Multi-scale eddy identification method based on topology analysis

Abstract

The invention discloses a multi-scale vortex recognition method based on topology analysis, and aims to solve the problems that an existing vortex recognition method depends on a single scale and is insufficient in adaptability, limited in generalization ability, poor in visualization effect and the like. According to the method, firstly, a merge tree is constructed to obtain a multi-scale topological structure of a flow field, candidate vortex regions are screened based on extreme point-saddle point branches, and multi-scale vortex extraction is carried out in combination with a scalar criterion, so that dependence of a traditional method on a fixed threshold is avoided. In order to adapt to unstructured grid data, the method enhances the applicability and robustness of the method in a complex flow environment through adjacency relation reconstruction. In addition, a region diffusion algorithm is adopted to identify the vortex region, and surface extraction and smoothing processing are combined to optimize the visualization effect, so that the boundary of the vortex structure is more continuous and natural. Experimental results show that the method can accurately extract vortex structures of different scales, shows good generalization ability on flow field data of different Reynolds numbers, and has higher adaptability on complex flow fields and unstructured grids compared with a traditional method. The method can be widely applied to turbulence research, aerodynamic optimization, meteorological analysis and engineering flow problems, and an efficient, robust and accurate vortex recognition technology is provided for fluid mechanics research.

Description

Technical Field

[0001] The present invention relates to the cross - field of computational fluid dynamics (CFD) and data science, and particularly to a vortex identification method based on multi - scale analysis, which is applicable to feature extraction and dynamic analysis of complex flow fields. This method utilizes topological structure analysis, region - growing algorithm and union - find data structure, combined with multi - scale data processing technology, to achieve accurate identification and hierarchical extraction of vortex structures, and can be widely applied in fields such as turbulence research, aerodynamic optimization, weather prediction, environmental simulation and bio - fluid mechanics. Background Art

[0002] Vortex is an important structural feature in fluid mechanics and has important significance in fields such as turbulence research, aerodynamic optimization, weather simulation, environmental fluid mechanics and bio - fluid mechanics. Accurately identifying the vortex structure in a flow field is crucial for understanding the laws of fluid motion, optimizing engineering designs and improving numerical simulation methods. However, due to the complexity of the flow field, traditional vortex identification methods often have limitations when facing multi - scale vortices, complex boundary conditions and high - noise data.

[0003] Existing vortex identification methods mainly include geometric methods based on vorticity, λ2 - criterion, Q - criterion, Ω - criterion, etc., and flow field decomposition methods based on topological analysis. Although these methods can reveal the vortex structure to a certain extent, they are usually sensitive to scale, difficult to handle vortices of different scales simultaneously, and are sensitive to noise in the flow field, easily leading to the identification of false vortex structures. In addition, most methods rely on global threshold setting and are difficult to adapt to local feature changes in complex flow fields, affecting the identification accuracy and robustness.

[0004] To overcome the above problems, a vortex identification method that can adapt to multi - scale features, has strong robustness to noise, and can accurately extract the topological structure of the flow field is needed. The present invention proposes a vortex identification method based on multi - scale analysis, which realizes accurate identification of vortex structures in complex flow fields by combining topological structure analysis, region - growing algorithm and union - find data structure, and improves the stability, accuracy and applicability of vortex identification. Summary of the Invention

[0005] The object of the present invention is to provide a vortex identification method based on multi - scale analysis, which realizes accurate extraction of vortex structures in complex flow fields by combining topological structure analysis, region - growing algorithm and union - find data structure. This method can overcome the deficiencies of traditional vortex identification methods in multi - scale adaptability, noise robustness and local feature capture, and provide more stable and accurate vortex identification results.

[0006] First, numerically perturb the scalar field data of the original flow field to ensure that the scalar values are unique. For example, add a small noise (e.g., 1E-4) to the repeated scalar values. This can affect the originality of the flow field at the lowest cost and also ensure the successful construction of the merge tree. This step is the basis for subsequent topological analysis and ensures the accuracy and robustness of the algorithm.

