Adaptive fork tree grid computing method and device for complex micro-scale structure

Abstract

This application relates to an adaptive cross-tree mesh computation method and apparatus for complex microscale structures. The method is applicable to efficient numerical solutions in automatically generated cross-tree meshes for complex micro-surfaces. Addressing the problems of large local geometric scale spans, complex microstructure surface morphology, difficulty in generating high-quality meshes near boundaries, and insufficient adaptability of traditional solvers to special meshes in complex microscale structure scenarios of aircraft, this invention constructs an adaptive cross-tree mesh computation method for complex microscale structures. By combining the adaptive cross-tree mesh with a flux-solving algorithm, stable and efficient numerical solutions for flow fields of complex shapes can be achieved, thereby improving the flexibility of mesh generation, flow field resolution, and overall computational efficiency under complex configuration conditions.

Description

Technical Field

[0001] This invention belongs to the field of computational fluid dynamics technology, and relates to an adaptive cross-tree mesh calculation method and apparatus for complex microscale structures. Background Technology

[0002] With the increasing complexity of hypersonic vehicle missions and the increasingly harsh flight environments, their optimized design faces severe challenges in aerodynamic heating and thermal protection. Against this backdrop, the fabrication of surfaces with nanometer to submicron roughness has shown great application potential. However, numerical simulations of such microscale surface structures are currently limited by the prohibitively high cost of mesh generation.

[0003] In the field of computational fluid dynamics, discretization methods are broadly classified into two categories: structured meshes and unstructured meshes. Structured meshes, with their ordered cell arrangement and regular data structure, offer significant advantages such as high generation efficiency, good numerical accuracy, simple computational matrix structure, and excellent locality of memory access. However, their strict topological connectivity also limits their applicability, especially when dealing with geometry with complex microscale features, such as nanoscale roughness, fine pores, or intricate surface morphology. It is difficult to achieve efficient meshing without compromising mesh orthogonality and uniformity, often resulting in insufficient local mesh refinement or a dramatic increase in overall mesh size.

[0004] In contrast, unstructured meshes have a natural ability to adapt to complex geometries, and can flexibly fill regions of arbitrary shapes with triangular, tetrahedral, or polyhedral elements. However, when dealing with surfaces with microscale structures, traditional unstructured mesh methods also face significant challenges: on the one hand, when generating regions with obvious anisotropic characteristics such as boundary layers, it is difficult to achieve smooth transitions and high aspect ratio stretching while maintaining element quality; on the other hand, for multi-scale coupled surface morphologies, distorted elements or locally overly dense meshes are prone to occur, leading to decreased numerical stability, reduced computational efficiency, and complex mesh quality control, making automated generation difficult.

[0005] Furthermore, given the complex microscale structures on aircraft surfaces, manually drawing high-quality boundary layer meshes often heavily relies on the experience and skills of the artist, and requires a significant amount of time and effort. Therefore, many automated mesh generation methods have been developed. Among these, the Cartesian mesh generation method offers advantages such as fast generation speed, strong robustness, high automation, and good mesh quality; however, its poor body fit makes it difficult to accurately capture near-wall flow details, thus affecting simulation accuracy.

[0006] To address the challenge of generating meshes for microscale structures, a novel anisotropic adaptive mesh generation technique for complex shapes has been developed. This technique can automatically generate meshes that meet basic requirements such as orthogonality and continuity, and exhibits good body fit. Its general structure is as follows:Figure 1 As shown.

[0007] Existing solvers are primarily designed for traditional structured and unstructured meshes, and their data structures and iterative logic cannot be directly applied to the cross-tree meshes involved in this scheme. Although such meshes are topologically similar to Cartesian meshes, their anisotropic adaptive characteristics based on orthogonal field growth, multi-level parent-child face relationships, and dynamic refinement mechanisms are fundamentally different from traditional uniform or simple adaptive Cartesian meshes, making it difficult for general solvers to be directly transferred or compatible. Summary of the Invention

[0008] To address the problems existing in the above-mentioned traditional methods, this invention proposes an adaptive cross-tree mesh calculation method and apparatus for complex microscale structures.

