Arbitrary polyhedron grid data structure and traversal method for fluid simulation
By constructing an arbitrary polyhedral mesh data structure for fluid simulation, the problems of low quality and uncertain traversal paths in traditional mesh generation are solved, achieving efficient and flexible fluid simulation calculations that can adapt to complex shapes and multi-physics coupling.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- AVIC SHENYANG AERODYNAMICS RES INST
- Filing Date
- 2025-08-21
- Publication Date
- 2026-07-03
AI Technical Summary
In fluid simulation, existing technologies suffer from several drawbacks. Traditional tetrahedral meshes generate low-quality data, hexahedral meshes are cumbersome to divide into blocks and have insufficient fitting ability, and polyhedral meshes have high data structure complexity, leading to uncertain traversal paths and significant performance challenges.
Design an arbitrary polyhedral mesh data structure for fluid simulation, including unit cells, faces, points, overall mesh composition and auxiliary information. Adopt a sequential traversal method, store 3D coordinates through vertices and define faces as an ordered vertex list to construct a topological network, add state identifiers and mesh hierarchy associations, and remove redundant storage of edge structures.
It improves the data structure efficiency and computational performance of polyhedral meshes, supports complex shape adaptation, reduces the complexity of topological relationship maintenance, enhances the computational efficiency and flexibility of fluid simulation, and adapts to multiphysics coupling and local mesh updates.
Smart Images
Figure CN121033325B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of fluid simulation data processing technology, specifically relating to an arbitrary polyhedral mesh data structure and traversal method for fluid simulation. Background Technology
[0002] In the field of fluid simulation, the application of arbitrary polyhedral meshes is becoming increasingly attractive. Faced with simulation scenarios involving complex geometric boundaries, traditional tetrahedral meshes, while easy to generate, suffer from low quality, while hexahedral meshes suffer from cumbersome block division and insufficient fitting ability. Polyhedral meshes, through a hybrid structure of "prism layers + polyhedral distribution," can flexibly adapt to complex curved surfaces, generating high-quality boundary layer meshes near the walls and avoiding the geometric distortion of traditional meshes. Polyhedral mesh elements have high degree of freedom in shape, and mesh quality can be optimized along the flow direction through anisotropic stretching, reducing numerical diffusion caused by elongated or distorted elements. Simultaneously, at the same geometric resolution, the number of elements can be reduced by 30% to 50% compared to tetrahedral meshes, significantly reducing memory usage and computational costs. It is gradually becoming an important alternative to traditional meshes, providing a new path for efficient simulation of complex flow fields.
[0003] The data and traversal of polyhedral meshes are significantly complex. Their diverse geometries (arbitrary numbers of points, edges, and faces) necessitate that the data structure dynamically stores variable compositions and connections. Furthermore, the uncertainty of the number of cell faces and adjacent cells during traversal means that traversal paths cannot rely on fixed patterns. Large-scale mesh traversal faces performance challenges such as cache misses and uneven parallel loads. Overall, a balance between flexibility and efficiency must be struck in data structure design, traversal algorithm optimization, and parallel computing strategies. Summary of the Invention
[0004] The problem this invention aims to solve is to improve the data processing capability of fluid simulation, and proposes an arbitrary polyhedral mesh data structure and traversal method for fluid simulation.
[0005] To achieve the above objectives, the present invention provides the following technical solution:
[0006] An arbitrary polyhedral mesh data structure for fluid simulation includes element composition, surface composition, point composition, overall mesh composition, auxiliary information, and mesh after dual transformation;
[0007] The composition of a unit cell includes the cell type, a list of faces contained in the unit cell, a list of points contained in the unit cell, the geometric properties of the unit cell, and does not store the adjacency relationships between individuals;
[0008] The composition of a face includes a list of points contained in the face, the relationship between the face and the body to which the face belongs, and the geometric properties of the face;
[0009] Points consist of three-dimensional coordinates and associated volume indexes;
[0010] The overall structure of the mesh includes a set of cells, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces;
[0011] Auxiliary information includes state identifiers added to the unit cell, the relationships between mesh levels added to the mesh, and parallel boundary information after mesh partitioning;
[0012] The mesh after dual transformation includes a set of elements, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces.
[0013] Furthermore, the types of the solid include tetrahedrons, hexahedrons, and polyhedra; the geometric properties of the unit solid include volume and body center coordinates.
