Full-hexahedron high-order curved grid generation method, system and device and medium

Abstract

The invention discloses a full-hexahedron high-order curved grid generation method, system and device and a medium, and relates to the technical field of computational fluid mechanics. The method comprises the following steps: carrying out unit subdivision processing on an initial straight grid to generate a full-hexahedron straight grid; the unit subdivision processing comprises the step of generating a plurality of hexahedron units through one or more times of subdivision aiming at mixed units contained in the initial straight grid; grid parallel order raising processing is carried out on the full-hexahedron straight grid based on a multi-thread parallel mode, and then the full-hexahedron straight grid is subjected to order raising to form a high-order curved grid; the grid parallel order-increasing processing comprises high-order point insertion, object plane point projection and spatial point deformation. According to the invention, through unit subdivision processing and grid parallel order raising processing, the high-order grid generation efficiency is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of computational fluid dynamics, and in particular to a method, system, device, and medium for generating fully hexahedral high-order curved meshes. Background Technology

[0002] With the increasing maturity of computational fluid dynamics (CFD) and the rapid development of computer technology, CFD is playing an increasingly prominent role in the aerodynamic performance analysis and optimization design of aircraft, as well as the analysis of complex flow mechanisms. Currently, most CFD software is based on second-order precision calculation schemes. Although these schemes have achieved great success in numerical simulations of complex flows with complex shapes, they suffer from significant numerical dissipation and dispersion. Therefore, for some very complex flow phenomena, second-order precision schemes still struggle to provide detailed flow field structures. This is especially true for fields such as computational aeroacoustics (CAA), large eddy simulation (LES) of turbulence, and direct numerical simulation (DNS), which require higher-order precision schemes with lower dissipation and dispersion.

[0003] Many challenges remain in the research of high-precision computational methods, and the handling of surface boundaries (especially curved surface boundaries) is one of the key issues, once considered one of the four most important problems in geometry and meshing. High-precision schemes are generally very sensitive to the methods used to handle curved boundaries. Inappropriate handling of curved boundaries will lead to poor convergence of high-precision schemes, thus negating the advantages of high-precision methods.

[0004] In order to fully leverage the computational advantages of high-precision formats and obtain stable numerical calculation results with low dissipation and dispersion, the generation of high-order curved meshes is a problem that must be solved for high-precision formats to be applied in engineering. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method, system, device, and medium for generating fully hexahedral high-order curved meshes. Through element subdivision processing and parallel mesh order-up processing, the efficiency of generating high-order meshes is greatly improved.

[0006] The technical solution adopted in this invention is as follows: A method for generating fully hexahedral high-order curved meshes includes: The initial straight mesh is subjected to element subdivision processing to generate a fully hexahedral straight mesh; the element subdivision processing includes generating a number of hexahedral elements by subdividing the mixed elements contained in the initial straight mesh through one or more subdivisions. The parallel meshing process is based on a multi-threaded parallel approach to perform parallel meshing of the full hexahedral straight mesh, which is then upgraded to a higher-order curved mesh. The parallel meshing upgrade process includes higher-order point insertion, object surface point projection, and spatial point deformation.

[0007] Furthermore, the insertion of higher-order points includes: dividing the full hexahedral straight mesh data into blocks, configuring a thread pool and a node hash table, and inserting higher-order points in parallel using multiple threads based on the node hash table.

[0008] Furthermore, the step of dividing the full hexahedral grid data into blocks, configuring a thread pool and a node hash table, and inserting higher-order points in parallel using multiple threads based on the node hash table includes: The hexahedral grid data is divided into blocks, with each block managed by a thread; at the same time, a node hash table shared by all threads is maintained to establish a one-to-one correspondence between node objects and hashkey values. When inserting a new point in parallel using multiple threads, each thread generates a unique hashkey value based on its three-dimensional coordinates and queries in parallel whether the new point is in the node hash table. If the new node is not in the node hash table, insert the new node's hashkey value and the address of the node object into the node hash table; if it already exists, return the existing node object.

