A topology optimization result geometry reconstruction method for maintaining flow passage performance

Abstract

The application provides a topology optimization result geometry reconstruction method for maintaining flow channel performance, comprising the following steps: obtaining a triangular mesh model to be reconstructed; performing mesh preprocessing to eliminate the problems of inconsistent normal, isolated structure, repeated surface and open boundary; performing surface smoothing processing, performing Laplace smoothing iteration on the triangular mesh model, calculating the current mesh volume after each iteration and comparing the current mesh volume with a target volume, if the current mesh volume is greater than the target volume, the smoothing is continued, if the current mesh volume is less than the target volume, the volume is compensated by moving the vertex normal, until the convergence condition is met, and a triangular mesh model with continuous and smooth surface and controllable volume is obtained; performing re-meshing processing to convert the triangular mesh model into a quadrilateral mesh model; and performing solidification processing to convert the quadrilateral mesh model into a three-dimensional solid model. By introducing the volume-controllable Laplace smoothing mechanism in the geometry reconstruction, the volume shrinkage or expansion problem caused by the conventional smoothing is effectively avoided, and the fluid performance of the flow channel topology optimization result can be maintained while the reconstruction efficiency is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of geometric reconstruction technology in topology optimization post-processing, specifically to a method for geometric reconstruction of topology optimization results while preserving flow channel performance. Background Technology

[0002] With the widespread application of topology optimization methods in fluid machinery, heat exchange structures, and aerospace flow channel design, flow channel topology optimization results obtained from numerical optimization have gradually become an important basis for the design of complex flow channel structures. These topology optimization results usually exist in the form of voxel models or triangular meshes, and are characterized by complex structural morphology and geometric irregularities, making them difficult to directly use for subsequent engineering analysis, manufacturing, or computer-aided design modeling.

[0003] In existing technologies, the topology optimization results for flow channels typically require geometric reconstruction to transform the discrete optimization results into a continuous model with well-defined geometric boundaries and topological relationships. In recent years, researchers have proposed several automated geometric reconstruction methods. For example, in 2024, Professor Jianbin Du's research group at Tsinghua University published a paper titled "AMRTO: Automated CAD model reconstruction of topology optimization result" in *Computer Methods in Applied Mechanics and Engineering*, proposing a general framework for automatically reconstructing CAD models from complex topology optimization results. This framework first performs conventional surface smoothing on the topology optimization results to generate triangular meshes, then introduces Instant-Meshes and generalized motorcycle diagrams for quadrilateralization, and finally generates NURBS representations through improved harmonic mapping and adaptive sampling methods, ultimately obtaining a boundary representation model. In addition, Chinese patent CN117574470B discloses an "intelligent model reconstruction method and device for industrial structures", the technical solution of which includes: generating a triangular mesh model based on the structural optimization results; regrinding the triangular mesh model to obtain a quadrilateral mesh model; performing harmonic mapping and uniform sampling on the quadrilateral mesh model; and using the sampling points as fitting points to perform NURBS surface fitting to obtain a CAD model.

[0004] However, the aforementioned existing technical solutions still generally have the following shortcomings when applied to the geometric reconstruction of flow channel topology optimization results:

[0005] On the one hand, since the channel topology optimization results contain a large number of fine-scale structural features and irregular boundaries, smoothing, simplification, or remodeling operations are often required during the reconstruction process. However, existing methods (including the AMRTO method and CN117574470B) all use conventional smoothing methods in the surface smoothing stage, lacking an effective monitoring and compensation mechanism for the volume of the smoothed model. For the channel structure, the volume (i.e., the channel capacity) directly determines the fluid flow rate and pressure drop characteristics. Even a small deviation in volume can lead to significant changes in the channel cross-sectional shape, local curvature, or connectivity, resulting in deviations in key fluid properties such as flow resistance, pressure drop, or flow distribution, causing a loss of channel performance and making it difficult to ensure that the performance advantages of the optimization results are maintained after reconstruction.

[0006] On the other hand, the existing geometric reconstruction process of flow channel topology optimization results, especially the conventional smoothing and subsequent processing procedures used in the above-mentioned existing methods, has achieved a certain degree of automation. However, when processing flow channel topology optimization results, it often relies on multi-stage processing procedures, including mesh cleaning, surface fitting and solid modeling. Moreover, due to the lack of targeted preprocessing and performance preservation mechanisms, the overall reconstruction cycle is long and there is still room for improvement in efficiency, which makes it difficult to fully meet the needs of rapid iteration and efficient optimization in engineering design.