[0014] Furthermore, the relationship between the face and the bodies is defined as follows: one is the owner, and the other is the neighbor; the geometric properties of the face include area and normal vector, and the point list and normal vector are specified to point from the owner to the neighbor.
[0015] Furthermore, the associated volume index in the point configuration records a list of all unit volume indexes containing that point.
[0016] Furthermore, the set of units stores all unit instances; the set of faces includes all faces within the mesh; the set of points includes the three-dimensional coordinate information of all vertices, and also stores the associated unit index list; the set of boundary faces and the face list corresponding to the set of boundary faces are used to store boundary face indexes separately, and are classified and managed according to boundary type.
[0017] Furthermore, the status identifiers added to the unit include active and frozen; the mesh hierarchy added to the mesh is the parent-child relationship; and the parallel boundary information after mesh partitioning records the mesh information interaction relationship on the parallel boundary.
[0018] Furthermore, the mesh after dual transformation has the following characteristics: the body center of the element is the vertex of the original mesh, the face center is the midpoint of the edge of the original mesh, and the boundary element is half an element of the original mesh.
[0019] A traversal method for arbitrary polyhedral mesh data structures for fluid simulation is proposed. The method follows a sequential traversal approach, accessing each element in turn according to the storage order of the element set. Then, face traversal is performed, which is an operation process that uses the faces in the mesh as the access objects. The method mainly adopts a sequential traversal approach, accessing each face sequentially through array indexes.
[0020] The beneficial effects of this invention are:
[0021] This invention discloses an arbitrary polyhedral mesh data structure for fluid simulation. By constructing a unified data structure and rules, the polyhedral mesh can simultaneously adapt to arbitrary polyhedra as well as traditional tetrahedrons and hexahedrons. Based on storing 3D coordinates at vertices, faces are defined as ordered lists of vertices, and volumes are enclosed by sets of faces. These three types of structures are linked to form a topological network. This design retains the processing logic of traditional structures while flexibly extending to complex shapes, providing a mesh solution for fluid simulation that combines flexibility and practicality.
[0022] This invention discloses an arbitrary polyhedral mesh data structure for fluid simulation. By discarding edge structures, the polyhedral mesh significantly improves data structure efficiency and computational performance. Removing the independent storage of edges avoids the complexity of maintaining topological relationships, reduces topological data redundancy, and allows flux integration and gradient interpolation in fluid simulations to be performed directly based on surface information.
[0023] This invention discloses an arbitrary polyhedral mesh data structure for fluid simulation. By adding auxiliary information such as element state identifiers and mesh hierarchy associations to the polyhedral mesh, the practicality and efficiency of the mesh can be significantly improved. State identifiers can accurately control the computational participation state of the control unit, such as freezing non-critical regions during nested mesh traversal to reduce redundant calculations, while also supporting function switching during multi-physics coupling. Mesh hierarchy associations establish parent-child mesh relationships, facilitating adaptive refinement / coarsening of local mesh updates and data transfer and collaborative computation between multi-resolution models. Attached Figure Description
[0024] Figure 1 This is a schematic diagram of the unit body structure of the present invention;
[0025] Figure 2 This is a schematic diagram of the surface configuration of the present invention;
[0026] Figure 3 This is a schematic diagram comparing the original mesh and the dual mesh of the present invention. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.
[0028] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.
[0029] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 3 Detailed explanation is as follows:
[0030] Example 1:
[0031] An arbitrary polyhedral mesh data structure for fluid simulation includes element composition, surface composition, point composition, overall mesh composition, auxiliary information, and mesh after dual transformation;
[0032] The composition of a unit cell includes the cell type, a list of faces contained in the unit cell, a list of points contained in the unit cell, the geometric properties of the unit cell, and does not store the adjacency relationships between individuals;
[0033] The composition of a face includes a list of points contained in the face, the relationship between the face and the body to which the face belongs, and the geometric properties of the face;
[0034] Points consist of three-dimensional coordinates and associated volume indexes;
[0035] The overall structure of the mesh includes a set of cells, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces;
[0036] Auxiliary information includes state identifiers added to the unit cell, the relationships between mesh levels added to the mesh, and parallel boundary information after mesh partitioning;
[0037] The mesh after dual transformation includes a set of elements, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces.
[0038] Furthermore, the types of the solid include tetrahedrons, hexahedrons, and polyhedra; the geometric properties of the unit solid include volume and body center coordinates.