[0009] Furthermore, the object surface point projection includes: projecting the newly inserted object surface points in parallel onto the geometric shape, wherein the newly inserted object surface points include the object surface straight mesh points inserted during the element subdivision process, as well as the newly inserted higher-order points.

[0010] Furthermore, the spatial point deformation includes: RBF interpolation: The displacement of points on the object surface is interpolated to points in space using the radial basis function method, thereby deforming the overall mesh; Influence radius setting: By setting the influence radius, points that are more than the distance from the object surface will not be deformed.

[0011] Furthermore, the spatial point deformation also includes ADT tree-assisted query of local reference points: by using ADT tree-assisted query of multiple points closest to the point to be interpolated, the local reference points of the point to be interpolated are used, thereby transforming a large matrix inversion into multiple small-scale matrix inversions.

[0012] Furthermore, the spatial point deformation is performed in a multi-threaded parallel manner: the spatial points to be deformed within the influence radius are divided into blocks and processed in a multi-threaded parallel manner; each thread performs a local reference point search based on the ADT tree for the spatial points, calculates the inverse matrix of the interpolation coefficient matrix and the weight coefficients of each reference point, and performs RBF interpolation in parallel to obtain the displacement of all spatial points.

[0013] A fully hexahedral high-order curved mesh generation system includes: The element subdivision processing module is configured to perform element subdivision processing on the initial straight mesh to generate a full hexahedral straight mesh; the element subdivision processing includes generating a number of hexahedral elements by subdividing the mixed elements contained in the initial straight mesh through one or more subdivisions. The parallel mesh upgrade processing module is configured to perform parallel mesh upgrade processing on a full hexahedral straight mesh in a multi-threaded parallel manner, thereby upgrading it to a higher-order curved mesh; the parallel mesh upgrade processing includes higher-order point insertion, object surface point projection, and spatial point deformation.

[0014] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method for generating fully hexahedral high-order curved meshes.

[0015] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for generating fully hexahedral high-order curved meshes.

[0016] The beneficial effects of this invention are as follows: This invention generates a fully hexahedral straight mesh by subdividing an initial straight mesh into elements, and then performs parallel mesh-leveling on this hexahedral straight mesh using a multi-threaded parallel approach, thereby elevating it to a higher-order curved mesh, significantly improving the efficiency of high-order mesh generation. Furthermore, the method was tested on two-dimensional and three-dimensional examples, and the results show that the multi-threaded approach greatly improves the efficiency of high-order mesh generation. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method for generating a fully hexahedral high-order curved mesh according to Embodiment 1 of the present invention.

[0018] Figure 2 This is a flowchart of the multi-threaded parallel interpolation process in Embodiment 1 of the present invention.

[0019] Figure 3 This is a flowchart of the multi-threaded parallel projection process in Embodiment 1 of the present invention.

[0020] Figure 4 This is a flowchart of the multi-threaded parallel RBF deformation process in Embodiment 1 of the present invention.

[0021] Figure 5 This is a comparison chart of SD7003 straight mesh, full quadrilateral mesh, and P2 / P3 order mesh.

[0022] Figure 6 This is a comparison diagram of the M6 ​​wing's straight mesh, full hexahedral mesh, and P2 / P3 order mesh.

[0023] Figure 7This is a comparison diagram of the M6 ​​wing leading edge with straight mesh, full hexahedral mesh, and P2 / P3 order mesh. Detailed Implementation

[0024] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0025] Example 1 like Figure 1 As shown, this embodiment provides a method for generating fully hexahedral high-order curved meshes, including: The initial straight mesh is subjected to element subdivision processing to generate a fully hexahedral straight mesh; this element subdivision processing includes generating several hexahedral elements by subdividing the mixed elements contained in the initial straight mesh through one or more subdivisions. The parallel meshing process of the full hexahedral straight mesh is performed using a multi-threaded parallel approach, and then upgraded to a higher-order curved mesh. This parallel meshing upgrade process includes higher-order point insertion, object surface point projection, and spatial point deformation.