[0007] Therefore, there is an urgent need for a method that can achieve efficient and automated geometric reconstruction while maintaining the original fluid performance of the channel topology optimization results, in order to solve the problems of easily damaged channel performance and low reconstruction efficiency in the existing technology. Summary of the Invention

[0008] The technical problem to be solved:

[0009] The results of flow channel topology optimization face multiple technical challenges in practical engineering applications. Specifically, these optimization results typically exist in discrete forms such as voxel models or triangular meshes, with complex structures and irregular geometry, making them difficult to directly use for downstream computer-aided design modeling, engineering analysis, or manufacturing. They must be transformed into continuous solid models with clear geometric boundaries and topological relationships through geometric reconstruction. However, existing geometric reconstruction methods, when processing flow channel topology optimization results, generally employ conventional smoothing methods in the surface smoothing stage, lacking effective monitoring and compensation mechanisms for the volume of the smoothed model. This leads to uncontrollable changes in the flow channel volume and cross-sectional shape during reconstruction, resulting in significant deterioration of fluid performance such as increased pressure drop and shifted flow distribution, causing a large loss of the hydraulic performance advantages gained from topology optimization during the reconstruction stage. Furthermore, the overall processing flow of existing methods remains relatively complex, with low reconstruction efficiency, making it difficult to meet the practical needs of rapid iterative optimization in engineering design.

[0010] To address the aforementioned issues, this invention proposes a geometric reconstruction method for topology optimization results that preserves channel performance. By introducing volume-controllable Laplace smoothing during the geometric reconstruction process, and combining it with systematic mesh preprocessing, quadrilateral remeshing, and NURBS solid conversion, a fully automated channel geometric reconstruction process is constructed. This aims to significantly improve reconstruction efficiency while effectively preserving the flow characteristics and hydraulic performance reflected in the topology optimization results.

[0011] The technical solution of this invention is as follows:

[0012] A method for geometric reconstruction of topology optimization results while preserving flow channel performance includes the following steps:

[0013] Step 1: Based on the flow channel topology optimization calculation results, obtain the triangular mesh model to be reconstructed. The triangular mesh model is used to describe the geometric boundary of the flow channel after topology optimization.

[0014] Step 2: Perform mesh preprocessing on the triangular mesh model to eliminate problems such as inconsistent normals, isolated structures, repeated faces, and open boundaries in the mesh, and obtain a topologically consistent and geometrically valid triangular mesh model;

[0015] Step 3: Perform surface smoothing on the topologically consistent and geometrically valid triangular mesh model obtained in Step 2. The surface smoothing process includes:

[0016] The triangular mesh model is subjected to Laplace smoothing iteration. After each iteration, the volume of the current mesh model is calculated, and the calculated volume is compared with the preset target volume.

[0017] If the current mesh model volume is larger than the target volume, then continue with the Laplace smoothing iteration;

[0018] If the current mesh model's volume is smaller than the target volume, then volume compensation is performed by moving the normals of the mesh model's vertices.

[0019] Repeat the above process until the deviation between the current mesh model volume and the target volume is less than the preset convergence condition, then stop the iteration to obtain a triangular mesh model with a continuous, smooth surface and controllable volume.

[0020] Step 4: The triangular mesh model with a continuous, smooth surface and controllable volume obtained in Step 3 is remeshed to convert the triangular mesh model into a topologically regular and parametrically friendly quadrilateral mesh model, so as to improve its applicability in the subsequent geometric reconstruction process.

[0021] Step 5: Perform solidification processing on the quadrilateral mesh model that has completed the remeshing process, transforming it into a topologically closed and geometrically valid three-dimensional solid model for subsequent fluid analysis or engineering applications.

[0022] A further preferred embodiment, the mesh preprocessing in step 2 specifically includes:

[0023] The triangular mesh model is subjected to mesh surface normal consistency detection. When the normal directions of adjacent patches are found to be inconsistent, the normal directions are corrected for consistency based on the adjacency relationship of the patches. The patches with flipped normals are reoriented to obtain a triangular mesh model with consistent mesh surface normals.

[0024] A connectivity analysis is performed on the triangular mesh model that has undergone normal consistency processing. Isolated mesh components are identified and deleted, and only the connected regions containing the maximum number of faces are retained to obtain the main connected triangular mesh model.

[0025] The main connected triangular mesh model is identified for repeated triangular face definitions. When repeated faces exist, they are deleted to obtain a triangular mesh model without redundant structure.

[0026] The watertightness of the triangular mesh model without redundancy is tested. When an open boundary is detected, void identification and boundary stitching are performed on the open boundary to obtain a topologically closed watertight triangular mesh model.

[0027] In a further preferred embodiment, the target volume in step 3 is determined based on the initial volume of the triangular mesh model, and the target volume is the product of the initial volume and a preset scaling factor.

[0028] A further preferred embodiment, step 3, includes the Laplace smoothing iteration:

[0029] Constructing the first based on grid topology The neighborhood set of each vertex Calculate the first Average neighborhood position of each vertex:

[0030]

[0031] in For the first Spatial coordinates of the vertices of the neighborhood;

[0032] The first is determined based on the average neighborhood position. The vertex of the first vertex Second-smooth displacement vector:

[0033]

[0034] And in accordance with the first The smoothing step size during the next smoothing iteration For the Update the position of each vertex:

[0035]

[0036] in For the first The vertex at the th The average neighborhood position during the next smoothing iteration For the first The vertex at the th Spatial coordinates during the next smoothing iteration. No. The vertex at the th Spatial coordinates during the next smoothing iteration.