[0007] Then, reconstruct the unit edge adjacency relationship. Traverse all units, extract the ordered edge information between nodes, and uniformly map heterogeneous units to a set of standardized edges (point pairs). The specific steps are as follows:

[0008] In the first step, dynamically analyze the local topology for different unit types. For example, the six edges of a tetrahedron or the twelve edges of a hexahedron. This step ensures that the algorithm can adapt to different types of mesh structures and improves the generality of the algorithm;

[0009] In the second step, force the nodes of the edge to be sorted in descending order of scalar value (for example, merge the edge (A, B) and (B, A) into (B, A)). This normalization process eliminates the redundant storage of duplicate edges, establishes a globally unique edge identifier, and solves the problem of ambiguous adjacency relationships caused by irregular node connections in unstructured meshes. This step provides convenience for subsequent topological operations and improves the efficiency of the algorithm.

[0010] Secondly, perform topological analysis on the flow field scalars, construct a merge tree (JT) and perform branch decomposition. The specific steps are as follows:

[0011] In the first step, initialize the union-find set to save the information of connected components. The union-find set is an efficient data structure for managing element grouping information, which is convenient for subsequent merge operations;

[0012] In the second step, traverse the points sorted in descending order. For each point, check the nodes with smaller scalar values in its neighbor set. If two points belong to different connected components, merge the connected components of these two points in the JT and record the connection relationship. This step constructs the topological structure of the flow field and provides a basis for the identification of vortex structures.

[0013] In the third step, save the merge tree to a Vtk Polydata file and save it in the form of branch decomposition. Each branch corresponds to a potential vortex region and can be processed separately, which is convenient for multi-scale vortex structure extraction. This step saves the topological structure in an easy-to-process form and provides convenience for subsequent region extraction and surface smoothing.

[0014] Next, perform the saddle point recognition operation. Read data from the Polydata file of the merge tree, and count the nodes that appear more than once in LINES, which are the saddle points. Then, according to the requirements of the scalar criterion (such as the λ2 criterion or Q criterion), select the branches where the enclosed volume from the extreme point to the region where the saddle point is located is not zero as the candidate vortex regions. The specific situation is as follows:

[0015] In the first case, if the λ2 scalar field of the flow field is selected to construct the merge tree, then according to the criterion, the region where λ2 < 0 is the region where vortices exist. Therefore, select the branch where the λ2 values of all nodes on the sub-branch from the extreme point to the saddle point are less than zero as the vortex region.

[0016] In the second case, if the Q scalar field of the flow field is selected to construct the merge tree, then select the sub-branch where the Q values of all nodes are greater than 0 as the vortex region.

[0017] Finally, perform multi-scale vortex structure extraction on the candidate vortex regions and perform surface extraction and smoothing operations. Take the extreme point of the candidate branch as the starting point, and according to the judgment requirements of the scalar criterion, diffuse outward from the cell where the extreme point is located, and gradually merge the cells that meet the requirements to complete the extraction of the vortex region. The specific steps are as follows:

[0018] The first step is to perform operations based on the Vtk file. Use the breadth-first search mechanism, utilize the local extreme value distribution characteristics of the scalar field and the connectivity of the nodes to guide the region diffusion process to adaptively extract vortex regions of different scales. This step can effectively extract vortex structures of different scales and overcome the deficiencies of traditional methods in multi-scale adaptability;

[0019] The second step is to eliminate the isolated cells protruding from the region boundary to make the region boundary smooth. This step improves the recognition accuracy of the vortex structure and makes it closer to the real shape;

[0020] The third step is to strip the internal structure in the vortex region and only retain the surface geometric information of the outer contour of the region to construct a continuous and closed polygon surface mesh. This step provides a basis for subsequent surface smoothing;

[0021] The fourth step is based on the Laplace smoothing principle. By iterating multiple times, gradually adjust the positions of each mesh vertex on the surface to make the surface tend to be smooth. This step can effectively eliminate surface noise and improve the visualization effect of the vortex structure.