[0026] The relevant terms used in this embodiment are explained as follows: (1) LINE_2 / LINE_3: that is, “unit type_number of nodes”, LINE_2 is a line segment with 2 points, and LINE_3 is a line segment with 3 points.

[0027] (2) TRI_3 / TRI_6 / TRI_x: Same as “cell type_number of nodes”, TRI_3 is a triangle with 3 points, TRI_6 is a triangle with 6 points, and TRI_x is a triangle with x nodes.

[0028] (3) QUAD_4 / QUAD_9 / QUAD_x: Same as “Unit type_Number of nodes”, which are quadrilaterals with 4 points, quadrilaterals with 9 points, and quadrilaterals with x nodes, respectively.

[0029] (4) TET_4 / TET_x: Tetrahedral elements with different numbers of nodes.

[0030] (5) PYRA_5 / PYRA_x: Pyramid units with different numbers of nodes.

[0031] (6) PRISM_6 / PRISM_x: Triangular prism elements with different numbers of nodes.

[0032] (7) HEXA_8 / HEXA_x: Hexahedral elements with different numbers of nodes.

[0033] (8) P1 / P2 / P3: First order / second order / third order, referring to the order of the mesh element. P1 is a straight mesh, and P2 and P3 are high-order curved meshes.

[0034] (9)RBF: Radial Basis Function.

[0035] (10) ADT: Alternating Digital Tree.

[0036] (11) OCC: OpenCascade, an open-source geometry toolbox. The OCC API is the geometry toolbox interface.

[0037] (12) Hashtable: Hash table.

[0038] (13) TBB: Threading Building Blocks, a C++ multithreaded parallel programming template library.

[0039] Specifically, the cell partitioning process, the parallel mesh upgrade process, and the test verification method of this embodiment are described below.

[0040] I. Element Subdivision Process In engineering applications, straight meshes typically include different element types, such as two-dimensional triangles and quadrilaterals, and three-dimensional tetrahedrons, pyramids, triangular prisms, and hexahedrons. Various elements can be subdivided once or multiple times to generate multiple hexahedral elements. The node forms of various elements and their subdivided forms are shown in Table 1.

[0041] Table 1 - Types of P1-order elements and their meshing methods in commonly used straight meshes

[0042] It should be noted that the PYRA_5 pyramid element needs to be subdivided twice to be completely subdivided into hexahedral elements. The first subdivision divides it into 4 tetrahedrons, and then the 4 tetrahedrons are further subdivided into 16 hexahedrons.

[0043] In addition, there are two ways to divide a triangular prism element: one triangular prism can be divided into three hexahedrons, or one triangular prism can be divided into six hexahedrons. Table 1 only shows the way a triangular prism can be divided into six hexahedron elements.

[0044] II. Grid Parallel Upgrade Processing After obtaining a fully hexahedral straight mesh, by performing high-order point insertion, object surface point projection, and spatial point deformation processing on the fully hexahedral straight mesh, the P1-order fully hexahedral straight mesh can be upgraded to P2-order and P3-order high-order curved meshes.

[0045] To improve the efficiency of generating high-order curved meshes, this embodiment employs multi-threading technology to achieve parallelism, such as the C++ standard library. <thread>Examples of parallel threading methods include OpenMP thread parallelism and Intel TBB thread pools. The key to thread parallelism lies in resolving data contention issues. This embodiment employs different methods to address data contention problems for steps such as interpolation, projection, and transformation.

[0046] (1) Insertion of higher-order points In this embodiment, the P1-order hexahedron insertion points generate P2-order HEXA_27 hexahedrons and P3-order HEXA_64 hexahedrons, and their specific node forms are shown in Table 2. The coordinates of the insertion points are the bisection / trisection points of the line segment, the centroid of the quadrilateral face, the trisection points of the quadrilateral face diagonals, the body center of the hexahedron, and other specific locations.