[0009] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: On the one hand, an adaptive cross-tree mesh computation method for complex microscale structures is provided, which includes the following steps: Step 1: Obtain the geometric description of the complex microscale structure of the aircraft, establish the spatial index of the computational domain, construct an initial uniform cross-tree mesh, and then generate an adaptive cross-tree mesh of the complex microscale structure of the aircraft through orthogonal field alignment and geometric boundary processing.

[0010] Step 2: Abstract all cell types in the adaptive crosstree mesh into generalized polygons, use the shoelace formula to calculate the area and centroid of each mesh cell, and construct a unified memory data structure.

[0011] Step 3: Initialize the flow field state variables for each grid cell.

[0012] Step 4: Reconstruct the flow field state variables on the left and right sides of the interface using a spatial second-order precision format.

[0013] Step 5: Based on the flow field state variables on both sides of the interface obtained from the reconstruction, calculate the interface flux using the Riemann approximation solver; the interface flux includes: convective flux and viscous flux.

[0014] Step 6: Based on the interface flux and conserved variables, solve the control equations using a time format, update the flow field state variables, and continue to step 4 to continue the calculation until the preset termination condition is met, thus obtaining the flow field calculation results of the complex microscale structure of the aircraft.

[0015] On the other hand, an adaptive cross-tree grid computing device for complex microscale structures is also provided, the device comprising: The adaptive cross-tree mesh generation module is used to obtain the geometric description of the complex micro-scale structure of the aircraft, establish the spatial index of the computational domain, construct the initial uniform cross-tree mesh, and then generate the adaptive cross-tree mesh of the complex micro-scale structure of the aircraft through orthogonal field alignment and geometric boundary processing.

[0016] The grid cell abstraction module is used to abstract all cell types in the adaptive cross-tree grid into generalized polygons, calculate the area and centroid of each grid cell using the shoelace formula, and construct a unified memory data structure.

[0017] The flow field initialization module is used to initialize the flow field state variables for each grid cell.

[0018] The flow field reconstruction module is used to reconstruct the flow field state variables on the left and right sides of the interface using a spatial second-order precision format.

[0019] The interface flux calculation module is used to calculate the interface flux using a Riemann approximation solver based on the flow field state quantities on both sides of the reconstructed interface. The interface flux includes convective flux and viscous flux.

[0020] The flow field calculation module is used to solve the control equations in a time format based on the interface flux and conserved variables, update the flow field state variables, and then transfer to the flow field reconstruction module to continue the calculation until the preset termination condition is met, so as to obtain the flow field calculation results of the complex microscale structure of the aircraft.

[0021] The aforementioned adaptive cross-tree mesh computation method and apparatus for complex microscale structures are applicable to efficient numerical solutions in automatically generated cross-tree meshes for complex micro-surfaces. Addressing the challenges of large local geometric scales, complex microstructure surface morphology, difficulty in generating high-quality meshes near boundaries, and insufficient adaptability of traditional solvers to special meshes in complex microscale structure scenarios of aircraft, this invention constructs an adaptive cross-tree mesh computation method for complex microscale structures. By combining the adaptive cross-tree mesh with a flux-solving algorithm, stable and efficient numerical solutions for flow fields of complex shapes can be achieved, thereby improving the flexibility of mesh generation, flow field resolution, and overall computational efficiency under complex configuration conditions. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1Here is an example diagram of an adaptive non-uniform cross-tree mesh in one embodiment; Figure 2 This is a schematic diagram of an adaptive cross-tree mesh computation method for complex microscale structures in one embodiment; Figure 3 This is a schematic diagram of the mesh cell type in one embodiment, wherein Figure 3 Image (a) is a schematic diagram of a four-node element mesh. Figure 3 (b) is a schematic diagram of a five-node mesh element. Figure 3 (c) is a schematic diagram of a six-node mesh element. Figure 3 (d) is a schematic diagram of a seven-node mesh element. Figure 3 (e) is a schematic diagram of an eight-node mesh element; Figure 4 This is a schematic diagram of the array used to store grid cell node information in one embodiment; Figure 5 This is a schematic diagram of linear reconstruction of the lattice-centered scheme in a two-dimensional case in one embodiment; Figure 6 This is a schematic diagram of flux calculation in a two-dimensional case in one embodiment; Figure 7 This is a schematic diagram of the cylindrical mesh portion in one embodiment, wherein... Figure 7 (a) is a schematic diagram of the structural mesh. Figure 7 (b) is a schematic diagram of a cross-tree grid; Figure 8 This is a flow simulation pressure contour plot in one embodiment. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0026] It should be noted that, in this document, the reference to "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The presentation of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will understand that the embodiments described herein can be combined with other embodiments. The term "and / or" as used herein refers to any combination of one or more of the associated listed items, and all possible combinations, including such combinations.

