and a one-dimensional discrete mesh of the target model is generated according to the discretization information; C. According to step A, the geometric faces, geometric edges, geometric vertices and their topological relationships are obtained, and combined with the one-dimensional discrete grid obtained in step B, the discrete points of the geometric edges contained in a single geometric face are combined into the boundary discrete points of the geometric face, and the connection relationship between the boundary discrete points; D. Combine the parameter domain information of the current geometric surface, construct a parameter plane, and map the boundary discrete points obtained in step C to the parameter plane to obtain the boundary discrete points and mapping relationship on the parameter plane of the current geometric surface; E. Based on the boundary discrete points on the parameter plane of the current geometric surface obtained in step D, an incremental interpolation algorithm is used to insert the boundary points and perform boundary recovery to construct an initial triangulated mesh of the current geometric surface; F. Based on the initial triangulated mesh of the current geometric surface obtained in step E, traverse the initial triangulated mesh, generate and insert internal points, and update the initial triangulated mesh to obtain a triangulated mesh of the current geometric surface that meets the mesh discrete size requirements; G. Based on the triangular mesh of the single geometric surface finally generated in step F, perform mesh quality optimization to obtain an optimized triangular mesh of the single geometric surface; H. Repeat steps C to G until all individual geometric faces in the geometric face list have been traversed, and obtain triangular meshes of all individual geometric faces in the geometric face list; I. Based on the topological relationship obtained in step A, the mapping relationship in step D and the triangular mesh obtained in step H, the triangular meshes of all individual geometric faces are reversely mapped from the parameter plane back to the three-dimensional real space to obtain the surface triangular mesh of the target structure outline.

2. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: The discretization of the geometric edges in step B is specifically as follows: for each geometric edge, based on the sampling size, a numerical integration algorithm is used to calculate the arc length and the sampling distance is corrected to obtain the distance between the sampling point and the starting point of the curve: where s i is the distance from the i-th sampling point to the starting point of the curve, u i is the parameter coordinate of the i-th sampling point, r(t) is the curve equation, m is the total number of sampling points, and l is the arc length of the curve; Solve the integral of formula (1) to obtain the parameter coordinates of the sampling points, and then discretize the geometric edges in the one-dimensional parameter space according to the size information of the sampling points to obtain the one-dimensional parameter coordinates of the discrete points; Then, through the geometric modeling kernel, based on the one-dimensional parameter coordinates of the discrete points and the information of the geometric edges, the three-dimensional real space coordinates of the discrete points are obtained through the ACIS geometric kernel; After all geometric edges are discretized, a one-dimensional grid is generated according to the three-dimensional real space coordinates of the discrete points of all geometric edges, so as to obtain the connection relationship between the discrete points of all geometric edges and obtain a one-dimensional discrete grid.

3. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: The step D is specifically as follows: According to the parameter domain information of a single geometric surface, the parameter range of the parameter domain of the geometric surface is obtained through the ACIS geometric kernel, and a parameter plane is constructed; then, according to the boundary discrete points of the single geometric surface obtained in step C and the geometric surface information, the boundary discrete points are mapped to the parameter plane through the ACIS geometric kernel, and at the same time, it is recorded which boundary discrete points on the parameter plane are mapped from, thereby obtaining the boundary discrete points on the parameter plane of the single geometric surface and the mapping relationship.

4. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: The step E uses the constrained Delaunay method to insert boundary points.

5. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: The step E is specifically as follows: According to the parameter plane constructed in step D, a super triangle containing all the boundary discrete points on the parameter plane of a single geometric face is constructed; using the super triangle as the initial triangulation, the boundary discrete points on the parameter plane of the single geometric face are inserted one by one using the Bowyer-Watson incremental interpolation algorithm; then, the boundary is restored according to the connection relationship between the discrete points obtained in step B, and a triangulated mesh containing external units is obtained; Based on the triangulated mesh containing external cells, search for a triangle containing super-triangle vertices, and set the attributes of the triangle to invalid; and use this triangle as the starting point to set the attributes of the surrounding triangles according to the triangle adjacency relationship: if the two vertices of the common edge of the two triangles are both boundary discrete points on the parameter plane and they are connected, the attributes are reversed; otherwise, the attributes are the same; after setting the valid attributes of all triangles in the triangulated mesh containing external cells, delete the triangles with invalid attributes to obtain the initial triangulated mesh of a single geometric surface.

6. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: The step F is specifically as follows: According to the initial triangulated mesh of a single geometric face obtained in step E, traverse the triangles in the initial triangulated mesh to determine whether the current triangle meets the requirements of the mesh discrete size: if not, calculate the parameter coordinates of the point P to be inserted based on the parameter coordinates of the three vertices of the current triangle and the Riemann metric of the three vertices: (P u ,P v )(2) P u =(size 1u ×P 1u +size 2u ×P 2u +size 3u ×P 3u ) / (size 1u +size 2u +size 3u ) (3) P v =(size 1v ×P 1v +size 2v ×P 2v +size 3v ×P 3v ) / (size 1v +size 2v +size 3v ) (4) Where P u is the u-direction coordinate of the insertion point P, where P v is the v direction coordinate of the insertion point P, P 1u ,P 2u ,P 3u , are the u-direction coordinates of the three vertices, P 1v ,P 2v ,P 3v , respectively, the v-direction coordinates of the three vertices, size 1u size 2u ,size 3u The discrete size of the mesh in the u direction of the three vertices of the current triangle, size 1v ,size 2v ,size 3v They are the discrete mesh sizes in the v direction of the three vertices of the current triangle respectively; According to the combined Delaunay criterion for parametric planes: where α p is the Delaunay metric of the insertion point, Delaunay metric of the three vertices v1, v2, and v3 of the current triangle; Taking the current triangle as the base unit and combining the adjacency relationship of the triangle, search for all triangles containing the insertion point, form a cavity and insert the point to be inserted, and generate a new triangle; the destroyed triangle has its attributes set to invalid, and the current triangulated mesh and the adjacency relationship of the internal triangles are updated; The updated new triangles are traversed to determine whether they meet the requirements of the mesh discrete size. If not, the internal points are generated and inserted until the current triangulated mesh is traversed and meets the requirements of the mesh discrete size, and all triangles with invalid attributes are deleted.

7. The efficient Delaunay surface triangular mesh generation method according to claim 1, characterized in that: Step G uses the gradient descent method to optimize the grid quality: According to the triangular mesh of a single geometric face generated in step F, the square of the difference between the actual mesh edge length and the ideal mesh edge length required by the mesh discrete size is used as the energy function: Where E is the energy function, N is the total number of edges of the triangulated mesh of a single geometric face generated in step F, and L i is the length of the ith side, L i0 is the ideal mesh edge length required by the mesh discretization size of the i-th edge; The gradient of the energy function to the actual mesh edge length is calculated, and the mesh points except the discrete points on the boundary are moved in the gradient direction until the energy function meets the set convergence conditions, and the optimized triangular mesh of a single geometric surface is obtained.

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