[0047] Table 2 - Specific node forms for P1 order hexahedral element interpolation upgrade.

[0048] To achieve parallelization of the insertion process, this embodiment divides the full hexahedral straight mesh data into blocks, configures a thread pool and a node hash table, and inserts higher-order points in parallel using multiple threads based on the node hash table.

[0049] Preferably, such as Figure 2 As shown, multi-threaded parallel insertion points can be implemented in the following ways: The straight grid data is divided into blocks, each block is managed by a thread, and a node hash table shared by all threads is maintained to establish a one-to-one correspondence between node objects and hash key values. When inserting a new point in parallel using multiple threads, each thread generates a unique hashkey value based on its three-dimensional coordinates and checks in parallel whether the new point is in the node_hashtable. If the new point is not in the node_hashtable, the hashkey value of the new point and the address of the node object are inserted into the node_hashtable. If it already exists, the existing node object is returned.

[0050] Since it involves parallel insertion and querying, a concurrent hash table is required. Queries are performed in parallel, and exclusive locks are used during insertion to avoid data contention, ultimately achieving multi-threaded parallelism for insertion.

[0051] (2) Projection of object surface points Since the position of the insertion point is determined based on the division points, it is usually not on the geometric shape. To ensure that the higher-order mesh accurately reflects the geometric shape, it is necessary to move the newly inserted point onto the geometry.

[0052] Conventional methods for generating high-order curved meshes only require projecting high-order points. However, the method in this embodiment does not guarantee the geometric shape when generating hexahedrons from straight meshes. Therefore, in addition to high-order points, the straight mesh points newly inserted during element subdivision also need to be projected. Since the operations between points in the projection process are relatively independent, data partitioning and multi-threaded parallelism can be easily performed without considering data contention between threads.

[0053] Preferably, the multi-threaded parallel projection process in this embodiment is as follows: Figure 3 As shown.

[0054] (3) Spatial point deformation processing After the object surface point is projected, if the position of the spatial point remains unchanged, if the projection displacement is too large, small-sized units near the object surface are very likely to generate negative volumes. Therefore, the position of the spatial point needs to be adjusted accordingly.

[0055] This embodiment uses the RBF interpolation method to interpolate the displacement of the object surface points to spatial points, thereby deforming the overall mesh. To improve deformation efficiency, techniques such as setting the influence radius, using ADT to assist in querying local reference points, and multi-threaded parallel processing are employed, which are described in detail below.

[0056] The principle of RBF interpolation is shown in the following equation:

[0057] in, Let be the displacement of the point to be determined. Let be the position vector of the point to be determined. The position vector of the reference point. is the Euclidean distance between the reference point and the point to be determined; N is the number of reference points. The weight coefficient for the i-th reference point; For RBF basis functions, this embodiment uses Wendland's C2 basis functions, as shown in the following equation:

[0058] in, The distance is dimensionless.

[0059] Setting the radius of influence: In this embodiment ,in The point whose distance from the object surface exceeds the radius of influence. No deformation occurs. By setting the influence radius, the number of spatial points requiring deformation can be significantly reduced.

[0060] For the case with N reference points, the interpolation coefficient matrix is:

[0061] ADT-assisted query for local reference points: During RBF interpolation, the weight coefficient matrix of each reference point... It is obtained based on the displacement of the reference point satisfying the above RBF interpolation principle formula. During the solution process... The solution needs to be found in the middle. The inverse matrix of a matrix can be extremely inefficient if the number of reference points is too large. Therefore, this embodiment uses an ADT tree to assist in querying multiple points (e.g., 20 points) closest to the point to be interpolated as local reference points for the point to be interpolated, transforming a large matrix inversion into multiple small matrix inversions, which greatly saves memory and computation.