[0037] In a further preferred embodiment, step 3, calculating the volume of the current mesh model, includes:

[0038] Using the origin of the world coordinate system as a reference point, calculate the current mesh volume according to the following formula:

[0039]

[0040] in For the first A triangular facet The coordinate vectors of the three vertices relative to the origin. For the first After the next smoothing iteration, the set of all triangular faces of the current triangular mesh model.

[0041] A further preferred embodiment, step 3, which involves volume compensation through normal movement of the vertices of the mesh model, includes:

[0042] Calculate the first based on the current mesh model. The unit normal vector of each vertex:

[0043]

[0044] in Indicates that it contains vertices The A triangular facet, Indicates the first The unit normal vector of a triangular facet;

[0045] The normal correction coefficient is determined according to the following formula. :

[0046]

[0047] in This represents the total number of vertices in the current mesh model. For the target volume, For the first The mesh volume after the second smoothing iteration is then corrected by volume compensation at the vertex positions:

[0048] .

[0049] A further preferred embodiment is that the preset convergence condition in step 3 is:

[0050]

[0051] in This is the current volume deviation. Let this be the initial volume of the triangular mesh model. This is a preset volume error threshold.

[0052] A further preferred embodiment is the smoothing step size mentioned in step 3. During the iteration process, decay control is performed according to the following formula:

[0053]

[0054] in This is the attenuation coefficient.

[0055] A further preferred embodiment, the remeshing process in step 4 specifically includes:

[0056] The triangular mesh model is converted into an intermediate mesh model that can be recognized by the quadrilateral remeshization algorithm;

[0057] A quadrilateral mesh reconstruction operation is performed based on the intermediate mesh model, and the overall resolution of the reconstructed quadrilateral mesh model is controlled by setting the number of target patches;

[0058] The generated quadrilateral mesh model is smoothed to obtain a topologically regular and parameter-friendly quadrilateral mesh model.

[0059] In a further preferred embodiment, in the quadrilateral mesh reconstruction operation described in step 4, the number of target facets is set. This will increase the number of quadrilateral facets generated in the end. satisfy

[0060]

[0061] in This is the allowable error threshold.

[0062] A further preferred embodiment, the materialization process in step 5 includes:

[0063] Import the quadrilateral mesh model into the geometric modeling environment;

[0064] Based on the topological connection relationship between quadrilateral mesh patches, each quadrilateral patch is mapped to a corresponding parametric surface, generating a geometric model composed of continuous splicing of parametric surfaces;

[0065] Apply G1 continuity constraints to the common boundary of adjacent parametric surfaces;

[0066] The parametric surface is stitched and closed to generate a three-dimensional solid model.

[0067] Beneficial effects

[0068] Compared with existing technologies, the geometric reconstruction method for topology optimization results that preserves flow channel performance proposed in this invention has technical advantages, mainly in the following aspects:

[0069] 1. Effectively maintains the hydraulic performance of the flow channel:

[0070] This invention introduces volume-controllable Laplace smoothing during geometric reconstruction. The volume of the smoothed mesh model is iteratively calculated and compared with the target volume. When the volume is greater than the target volume, Laplace smoothing continues; when the volume is less than the target volume, the missing volume is compensated by moving the normals of the mesh model vertices, forming a complete closed-loop control of calculation-comparison-recovery. Compared to conventional surface smoothing methods such as AMRTO, this control method effectively avoids volume shrinkage or expansion caused by surface smoothing, thus preventing fluid performance degradation caused by changes in the cross-sectional shape and volume of the flow channel. Furthermore, using the mesh model obtained from topology optimization as the basis for geometric reconstruction effectively preserves the key morphology and hydraulic characteristics of the flow channel, ensuring that the reconstructed model maximizes the inheritance of the optimization effect of topology optimization and maintains the hydraulic performance intended for the original flow channel design.

[0071] 2. Achieve automated and efficient refactoring:

[0072] The geometric reconstruction process of this invention is fully automated, requiring no manual intervention. By automatically executing steps such as mesh preprocessing, volume-controlled surface smoothing, quadrilateral remeshing, and mesh-to-solid model conversion, it significantly reduces errors and uncertainties introduced by human operation, improves reconstruction efficiency and model consistency, thereby ensuring the reliability and repeatability of the reconstruction process. Compared to existing reconstruction processes that rely on manual intervention or multi-stage complex operations, this invention can significantly shorten the reconstruction cycle, increase design iteration speed, and enable engineering designs to quickly obtain usable flow channel models, thus meeting the demand for efficient and rapid modeling in complex flow channel optimization design.

[0073] 3. It has the dual advantages of reconfiguration efficiency and flow channel performance:

[0074] This invention comprehensively addresses issues of normal consistency, connectivity, redundant structures, and watertightness during the mesh preprocessing stage, providing a reliable geometric foundation for subsequent volume-controllable smoothing processing and achieving a synergistic effect between preprocessing and smoothing. Comparative data in the embodiments show that, compared to models obtained using existing methods, the model obtained using the method of this invention exhibits a 21.3%–47.6% reduction in channel pressure drop and a 7–16 times improvement in geometric reconstruction efficiency. It outperforms existing geometric reconstruction methods in both reconstruction efficiency and channel performance, demonstrating significant engineering application value.