[0039] Furthermore, the relationship between the face and the bodies is defined as follows: one is the owner, and the other is the neighbor; the geometric properties of the face include area and normal vector, and the point list and normal vector are specified to point from the owner to the neighbor.
[0040] Furthermore, the associated volume index in the point configuration records a list of all unit volume indexes containing that point.
[0041] Furthermore, the set of units stores all unit instances; the set of faces includes all faces within the mesh; the set of points includes the three-dimensional coordinate information of all vertices, and also stores the associated unit index list; the set of boundary faces and the face list corresponding to the set of boundary faces are used to store boundary face indexes separately, and are classified and managed according to boundary type.
[0042] Furthermore, the status identifiers added to the unit include active and frozen; the mesh hierarchy added to the mesh is the parent-child relationship; and the parallel boundary information after mesh partitioning records the mesh information interaction relationship on the parallel boundary.
[0043] Furthermore, the mesh after dual transformation has the following characteristics: the body center of the element is the vertex of the original mesh, the face center is the midpoint of the edge of the original mesh, and the boundary element is half an element of the original mesh.
[0044] like Figure 1 As shown, the unit cell type is hexahedron; the list of unordered faces is {F0, F1, F2, F3, F4, F5}; the list of unordered points is {N0, N1, N2, N3, N4, N5, N6, N7}; and the geometric properties are volume and body center coordinates.
[0045] like Figure 2 As shown, the ordered point list is: {N0, N1, N2, N3, N4}; the owner cell is V0; the neighboring cell is V1; the geometric properties are area and normal vector (from V0 to V1).
[0046] Example 2:
[0047] An embodiment 1 describes a traversal method for an arbitrary polyhedral mesh data structure for fluid simulation. The method involves sequentially traversing each element according to the storage order of the element set. Then, face traversal is performed. Face traversal is an operation process that uses faces in the mesh as access objects. It mainly adopts a sequential traversal method and accesses each face sequentially through array index.
[0048] The technical solution of this embodiment is described in detail below:
[0049] S1: The element mainly consists of the element's type, a list of its faces, a list of its points, and geometric properties (such as volume and volume center coordinates). (See reference) Figure 1 The specific description is as follows:
[0050] S11: Type of Unit. Clearly indicate the geometric type of the unit, such as tetrahedron, hexahedron, or any polyhedron. This identifier facilitates rapid identification of the unit shape by subsequent algorithms, providing a foundation for targeted processing of different unit types.
[0051] S12: List of Faces: This list clearly records all faces that make up the unit volume through an array of stored face indices. A closed topological structure is established using this list, enabling the association between faces and the volume.
[0052] S13: List of points: A list of points is stored in an index array to clearly record all points that make up the unit volume. This list establishes a closed topological structure, realizing the relationship between points and the volume.
[0053] S14: Geometric Attributes: Stores key geometric information of the unit cell, including volume and volume center coordinates, which are calculated based on vertex coordinates.
[0054] S2: A face primarily consists of a list of points, relationships with other objects (specifying one owner and another neighbor), and geometric properties (such as area and normal vector). (See reference) Figure 2 The specific description is as follows:
[0055] S21: List of contained points. The face forms a closed vertex cycle by storing vertex indices in an ordered manner. The order of the points follows the right-hand rule to ensure the consistency of the normal vector direction.
[0056] S22: Ownership Relationships. The topological ownership of a face is defined by two attributes: Owner and Neighbor. The owner represents the primary unit to which the face belongs, while the neighbor is another unit that shares the face with the owner. When the neighbor is None, the face is a boundary face.
[0057] S23: Geometric Attributes. The area of the surface is calculated using vertex coordinates, and normal vectors are generated using mathematical methods such as vector cross products, combined with the point list order. Normal vectors are uniformly defined to point from their owner to their neighbors, ensuring the directionality of flux calculation and providing accurate geometric information support for flux calculation and boundary condition application in fluid simulations.
[0058] S3: A node primarily consists of three-dimensional coordinates and associated volume indexes. A detailed description follows:
[0059] S31: Three-dimensional coordinates. Stores the precise location (x, y, z) of a point in space, which is the foundation for constructing complex structures such as surfaces and volumes.
[0060] S32: Associated volume index. Records a list of all unit volume indices containing this point, establishing a bidirectional link between the point and the volume. This index allows for quick location of all unit volumes to which the point belongs.