[0022] Compared with the prior art, the advantages of the present invention are as follows:

[0023] (1) The present invention adopts a merging tree method based on topological structure to hierarchically analyze the vortex structures in the flow field, without relying on fixed threshold setting. This method can simultaneously identify vortex structures of different scales, and can effectively detect both micro-scale and large-scale vortices, and is applicable to complex flow field environments such as turbulent flow and shear flow. Compared with the traditional method based on fixed threshold, the present invention can maintain a high recognition accuracy under different flow field conditions, improving the applicability and robustness.

[0024] (2) The present invention analyzes the flow field characteristics through topological structure, which can effectively avoid the influence of local data perturbation on the recognition result. At the same time, in the process of multi-scale vortex extraction, the grid filtering method is used to remove isolated regions, reducing the interference of numerical errors on the result. Compared with the traditional vortex identification methods based on gradient or curl threshold, the present invention can maintain a high stability in experimental data and numerical simulation results, improving the accuracy and reliability of vortex identification.

[0025] (3) The present invention adopts an efficient data structure and optimization algorithm, including using the union-find set to optimize the merging tree construction process and parallel accelerating the region expansion calculation. By reducing repeated calculations and improving the calculation efficiency, this method can significantly reduce the calculation cost when processing large-scale computational fluid dynamics (CFD) data. Compared with the traditional vortex identification method of point-by-point calculation, the present invention has an obvious advantage in calculation speed and can meet the rapid processing requirements of high-dimensional flow field data.

[0026] Other features and advantages of the present invention will be described in detail in the subsequent specific implementation part. Brief Description of the Drawings

[0027] By describing the exemplary embodiments of the present invention in more detail in combination with the drawings, the above and other objects, features and advantages of the present invention will become more obvious, wherein, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0028] Figure 1 Shows the overall flow schematic diagram of a multi-scale vortex identification method based on topological analysis according to an embodiment of the present invention.

[0029] Figure 2 Shows the schematic diagram of the decomposition of the branches of the merging tree (JT) according to an embodiment of the present invention.

[0030] Figure 3 Shows the schematic diagram of the extraction of candidate regions of the merging tree (JT) according to an embodiment of the present invention.

[0031] Figure 4 Shows the schematic diagram of the vortex extraction result and the vortex surface after surface extraction and smoothing processing according to an embodiment of the present invention. Detailed Implementation Manner

[0032] To more clearly elaborate on the technical solution of the present invention, the present invention will be described in detail below in conjunction with specific implementation manners. After reading this specification, those skilled in the art can, without departing from the spirit and scope of the present invention, adjust and modify the technical solution of the present invention, and these adjustments and modifications should all be regarded as the protection scope of the present invention.

[0033] The present invention provides a multi-scale vortex identification method based on topological analysis, which includes two core parts: Merge Tree construction and multi-scale vortex extraction. This method is applicable to computational fluid dynamics (CFD) data analysis, can automatically identify vortex structures of different scales, and improve the accuracy and computational efficiency of vortex detection.

[0034] 1. Merge Tree Construction Method Based on Union-Find Set

[0035] In one example, this method can be divided into four steps: adjacency relationship construction, grid point sorting, union-find set initialization, and merge tree construction.

[0036] Step 1: In one example, the following steps can be used to establish the adjacency relationship between grid points by extracting the edge set of the flow field grid, so as to perform the connectivity analysis of the vortex region on the grid topology structure:

[0037] First, extract the edge set of the flow field grid from the input data to establish the adjacency relationship between grid points, so as to perform the connectivity analysis of the vortex region on the grid topology structure subsequently;

[0038] Then, initialize the data structure. Set an empty dictionary JT_branch to store the merge tree structure; set an adjacency list edge_dict to record the adjacent point information of each grid point;