[0075] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0076] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0077] Figure 1 This is a flowchart of a topology optimization geometry reconstruction method for maintaining flow channel performance provided by the present invention.

[0078] Figure 2 (a) is the design domain before the flow channel topology optimization in this invention: the fluid has one inlet and one outlet, flowing into the design domain from the arrow pointing to the flow channel and flowing out of the flow channel from the arrow leaving the flow channel.

[0079] Figure 2 (b) is a schematic diagram of the flow channel structure after density filtering based on the flow channel topology optimization density cloud map in this invention.

[0080] Figure 3 This is a schematic diagram of the triangular mesh model obtained based on the flow channel topology optimization results in this invention and its mesh preprocessing.

[0081] Figure 4 This is a schematic diagram of a triangular mesh model with controllable volume and continuous smooth surface obtained after smoothing the triangular mesh model based on the Laplace smoothing method in this invention.

[0082] Figure 5 This is a schematic diagram of the quadrilateral mesh model obtained after mesh re-division based on the smooth triangular mesh model in this invention.

[0083] Figure 6 This is a schematic diagram of the present invention performing NURBS transformation on the remeshized mesh model in Embodiment 1 to obtain a topologically closed and geometrically valid solid model.

[0084] Figure 7(a) is a schematic diagram of a three-dimensional model obtained by geometrically reconstructing the flow channel topology optimization results of Example 1 using existing geometric reconstruction methods;

[0085] Figure 7 (b) is a schematic diagram of the three-dimensional model obtained by geometrically reconstructing the flow channel topology optimization results of Example 1 using the existing geometric reconstruction method 2;

[0086] Figure 8 This is a schematic diagram of the present invention performing NURBS transformation on the remeshized mesh model in Embodiment 2 to obtain a topologically closed and geometrically valid solid model.

[0087] Figure 9 (a) is a schematic diagram of a three-dimensional model obtained by geometrically reconstructing the flow channel topology optimization results of Example 2 using existing geometric reconstruction methods;

[0088] Figure 9 (b) is a schematic diagram of the three-dimensional model obtained by geometrically reconstructing the flow channel topology optimization results of Example 2 using the existing geometric reconstruction method 2. Detailed Implementation

[0089] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0090] This invention provides a geometric reconstruction method for topology optimization results while maintaining flow channel performance. It employs volume-controllable Laplacian smoothing to smooth the mesh model, directly reconstructing the geometric results of the flow channel topology optimization. This solves the problem of balancing reconstruction efficiency and flow channel performance in flow channel topology optimization, achieving efficient and consistent geometric reconstruction of flow channel topology optimization results. Compared with existing flow channel topology optimization methods, the proposed method effectively ensures topological consistency between the reconstructed model and the original model, improving reconstruction efficiency while reducing geometric deviations. The overall process is fully automated, robust, feasible, and computationally efficient.

[0091] Example 1:

[0092] Step 1: Based on the flow channel topology optimization calculation results, obtain the triangular mesh model to be reconstructed. The triangular mesh model is used to describe the topology optimization results of the flow channel.

[0093] In this embodiment, Figure 2 An initial design model of a flow channel is shown, featuring one inlet and one outlet. The design domain is defined based on the inlet and outlet, with a volume constraint set to 0.3. Topology optimization yields the optimized density field. Density filtering of each element results in a triangular mesh model to be preprocessed.

[0094]

[0095] in, Representing the Density of each unit This represents the density after filtration.

[0096] Step 2: Perform mesh preprocessing on the triangular mesh model to be reconstructed, including mesh surface normal consistency detection and repair, connectivity analysis, redundant structure removal, and watertightness detection, to obtain a topologically consistent and geometrically valid preprocessed triangular mesh model. The original triangular mesh model to be reconstructed originated from the flow channel topology optimization calculation results, and its boundaries exhibited jagged features and contained redundant vertices. The preprocessed triangular mesh model, however, does not have jagged boundaries or redundant vertices.

[0097] In this embodiment, refer to Figure 3 The triangular mesh model to be preprocessed can be represented as: ,in The set of all vertices of the triangular mesh model. This is the set of all triangular faces in the triangular mesh model. The number of vertices in the triangular mesh model. This represents the total number of triangular faces in the triangular mesh model.

[0098] Any triangular facet is represented as The geometric normal vector of the triangular facet is defined as:

[0099]

[0100] For any two adjacent triangular faces sharing a common edge, if If the normals of the two are inconsistent, then surface normal consistency correction is performed. The specific process is as follows:

[0101] A face adjacency graph is constructed based on face adjacency relationships. Starting from any initial face, its adjacent faces are traversed. When an inconsistency in the normals of adjacent faces is detected, the normals are flipped by swapping the indices of two vertices of the triangle face. For example, the vertex sequence is changed. Rearranged as This ensures that the normal directions of adjacent facets are kept consistent, resulting in a triangular mesh model with consistent facet normals. This step ensures that the triangular mesh model has a unified geometric orientation, providing a foundation for subsequent volume calculations and geometric reconstruction.