[0062] Multithreaded parallelism: such as Figure 4 As shown, this embodiment divides the spatial points to be deformed within the radius of influence into blocks and uses multi-threaded parallel processing. Each thread performs local reference point search based on ADT for the spatial points, calculates the inverse matrix of the interpolation coefficient matrix and the weight coefficients of each reference point, performs RBF interpolation in parallel, and finally obtains the displacement of all spatial points.

[0063] III. Testing and Verification This embodiment tests the method on two-dimensional and three-dimensional examples. The two-dimensional example uses an SD7003 airfoil hybrid mesh as the initial mesh, and the three-dimensional example uses an M6 airfoil hybrid mesh as the initial mesh. After meshing and order upgrading, a fully hexahedral high-order mesh (a two-dimensional fully quadrilateral high-order mesh) is generated. The test hardware is: Intel(R) Xeon(R) Gold 6254 CPU @3.10GHz, 18 cores, 36 threads, 1TB of memory.

[0064] For example, mesh pairs Figures 5-7 As shown in Table 3, the detailed information of the initial mesh and higher-order curved meshes is presented. Test results show that this invention can correctly generate fully hexahedral higher-order curved meshes with hundreds of thousands of elements.

[0065] in, Figure 5 A comparison of SD7003 straight mesh, full quadrilateral mesh, P2 order, and P3 order mesh is given. Figure 5 (a) is a P1 order hybrid straight mesh. Figure 5 (b) is a P1 order full quadrilateral straight mesh. Figure 5 (c) is a P2 order fully quadrilateral high-order curved mesh. Figure 5 (d) is a P3 order full quadrilateral high-order curved mesh.

[0066] Figure 6 A comparison of straight mesh, full hexahedral mesh, P2 order, and P3 order meshes for the M6 ​​wing is presented. Figure 6 (a) is a P1 order hybrid straight mesh. Figure 6 (b) is a P1 order fully hexahedral straight mesh. Figure 6 (c) is a P2 order fully hexahedral high-order curved mesh. Figure 6 (d) is a P3 order fully hexahedral high-order curved mesh.

[0067] Figure 7 A comparison of local straight mesh, full hexahedral mesh, P2 order, and P3 order meshes is presented for the leading edge of the M6 ​​wing. Figure 7 (a) is a P1 order hybrid straight mesh. Figure 7 (b) is a P1 order fully hexahedral straight mesh. Figure 7 (c) is a P2 order fully hexahedral high-order curved mesh. Figure 7 (d) is a P3 order fully hexahedral high-order curved mesh.

[0068] Table 3 - Comparison of Initial Mesh and Higher-Order Mesh

[0069] Table 4 - Parallel Processing Time Statistics

[0070] Table 4 shows the time consumption test for generating the P2 order curved mesh of the M6 ​​wing. When using 12 threads in parallel, the time consumption is 138.4 seconds, which is only 15% of that of single-threaded generation, achieving a speedup of 6.5 times. This demonstrates that using multi-threading significantly improves the efficiency of high-order mesh generation.

[0071] Example 2 This embodiment is based on embodiment 1: This embodiment provides a fully hexahedral high-order curved mesh generation system, including: The element meshing module is configured to perform element meshing on the initial straight mesh to generate a full hexahedral straight mesh; the element meshing process includes generating several hexahedral elements by one or more meshing operations on the mixed elements contained in the initial straight mesh. The parallel mesh upgrade processing module is configured to perform parallel mesh upgrade processing on a full hexahedral straight mesh in a multi-threaded parallel manner, thereby upgrading it to a higher-order curved mesh; the parallel mesh upgrade processing method includes higher-order point insertion, object surface point projection, and spatial point deformation.

[0072] Example 3 This embodiment is based on embodiment 1: This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method for generating fully hexahedral high-order curved meshes of Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form.

[0073] Example 4 This embodiment is based on embodiment 1: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for generating fully hexahedral high-order curved meshes of Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc. It should be noted that the content contained in the storage medium can be appropriately added to or subtracted according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the storage medium does not include electrical carrier signals and telecommunication signals.