[0061] S4: The overall structure of a mesh mainly includes a set of elements, a set of faces, a set of points, a set of boundary faces, and a corresponding list of faces. A detailed description follows:
[0062] S41: The collection of elements {Element}. Stores all element instances, including tetrahedrons, hexahedrons, polyhedra, and other types. Each element constructs a closed structure through a list of face indices and carries geometric attributes such as volume and centroid, as well as state identifiers such as active and frozen. It is the basic unit for physics field calculations.
[0063] S42: The set of faces {Face}. It contains all faces within the mesh, divided into internal faces connecting two cells and boundary faces belonging to only one cell. The topological relationship between the face and the cell is defined by the owner and neighbor attributes. The normal vector points from the owner to the neighbor, providing a directional basis for flux calculation.
[0064] S43: The set of points {Node}. It records the 3D coordinate information of all vertices and stores the associated unit cell index list. It supports a vertex being shared by multiple unit cells and is the geometric basis for constructing surfaces and volumes.
[0065] S44: The set of boundary surfaces and the corresponding list of surfaces. Boundary surface indexes are stored separately and categorized by boundary type (e.g., entrance, wall, exit) for easy and quick location of boundary areas, facilitating the application of boundary conditions and visualization rendering.
[0066] S5: Auxiliary information mainly includes adding status markers to unit cells, adding mesh hierarchy associations to the mesh, and parallel boundary information after mesh partitioning. Specific descriptions are as follows:
[0067] S51: Element State Identifier. A state identifier (such as active, frozen, etc.) is added to the element to dynamically control the computational participation status of the control unit. For example, in nested mesh traversal, elements in non-critical regions can be set to a frozen state to avoid invalid calculations; in multiphysics coupled simulations, element properties can be quickly changed through state switching, achieving functional conversion without reconstructing the mesh, significantly improving computational efficiency and resource utilization.
[0068] S52: Mesh Hierarchical Association. A hierarchical association mechanism is added to the mesh structure, clearly defining the hierarchy between parent and child meshes, supporting mesh aggregation and adaptive mesh operations. In mesh aggregation, the parent mesh describes large-scale flow, while the child mesh describes small-scale flow. Data transfer algorithms can be constructed through hierarchical association, and local refinement / coarsening can also be achieved, ensuring seamless data transfer and collaborative computation between models of different resolutions.
[0069] S53: Parallel Boundary Information. For parallel computing scenarios after mesh partitioning, this records the mesh information interaction relationships at the parallel boundaries. In large-scale numerical simulations, when the mesh is divided into multiple sub-regions and assigned to different computing nodes, parallel boundary information can accurately define the data communication rules between nodes, ensuring the consistency of computational results across nodes and significantly improving the efficiency and stability of parallel computing.
[0070] S6: Dualized meshes construct novel mesh systems that satisfy polyhedral structures by geometrically transforming the original mesh. Their data descriptions exhibit distinct topological and geometric characteristics. (Reference) Figure 3 The specific information is as follows:
[0071] S61: Geometric Correspondence: The volume centers of the dualized mesh correspond one-to-one with the vertices of the original mesh, while the face centers are located at the midpoints of the edges of the original mesh. This correspondence redefines the topological connectivity of the mesh, forming a completely new geometric structure.
[0072] S62: Polyhedral structure characteristics: The mesh after dual transformation still retains the polyhedral structure. Whether it is the original mesh of tetrahedron, hexahedron or any complex polyhedron, the corresponding polyhedral mesh can be generated after dualization, ensuring the universality of data structure and algorithm compatibility.
[0073] S63: Boundary element definition: The boundary element of the dual mesh consists of half an element of the original mesh. This design retains the boundary information of the original mesh and adapts to the topological rules of the dual mesh. Special processing of the solution algorithm is required when dealing with boundary conditions.
[0074] S7: Traversal is the core mechanism for polyhedral mesh data manipulation, mainly including two modes: cell traversal and face traversal. Its design logic and application scenarios are as follows:
[0075] S71: Element Traversal. Element traversal primarily employs a sequential traversal method, accessing each element in turn according to the storage order of the element set, such as array indexing or list order. This method is suitable for global batch operations, such as element data initialization and statistics, without relying on the topological relationships between elements. For fluid simulation, element traversal is used for integrating source terms of the control equations (the influence of volume forces, chemical reaction source terms, and porous media resistance on the fluid state), calculating element physical quantities (updating basic physical quantities in the lattice scheme, physical quantities in turbulence model equations, volume fractions in multiphase flow models, etc.), etc.