[0102] The triangular mesh model with uniform surface normals is abstracted as an undirected graph. Among them, undirected graphs The set of nodes in the diagram corresponds to the set of triangular facets. ; An undirected graph The set of edges is defined such that when any two triangular faces share a common edge, an edge is established between their corresponding nodes, thus defining the connectivity between the triangular faces. This connecting edge belongs to the set of edges. .

[0103] Based on the connectivity relationship, a connectivity analysis is performed on the undirected graph, dividing the triangular mesh model into several disconnected connected sub-mesh, denoted as:

[0104]

[0105] in, Indicates the first A connected subnetwork, Let be the number of connected subnetworks. Further, define the th... The size of a connected submesh is the number of triangular faces it contains:

[0106]

[0107] in, For the first The set of triangular faces corresponding to each connected submesh.

[0108] Select the connected subnetwork that satisfies the following formula as the main connected region:

[0109]

[0110] That is, the connected subnetwork containing the largest number of triangular faces is selected as the main connected triangular mesh model. All other connected subnetworks other than the main connected region are determined to be isolated meshes and deleted, thus obtaining a triangular mesh model containing only the main connected region.

[0111] Through the above connectivity analysis and main connected region extraction process, isolated grid components and numerical noise structures generated in the topology optimization results can be effectively eliminated, ensuring that the subsequent geometric reconstruction process is performed on the main flow channel structure.

[0112] For any two sets of triangular faces in the triangular mesh model that has undergone connectivity analysis If satisfied If the two are found to be duplicate triangular faces, then only one of them is retained, and the rest are deleted, thus obtaining a triangular mesh model without redundant structure.

[0113] For a triangular mesh model with redundant structures removed, let any side of the triangular mesh... The number of referenced face pieces is When satisfied When this occurs, the edge is defined as an open boundary edge. Several boundary cycles are formed by all open boundary edges. ,in The set representing the boundary ring, Each element in This represents a boundary loop, with each boundary loop corresponding to a geometric void region to be repaired. For each identified boundary loop, a new set of facets is generated using boundary triangulation. and update the mesh set. This ensures that all edges in the grid satisfy the condition. This yields a topologically closed watertight triangular mesh model.

[0114] Through the above mesh preprocessing steps, a geometric model with consistent triangular mesh normals, topological connectivity, no redundant structure, and overall watertightness was achieved, laying a stable and reliable geometric foundation for maintaining geometric smoothness and reconstruction of flow channel performance.

[0115] Step 3: Perform surface smoothing on the topologically consistent and geometrically valid triangular mesh model using Laplacian smoothing to remove jagged boundary features caused by mesh discretization and improve local geometric continuity. During this process, the volume of the smoothed mesh model is continuously calculated and compared with the target volume. If it is greater than the target volume, Laplacian smoothing continues; if it is less than the target volume, the missing volume is compensated by moving the normals of the mesh model vertices. After a finite number of iterations, the iteration stops when the difference between the mesh model and the target volume is less than the convergence condition, resulting in a mesh model with a continuous, smooth surface and controllable volume.

[0116] In this embodiment, refer to Figure 4 The topologically consistent and geometrically valid triangular mesh model consists of a set of vertices. and triangular facet set Composition, in which Indicates the first The spatial coordinates of each vertex are used to calculate the initial volume of the triangular mesh model. Set target volume Here Take 0.85.

[0117] In the smoothing iteration process, the first step is to construct the first... The neighborhood set of each vertex And calculate the first Average neighborhood position of each vertex:

[0118]

[0119] The first is determined based on the average neighborhood position. The vertex of the first vertex Second-smooth displacement vector:

[0120]

[0121] in For the first The vertex at the th The average neighborhood position during the next smoothing iteration For the first The vertex at the th Spatial coordinates during the second smoothing iteration; and according to the... The smoothing step size during the next smoothing iteration For the Update the position of each vertex:

[0122]

[0123] After updating the positions of all vertices, calculate the current mesh volume with the world coordinate system origin as the reference point:

[0124]

[0125] in For the first A triangular facet The coordinate vectors of the three vertices relative to the origin. For the first After the smoothing iteration, the set of all triangular faces of the current triangular mesh model. Then, the current volume deviation is calculated:

[0126]

[0127] The smoothing iteration terminates when the following convergence condition is met:

[0128]

[0129] in To preset the volume error threshold, here Pick .

[0130] If the convergence condition is not met, a volume correction step is introduced. Specifically, the volume correction step is calculated based on the current mesh model. The unit normal vector of each vertex:

[0131]

[0132] in Indicates that it contains vertices The A triangular facet, Indicates the first The unit normal vector of each triangular facet; in this embodiment, for a triangular mesh model with a relatively uniform mesh distribution after preprocessing, the unit normal vector of the vertex is calculated by summing the normal vectors of adjacent facets with equal weights and then normalizing them; for cases with uneven mesh distribution, a facet area weight coefficient can be introduced during summation for weighted averaging.