[0074] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.< / thread>

Claims

1. A method for generating a fully hexahedral high-order curved mesh, characterized in that, include: The initial straight mesh is subjected to element subdivision processing to generate a fully hexahedral straight mesh; the element subdivision processing includes generating a number of hexahedral elements by subdividing the mixed elements contained in the initial straight mesh through one or more subdivisions. The parallel meshing process is based on a multi-threaded parallel approach to perform parallel meshing of the full hexahedral straight mesh, which is then upgraded to a higher-order curved mesh. The parallel meshing upgrade process includes higher-order point insertion, object surface point projection, and spatial point deformation.

2. The method for generating a fully hexahedral high-order curved mesh according to claim 1, characterized in that, The insertion of higher-order points includes: dividing the full hexahedral straight grid data into blocks, configuring a thread pool and a node hash table, and inserting higher-order points in parallel using multiple threads based on the node hash table.

3. The method for generating a fully hexahedral high-order curved mesh according to claim 2, characterized in that, The process of dividing the full hexahedral straight mesh data into blocks, configuring a thread pool and a node hash table, and inserting higher-order points in parallel using multiple threads based on the node hash table includes: The hexahedral grid data is divided into blocks, with each block managed by a thread; at the same time, a node hash table shared by all threads is maintained to establish a one-to-one correspondence between node objects and hashkey values. When inserting a new point in parallel using multiple threads, each thread generates a unique hashkey value based on its three-dimensional coordinates and queries in parallel whether the new point is in the node hash table. If the new node is not in the node hash table, insert the new node's hashkey value and the address of the node object into the node hash table; if it already exists, return the existing node object.

4. The method for generating a fully hexahedral high-order curved mesh according to claim 1, characterized in that, The object surface point projection includes: projecting newly inserted object surface points in parallel onto the geometric shape, wherein the newly inserted object surface points include object surface straight mesh points inserted during element subdivision processing, as well as newly inserted higher-order points.

5. The method for generating a fully hexahedral high-order curved mesh according to claim 4, characterized in that, The spatial point deformation includes: RBF interpolation: The displacement of points on the object surface is interpolated to points in space using the radial basis function method, thereby deforming the overall mesh; Influence radius setting: By setting the influence radius, points that are more than the distance from the object surface will not be deformed.

6. The method for generating a fully hexahedral high-order curved mesh according to claim 5, characterized in that, The spatial point deformation also includes ADT tree-assisted query of local reference points: by using ADT tree to assist in querying multiple points closest to the point to be interpolated, these points serve as local reference points for the point to be interpolated, thereby transforming a large matrix inversion into multiple small-scale matrix inversions.

7. The method for generating a fully hexahedral high-order curved mesh according to claim 6, characterized in that, The spatial point deformation is performed in a multi-threaded parallel manner: the spatial points to be deformed within the influence radius are divided into blocks and processed in a multi-threaded parallel manner; each thread performs a local reference point search based on the ADT tree for the spatial points, calculates the inverse matrix of the interpolation coefficient matrix and the weight coefficients of each reference point, and performs RBF interpolation in parallel to obtain the displacement of all spatial points.

8. A system for generating fully hexahedral high-order curved meshes, characterized in that, include: The element subdivision processing module is configured to perform element subdivision processing on the initial straight mesh to generate a full hexahedral straight mesh; the element subdivision processing includes generating a number of hexahedral elements by subdividing the mixed elements contained in the initial straight mesh through one or more subdivisions. The parallel mesh upgrade processing module is configured to perform parallel mesh upgrade processing on a full hexahedral straight mesh in a multi-threaded parallel manner, thereby upgrading it to a higher-order curved mesh; the parallel mesh upgrade processing includes higher-order point insertion, object surface point projection, and spatial point deformation.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method for generating a fully hexahedral high-order curved mesh as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for generating a fully hexahedral high-order curved mesh as described in any one of claims 1-7.

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