[0039] Finally, traverse all edges to construct the adjacency list. For each edge (p1, p2) in the input edge set edges, add p2 to the set of adjacent points of edge_dict[p1], and add p1 to the set of adjacent points of edge_dict[p2]. In this way, each grid point can quickly query all directly adjacent points;

[0040] Step 2: In one example, the following steps can be used to ensure that the merge tree is constructed according to the hierarchical relationship of scalar values. It is necessary to sort the grid points in descending order of scalar values, that is, process them sequentially from high scalar value points to low scalar value points:

[0041] First step, extract the scalar values of all grid points through points_magnitude_dict. Second step, sort them in descending order of scalar values to obtain the sorted point list sorted_points. This sorting ensures that during subsequent construction, points with higher scalar values will be preferentially merged for connectivity.

[0042] Step 3: In one example, the union-find structure can be initialized through the following steps to maintain the connectivity information of the flow field topology:

[0043] First step, establish the union-find JT_UF to manage the connected components of grid points;

[0044] Second step, initialize each grid point as an independent component. For each point i in sorted_points, set JT_branch[i] = i, indicating that in the initial state, each point forms a separate connected component by itself.

[0045] Step 4: In one example, the grid points can be traversed in descending order through the following steps to perform connectivity merging and thus construct the merge tree:

[0046] First step, traverse each point i in sorted_points. For all its adjacent points j (obtained from edge_dict[i]), obtain the root nodes root i and root j ;

[0047] Second step, if root i is not equal to root j , it means that i and j are not yet in the same connected component. Record i as a child node of the merge tree in JT_branch[root j ;

[0048] Third step, perform the operation JT_UF.union(i, j) to merge i and j into the same connected component. This step is executed in descending order of scalar values, ensuring that regions with higher scalar values preferentially form independent vortex structures and gradually merge regions with lower scalar values as the calculation progresses, finally forming the complete merge tree JT_branch.

[0049] 2. Vortex extraction method based on topological analysis and region growing

[0050] In one example, this method can be divided into five steps: region identification initialization, seed point selection, region growing, and multi-scale screening.

[0051] Step 1: In one example, the region identification can be initialized through the following steps to ensure that the vortex regions in the flow field data can be effectively extracted:

[0052] First, create an array regiOn_id_array for region identification, whose length is equal to the total number of grid cells, and initialize all cells to 0, indicating that they have not been classified.

[0053] Second, create a set visited_nodes_set to store the visited grid points to avoid repeated calculations.

[0054] Third, create a dictionary region_queues for managing the growth process of different regions, where the key is the region number and the value is the queue of grid cells to be expanded in the current region.

[0055] Step 2: In one example, select seed points from the input start_nodes_list through the following steps and create a separate expansion queue for each seed point:

[0056] Traverse start_nodes_list, and for each starting point p:

[0057] First, create an independent region number re_id.

[0058] Second, create a new queue in region_queues and add p to this queue.

[0059] Third, add p to visited_nodes_set and mark it as visited.

[0060] Step 3: In one example, the region growth can be performed using breadth-first search (BFS) through the following steps:

[0061] First, traverse all the region queues in region_queues. For each region re_id, take out its queue q to be processed.

[0062] Second, if q is empty, skip the current region and continue to process other regions.

[0063] Third, take out the first grid cell cell_id from q and obtain its adjacent grid cells connected_cells.

[0064] Step 4: Traverse each adjacent cell neighbor_id in connected_cells. If the scalar values of all vertices of neighbor_id satisfy the vortex determination criterion and region_id_array[neighbor_id] is still 0 (unclassified), mark neighbor_id as the current region re_id, add neighbor_id to q for further expansion, and if neighbor_id has not been visited, add it to visited_nodes_set. This process continues until all region queues region_queues are empty, indicating that all possible vortex regions have been expanded.

[0065] Step 4: In one example, the following steps can be used to extract regions from the regions after region growing using the neighbor quantity threshold:

[0066] Step 1: Traverse all classified cells cell_id in region_id_array. For each cell_id, count the number of adjacent cells of cell_id;

[0067] Step 2: If the number of neighbors is less than the neighbor quantity threshold, mark cell_id as 0, that is, eliminate this cell and do not use it as the final vortex region.