[0133] The normal correction coefficient is determined according to the following formula. :

[0134]

[0135] in This represents the total number of vertices in the current mesh model. Volume compensation corrections are then applied to the vertex positions.

[0136]

[0137] To improve the stability of the smoothing volume correction process, the smoothing step size is attenuated during the iteration process, and its update form is as follows:

[0138]

[0139] Here the attenuation coefficient The value is set to 0.99. The maximum number of iterations is limited to 200. In this embodiment, after 5 iterations, a mesh model with a smooth surface and a volume of 85.8% of the original mesh model is obtained. Taking this embodiment as an example, the initial volume of the preprocessed triangular mesh model is 335.2 mm. 3 The target volume was set at 284.9 mm². 3 (That is, 85% of the initial volume). After 5 iterations, the final mesh volume is 287.6 mm. 3 The deviation from the target volume is less than the preset 1% convergence condition, which verifies the effectiveness of the volume control mechanism of the present invention.

[0140] Step 4: Remesh the continuous and smooth triangular mesh to transform it into a topologically regular and parametrically friendly quadrilateral mesh, thereby improving its applicability in subsequent geometric reconstruction.

[0141] In this embodiment, refer to Figure 5 The triangular mesh processed in the aforementioned steps is stored in STL format, and then converted to OBJ format mesh file through mesh format conversion. During the format conversion process, the geometric information of the triangular mesh remains unchanged, and its vertex coordinates can be represented as:

[0142]

[0143] The topological relationship of the facets is represented as:

[0144]

[0145] in For the set of vertices, It is a set of triangular facets.

[0146] The OBJ-formatted triangular facets are then imported into the quadrilateral mesh reconstruction module for directional constraint construction and parametric rearrangement of the mesh surface. The directional constraints are determined based on the local geometric features of the mesh surface, and their direction vectors can be approximated by the vertex normal or principal curvature direction as follows:

[0147]

[0148] in and Representing vertices respectively The principal curvature value at that point.

[0149] Under the stated directional constraints, the original triangular mesh is reparameterized, and adjacent triangular meshes are merged and rearranged to generate a mesh structure composed of quadrilateral meshes. This parametric rearrangement process achieves smoothing of the mesh model by iteratively optimizing the vertex positions of the quadrilateral meshes, resulting in a regular and parametrically friendly topological structure for the generated quadrilateral mesh. The set of quadrilateral meshes is represented as follows:

[0150]

[0151] To control the overall density of the reconstructed mesh, the target number of facets is preset during the quadrilateral mesh reconstruction process. Here, the target number of facets is set to 4000, which will result in the final number of quadrilateral facets generated. satisfy:

[0152]

[0153] in, This is the allowable error threshold.

[0154] After completing the quadrilateral mesh reconstruction, the resulting mesh model is validated. The validation method involves statistically analyzing the mesh patch types, with the following criteria:

[0155]

[0156] in, Indicates the composition of a facet The set of vertices, This indicates the number of vertices of the face. When the above condition is met, the reconstructed mesh model is determined to be a quadrilateral mesh model.

[0157] Step 5: After generating and verifying the quadrilateral mesh model, the quadrilateral mesh model is solidified to obtain a topologically closed and geometrically valid three-dimensional solid model that can be used for engineering design and manufacturing.

[0158] Specifically, the quadrilateral mesh model is imported into the geometric modeling environment. Based on the topological connections and parametric characteristics between the quadrilateral mesh patches, a conversion operation from discrete mesh to parametric surface is performed on the mesh model, mapping each quadrilateral patch to its corresponding parametric surface, thereby generating a geometric model composed of continuously stitched parametric surfaces. During the NURBS conversion, G1 continuous constraints are applied to the common boundaries of adjacent parametric surfaces to ensure a smooth transition of the reconstructed flow channel inner wall and avoid the generation of tiny creases at the patch junctions that could affect the accuracy of fluid simulation.

[0159] In this embodiment, refer to Figure 6 The geometric modeling environment is implemented using commercial geometric modeling software, such as importing the quadrilateral mesh model into Rhino software and performing a NURBS transformation operation on the mesh model. The NURBS operation is based on the patch topology of the quadrilateral mesh, converting each quadrilateral patch into a corresponding two-parameter NURBS patch, mathematically expressed as follows:

[0160]

[0161] in, This represents the generated NURBS surface. To control the vertices, and They are respectively direction and The order of the B-spline basis functions in the direction, and These are the B-spline basis functions in the corresponding parameter directions.

[0162] Through the above transformation, the geometric model originally represented by discrete mesh patches is transformed into a continuous parametric surface representation, maintaining topological consistency and geometric continuity between the surfaces, at least G0 continuity and G1 continuity. Furthermore, by stitching and closing these parametric surfaces, a closed set of surfaces is formed, thereby generating a three-dimensional solid model that satisfies the requirements of geometric continuity and topological closure. The resulting solid model can be directly used for subsequent structural analysis, fluid simulation, or manufacturing modeling.