[0076] S72: Face Traversal. Face traversal is an operation process that uses faces in a mesh as access objects. It mainly adopts a sequential traversal method, accessing each face in turn through array indices. Simultaneously, based on the face data structure, it is easy to obtain information about elements sharing that face. This method is suitable for calculating global face properties and face fluxes in the governing equations. For fluid simulation, face traversal is used for convection terms, diffusion terms, gradients, etc., in the governing equations. These calculations are closely linked to adjacent elements through face traversal, discretizing the continuous governing equations and enabling numerical simulation of complex fluid flow phenomena.
[0077] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0078] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.
Claims
1. A method for traversing arbitrary polyhedral mesh data structures for fluid simulation, characterized in that, Following the sequential traversal method, each unit is accessed in turn according to the storage order of the unit set; then, face traversal is performed. Face traversal is an operation process that uses the faces in the mesh as the access objects, and uses the sequential traversal method to access each face in turn through array index. The data structure includes unit cell composition, surface composition, point composition, overall mesh composition, auxiliary information, and mesh after dual transformation; S1. The composition of a unit cell includes the type of the cell, the list of faces contained in the unit cell, the list of points contained in the unit cell, the geometric properties of the unit cell, and does not store the adjacency relationships between individuals; S2. Surface composition includes a list of points contained in the surface, the relationship between the surface and the solid to which the surface belongs, and the geometric properties of the surface; S3. Points consist of three-dimensional coordinates and associated volume indexes; S4. The overall structure of the mesh includes a set of cells, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces; S5. Auxiliary information includes state identifiers added to the unit cell, the relationships between mesh levels added to the mesh, and parallel boundary information after mesh partitioning; S51. Element State Identifier: A state identifier is added to the element to indicate the computational participation status of the dynamic control unit; in nested mesh traversal, elements in non-critical regions are set to a frozen state to avoid invalid calculations; in multiphysics coupling simulation, element properties can be quickly changed through state switching, and functional conversion can be achieved without reconstructing the mesh, which greatly improves computational efficiency and resource utilization. S52. Mesh Hierarchical Association: A hierarchical association mechanism is added to the mesh structure to clarify the subordinate relationship between parent and child meshes, and to support mesh aggregation and adaptive mesh operations. In mesh aggregation, the parent mesh describes large-scale flow and the child mesh describes small-scale flow. Through hierarchical association, data transfer algorithms can be constructed to achieve local refinement / coarsening, and to ensure seamless data transfer and collaborative computation between models of different resolutions. S53. Parallel Boundary Information: For parallel computing scenarios after grid partitioning, it records the interaction relationship of grid information on the parallel boundary. In large-scale numerical simulations, when the grid is divided into multiple sub-regions and assigned to different computing nodes, the parallel boundary information accurately defines the data communication rules between nodes, ensuring the consistency of the calculation results of each node and significantly improving the efficiency and stability of parallel computing. S6. The mesh after dual transformation includes a set of elements, a set of faces, a set of points, a set formed by boundary faces, and a list of faces corresponding to the set formed by boundary faces.
2. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 1, characterized in that, The types of the solids include tetrahedrons, hexahedrons, and polyhedra; the geometric properties of the unit solids include volume and body-center coordinates.
3. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 2, characterized in that, The relationship between a face and its constituent bodies is defined as follows: one body is the owner, and the other is the neighbor. The geometric properties of a face include its area and normal vector, and the point list and normal vector are specified to point from the owner to the neighbor.
4. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 3, characterized in that, The associated volume index in the point structure records a list of all unit volume indexes that contain that point.
5. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 4, characterized in that, The set of units stores all unit instances; the set of faces includes all faces within the mesh; the set of points includes the 3D coordinate information of all vertices, and also stores the associated unit index list; the set of boundary faces and the list of faces corresponding to the set of boundary faces are used to store boundary face indexes separately and are classified and managed according to boundary type.
6. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 5, characterized in that, The status identifiers added to the unit include active and frozen; the mesh hierarchy added to the mesh is the subordinate relationship between parent and child units; after mesh partitioning, the parallel boundary information records the mesh information interaction relationship on the parallel boundary.
7. The traversal method for arbitrary polyhedral mesh data structures for fluid simulation according to claim 6, characterized in that, The mesh after dual transformation has the following characteristics: the body center of the element is the vertex of the original mesh, the face center is the midpoint of the edge of the original mesh, and the boundary element is half an element of the original mesh.