[0068] Step 5: In one example, the following steps can be used to visually store the extracted vortex regions:

[0069] Step 1: Convert region_id_array into a VTK format array as the grid cell data field Region_id;

[0070] Step 2: Retain the cells with Region_id > 0 and remove the screened non-vortex region cells;

[0071] Step 3: Generate filter_unstructured_grid containing the vortex region identifiers and output the final extraction result.

[0072] The embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

[0073] The content not described in detail in the present invention is well-known technology to those skilled in the art.

Claims

1. A multi-scale vortex identification method based on topological analysis, comprising: Collection and processing of flow field data, which can be structured grid or unstructured grid data, and numerical perturbation is performed on the scalar field data to ensure uniqueness and stability during topological analysis; Constructing a merge tree based on the scalar field data of the flow field, where the merge tree includes a Join Tree and a Split Tree, which are respectively used to track the evolution of the connected components of the flow field region during the decreasing and increasing processes of scalar values, so as to obtain the multi-scale topological features of the flow field; Based on the extreme point-saddle point branch characteristics in the merge tree, combined with scalar criteria (such as the Q criterion or the λ2 criterion), regions that may contain vortex structures are screened out, and regions that do not meet the vortex characteristics are removed by calculating the topological features and enclosed volumes of sub-branches; Based on the region diffusion algorithm, starting from the extreme points of the candidate vortex region, the vortex structure is gradually expanded and identified according to the change trend of the scalar field value, and the extraction range is adaptively adjusted according to the flow field characteristics at different scales to achieve accurate identification of multi-scale vortices; Visualization optimization of the vortex structure, surface extraction is performed on the identified vortex region, and the Laplace smoothing processing method is used to optimize the vortex boundary, making the vortex structure boundary more continuous and natural, improving the visualization effect, so as to more accurately reflect the fluid motion characteristics.

2. The method according to claim 1, wherein The method is applicable to unstructured grid data and adopts a reconstruction method based on adjacent edges to ensure the applicability of topological analysis. The steps include: The first step is to analyze the cell topology of the unstructured grid and construct an adjacent edge set to uniformly represent different types of grid structures; The second step is to uniquely process the adjacent edges in a descending order, eliminate redundant storage, and establish a standardized topological relationship; In addition, during the topological analysis process, the standardized adjacent edge set is used for connectivity calculation to improve the adaptability and calculation efficiency for complex flow fields.

3. The method according to claim 1, wherein The construction process of the merge tree includes: The first step is to analyze the grid topological structure of the flow field data, initialize the merge tree data structure, set an empty dictionary JT_branchJT to store the topological structure of the merge tree, and establish an adjacency list edge_dict to store the adjacency relationship of each node; The second step is to construct the adjacency list. Traverse each edge (p1, p2) in the edge set edges, and add the edge to edge_dict[p1] and edge_dict[p2] respectively to ensure the integrity of the adjacency information of each point; The third step is to sort all points in descending order according to the numerical values in the scalar value dictionary points_magnitude_dict, and use the numerical perturbation method to solve the problem of repeated scalar values to ensure the uniqueness and stability of the merge tree, and obtain the sorted point list sorted_points; The fourth step is to set each node as an independent connected component, initialize the parent nodes of all nodes in the union-find set JT_UF, and at the same time store the initial state of each node in the JT_branch structure, that is, JT_branch[i] = i; Step 5: For each node i in sorted_points, traverse all adjacent edges e recorded in edge[i]. If the current node i is the end point of edge e, determine the adjacent node j as the start point of e. Then, obtain the respective root nodes root i and root j of j and i through the union-find operation. If root i ≠ root j , perform the topological merging operation - record i as its child node in JT_branch[root j to represent its topological merging relationship; merge i and j into the same connected component through the union-find operation to maintain the topological structure of the merged tree. In the sixth step, after traversing all nodes, return JT_branch. This structure stores the hierarchical relationships of all topological connected components and can reflect the topological evolution processes at different scales in the flow field.