[0163] In this embodiment, to demonstrate the high efficiency and performance of geometric reconstruction of the flow channel topology optimization results using the present invention, other commonly used methods for geometric reconstruction of the flow channel topology optimization results are also used as comparative examples of the present invention. Among them, one existing geometric reconstruction method is a direct solid conversion method based on isosurface extraction (extracting isosurfaces using the MarchingCubes algorithm and directly converting them into a solid model), and another existing geometric reconstruction method is a surface fitting method based on Poisson reconstruction (reconstructing a Poisson surface from a triangular mesh and fitting it to a NURBS model). The flow channel geometric model obtained using the present invention is referred to as "A", and the flow channel geometric models reconstructed using other different methods are referred to as "B" and "C" respectively. See reference... Figure 7 .

[0164] The pressure drop performance, volume, and reconstruction time of the geometric reconstruction models for the three flow channel topology optimization results "A", "B", and "C" are shown in Table 1. The comparison results in Table 1 demonstrate that the method of this invention achieves significant technical improvements in both geometric reconstruction efficiency and flow channel hydraulic performance.

[0165] Specifically, compared with model B obtained by the existing geometric reconstruction method, model A obtained by the method of the present invention has a 21.3% lower flow channel pressure drop, indicating that the method of the present invention can effectively improve the hydraulic performance of the flow channel during the geometric reconstruction process. At the same time, the geometric reconstruction time of the method of the present invention is significantly shortened, and the reconstruction efficiency is improved by about 16 times compared with the existing method.

[0166] Furthermore, compared with model C obtained by the existing geometric reconstruction method 2, model A obtained by the method of the present invention improves the geometric reconstruction efficiency by about 8 times while reducing the flow channel pressure drop by about 38.2%, demonstrating that the method of the present invention has a more prominent advantage in geometric reconstruction of the flow channel topology optimization results while maintaining the flow channel performance.

[0167] Based on the above comparison results, it can be seen that the method of the present invention can significantly improve the efficiency of geometric reconstruction while effectively reducing the flow channel pressure drop of the reconstructed model, thus ensuring the performance of the flow channel topology optimization results. Therefore, it is superior to the existing geometric reconstruction methods in terms of both reconstruction efficiency and flow channel performance, and has good engineering application value.

[0168] Table 1. Pressure drop, volume, and reconstruction time of the geometric reconstruction model for the topology optimization results of three flow channels (A, B, and C).

[0169]

[0170] Example 2:

[0171] In this embodiment, the flow channel has one inlet and two outlets. The geometric model of the flow channel topology optimization result reconstructed using the present invention is "D". (See attached document). Figure 8 The geometric models of the channel topology optimization results reconstructed using other methods are "E" and "F". (See attached document.) Figure 9 .

[0172] The pressure drop performance, volume, and reconstruction time of the geometric reconstruction models for the three channel topology optimization results ("D", "E", and "F") are shown in Table 2. The comparison results in Table 2 demonstrate that the method of this invention achieves significant technical improvements in both geometric reconstruction efficiency and channel hydraulic performance.

[0173] Specifically, compared with model E obtained by the existing geometric reconstruction method, the flow channel pressure drop of model D obtained by the method of the present invention is reduced by 37.4%, indicating that the method of the present invention can effectively improve the hydraulic performance of the flow channel during the geometric reconstruction process; at the same time, the geometric reconstruction time of the method of the present invention is significantly shortened, and the reconstruction efficiency is improved by about 13 times compared with the existing method.

[0174] Furthermore, compared with model F obtained by the existing geometric reconstruction method 2, model D obtained by the method of the present invention improves the geometric reconstruction efficiency by about 7 times while reducing the flow channel pressure drop by about 47.6%, demonstrating that the method of the present invention has a more prominent advantage in geometric reconstruction of the flow channel topology optimization results while maintaining the flow channel performance.

[0175] Based on the above comparison results, it can be seen that the method of the present invention can significantly improve the efficiency of geometric reconstruction while effectively reducing the flow channel pressure drop of the reconstructed model, thus ensuring the performance of the flow channel topology optimization results. Therefore, it is superior to the existing geometric reconstruction methods in terms of both reconstruction efficiency and flow channel performance, and has good engineering application value.

[0176] Table 2. Pressure drop, volume, and reconstruction time of the geometric reconstruction model for the topology optimization results of three flow channels (D, E, and F).