4. The method according to claim 1, wherein The screening process of the candidate vortex regions includes: In the first step, count the extreme point-saddle point branches of the merge tree and analyze their local topological characteristics; In the second step, calculate the enclosed volume from the extreme point to the saddle point region. If this volume is close to 0, then eliminate this branch to avoid misidentification; In the third step, use the Q-criterion or λ2-criterion as the scalar judgment standard to screen the topological branches that meet the vortex characteristics to ensure that the identified regions are real vortex structures; In the fourth step, combine the gradient distribution of the scalar field to further optimize the screening criteria for the candidate regions and improve the robustness of the identification.

5. The method according to claim 1, wherein The multi-scale vortex structure extraction process uses breadth-first search (BFS) for regions and realizes the identification of local flow field structures through region growing and threshold screening algorithms. Its steps include: In the first step, create a region identification list region_id_array for grid cells, the length of which is equal to the number of unstructured grid cells, and initialize the region identification value region_id of all cells to 0, indicating the unclassified state; In the second step, establish a set of visited nodes visited_nodes_set to store all processed grid nodes. At the same time, create a region queue dictionary region_queues, where the key re_id represents the region number, and the corresponding value is the queue of vertices to be processed, which is used to perform region diffusion; In the third step, traverse the start node list start_nodes_list, assign an independent region number to each start node node, create a corresponding queue, add this point to the corresponding region queue q, and mark this point as visited; In the fourth step, when all region queues are non-empty, traverse each region queue (re_id,q) in the region queue dictionary region_queues. If the current queue q is empty, then skip this region and continue to process the next queue. Otherwise, take out the first node node_id in the current queue, obtain the list of grid cells connected to this node connected_cells, and then traverse each cell cell_id in connected_cells. If the scalar values of all nodes in this cell meet the preset scalar criterion and the region identification region_id_array[cell_id] of this cell is still 0, then set region_id_array[cell_id]=1, classify this cell into the current region, and add all unvisited nodes in this cell to the current region queue q and mark them as visited. Step 5: Perform region extraction. After completing region diffusion, traverse all cells cell_id with region identification values greater than 0, and check whether the number of its neighbors is less than the given threshold threshold. If the adjacency requirement is not met, set region_id_array[cell_id] to 0 and remove this cell to ensure stable connectivity of the identified regions and less noise. Step 6: Convert region_id_array into a VTK array and add it as a cell data field to the unstructured grid, with the field name set to "Region _ id". Retain all mesh cells with Region_id greater than 0 to generate the final filtered mesh object filterunstructured_gridfilte, which only contains the identified vortex core regions, thereby achieving precise extraction of multi-scale flow field structures.

6. The method according to claim 1, wherein The visualization optimization of the vortex structure includes surface extraction and smoothing processing, and its steps are as follows: Step 1: Identify the external mesh patches of the vortex region and construct a polygonal surface mesh; Step 2: Adopt the Laplace smoothing processing method to perform multiple iterative optimizations on the surface mesh vertices to make the vortex boundary smoother and reduce the influence of noise; Step 3: Combine the fluid flow direction to perform local optimization on the surface mesh to make the extracted vortex structure more in line with the actual flow characteristics and improve the visualization effect.

7. The method according to claim 1, characterized in that, This method does not need to rely on specific flow field parameters, can adapt to flow field data with different Reynolds numbers, and can still accurately identify vortex structures of different scales without additional parameter adjustment, thereby enhancing the generalization ability.

8. The method according to claim 1, wherein This method can be used for turbulence research, aerodynamic optimization, meteorological analysis and engineering flow problems. Through the vortex identification technology based on topological analysis, it realizes the efficient and robust extraction and visualization of vortex structures in complex flow fields, providing an accurate analysis tool for fluid mechanics research.

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