[0177]

[0178] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for geometric reconstruction of topology optimization results while preserving flow channel performance, characterized in that, Includes the following steps: Step 1: Based on the flow channel topology optimization calculation results, obtain the triangular mesh model to be reconstructed. The triangular mesh model is used to describe the geometric boundary of the flow channel after topology optimization. Step 2: Perform mesh preprocessing on the triangular mesh model to eliminate problems such as inconsistent normals, isolated structures, repeated faces, and open boundaries in the mesh, and obtain a topologically consistent and geometrically valid triangular mesh model; Step 3: Perform surface smoothing on the topologically consistent and geometrically valid triangular mesh model obtained in Step 2. The surface smoothing process includes: The triangular mesh model is subjected to Laplace smoothing iteration. After each iteration, the volume of the current mesh model is calculated, and the calculated volume is compared with the preset target volume. If the current mesh model volume is larger than the target volume, then continue with the Laplace smoothing iteration; If the current mesh model's volume is smaller than the target volume, then volume compensation is performed by moving the normals of the mesh model's vertices. Repeat the above process until the deviation between the current mesh model volume and the target volume is less than the preset convergence condition, then stop the iteration to obtain a triangular mesh model with a continuous, smooth surface and controllable volume. Step 4: Remesh the triangular mesh model with a continuous, smooth surface and controllable volume obtained in Step 3, and convert the triangular mesh model into a quadrilateral mesh model. Step 5: Perform solidification processing on the quadrilateral mesh model obtained in Step 4, converting the discrete mesh into a three-dimensional solid model.

2. The method according to claim 1, characterized in that, The mesh preprocessing described in step 2 specifically includes: The triangular mesh model is subjected to mesh surface normal consistency detection. When the normal directions of adjacent patches are found to be inconsistent, the normal directions are corrected for consistency based on the adjacency relationship of the patches. The patches with flipped normals are reoriented to obtain a triangular mesh model with consistent mesh surface normals. A connectivity analysis is performed on the triangular mesh model that has undergone normal consistency processing. Isolated mesh components are identified and deleted, and only the connected regions containing the maximum number of faces are retained to obtain the main connected triangular mesh model. The main connected triangular mesh model is identified for repeated triangular face definitions. When repeated faces exist, they are deleted to obtain a triangular mesh model without redundant structure. The watertightness of the triangular mesh model without redundancy is tested. When an open boundary is detected, voids are identified and the boundary is stitched together to obtain a topologically closed watertight triangular mesh model.

3. The method according to claim 1, characterized in that, The Laplace smoothing iteration in step 3 includes: Constructing the first based on grid topology The neighborhood set of each vertex Calculate the first Average position of the neighborhood of each vertex: in For the first Spatial coordinates of the vertices of the neighborhood; The first is determined based on the average neighborhood position. The vertex of the first vertex Second-smooth displacement vector: And in accordance with the first The smoothing step size during the next smoothing iteration For the Update the position of each vertex: in For the first The vertex at the th Average neighborhood position during the next smoothing iteration For the first The vertex at the th Spatial coordinates during the next smoothing iteration. No. The vertex at the th Spatial coordinates during the next smoothing iteration.

4. The method according to claim 3, characterized in that, Step 3, calculating the volume of the current mesh model, includes: Using the origin of the world coordinate system as a reference point, calculate the current mesh volume according to the following formula: in For the first A triangular facet The coordinate vectors of the three vertices relative to the origin. For the first After the next smoothing iteration, the set of all triangular faces of the current triangular mesh model.

5. The method according to claim 4, characterized in that, Step 3, which describes volume compensation through normal movement of the vertices of the mesh model, includes: Calculate the first based on the current mesh model. The unit normal vector of each vertex: in Indicates that it contains vertices The A triangular facet, Indicates the first The unit normal vector of a triangular facet; The normal correction coefficient is determined according to the following formula. : in This represents the total number of vertices in the current mesh model. For the target volume, For the first The mesh volume after the second smoothing iteration is then corrected by volume compensation at the vertex positions: 。 6. The method according to claim 5, characterized in that, The preset convergence condition mentioned in step 3 is: in This is the current volume deviation. Let this be the initial volume of the triangular mesh model. This is a preset volume error threshold.

7. The method according to claim 6, characterized in that, The smooth step size mentioned in step 3 During the iteration process, decay control is performed according to the following formula: in This is the attenuation coefficient.

8. The method according to claim 1, characterized in that, The remeshing process described in step 4 specifically includes: The triangular mesh model is converted into an intermediate mesh model that can be recognized by the quadrilateral remeshization algorithm; A quadrilateral mesh reconstruction operation is performed based on the intermediate mesh model, and the overall resolution of the reconstructed quadrilateral mesh model is controlled by setting the number of target patches; The generated quadrilateral mesh model is smoothed to obtain a topologically regular and parameter-friendly quadrilateral mesh model.

9. The method according to claim 8, characterized in that, In the quadrilateral mesh reconstruction operation described in step 4, the number of target facets is set. This will increase the number of quadrilateral patches generated in the end. satisfy in This is the allowable error threshold.

10. The method according to claim 1, characterized in that, The materialization process described in step 5 includes: Import the quadrilateral mesh model into the geometric modeling environment; Based on the topological connection relationship between quadrilateral mesh patches, each quadrilateral patch is mapped to a corresponding parametric surface, generating a geometric model composed of continuous splicing of parametric surfaces; Apply G1 continuity constraints to the common boundary of adjacent parametric surfaces; The parametric surface is stitched and closed to generate a three-dimensional solid model.

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