[0027] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0028] In one embodiment, such as Figure 2 As shown, an adaptive cross-tree mesh computation method for complex microscale structures is provided, which may include the following processing steps 1 to 6: Step 1: Obtain the geometric description of the complex microscale structure of the aircraft, establish the spatial index of the computational domain, construct an initial uniform cross-tree mesh, and then generate an adaptive cross-tree mesh of the complex microscale structure of the aircraft through orthogonal field alignment and geometric boundary processing.

[0029] Specifically, the process involves obtaining the geometric description of the complex microscale structure of the aircraft, inputting the surface mesh, calculating the propulsion height of the array, finding the minimum electric potential, generating equipotential surfaces, generating the layer mesh based on the geometric topological connection relationship, and splitting or merging the elements according to the geometric anisotropy adaptive strategy. This process is repeated layer by layer to generate the mesh until the required number of mesh layers is reached.

[0030] Step 2: Abstract all cell types in the adaptive crosstree mesh into generalized polygons, use the shoelace formula to calculate the area and centroid of each mesh cell, and construct a unified memory data structure.

[0031] Specifically, the cell types in this adaptive crosstree mesh cover various forms from four nodes to eight nodes, such as... Figure 3 As shown, where Figure 3 Image (a) is a schematic diagram of a four-node element mesh. Figure 3 (b) is a schematic diagram of a five-node mesh element. Figure 3 (c) is a schematic diagram of a six-node mesh element. Figure 3 (d) is a schematic diagram of a seven-node mesh element. Figure 3Figure (e) shows a schematic diagram of an eight-node mesh element. To uniformly handle these different types of elements, this method abstracts them all as generalized polygons for discretization and computation. Since a single element can contain a maximum of eight nodes, the system creates an array with a dimension of "8 × total number of elements" to centrally store the node information of all elements. The specific storage structure for the mesh element node information is as follows... Figure 4 As shown.

[0032] The various units, ranging from four to eight nodes, generated in the cross-tree mesh are uniformly abstracted into generalized polygons for processing. A compact "8 × total number of units" array storage structure is designed to achieve efficient and unified management of complex unit topologies.

[0033] The shoelace formula is adopted as a universal calculation method for the area and centroid of all types of mesh elements, which ensures the uniformity, accuracy and simplicity of geometric calculations during mesh adaptation.

[0034] Step 3: Initialize the flow field state variables for each grid cell.

[0035] Step 4: Reconstruct the flow field state variables on the left and right sides of the interface using a spatial second-order precision format.

[0036] Specifically, this method uses the finite volume method with a grid center to solve the Navier-Stokes equations, assuming that the flow field state variables are stored at the grid center point. Therefore, in order to calculate the flux at the grid interface, the flow field information needs to be reconstructed.

[0037] Step 5: Based on the flow field state variables on both sides of the interface obtained from the reconstruction, calculate the interface flux using the Riemann approximation solver; the interface flux includes: convective flux and viscous flux.

[0038] Specifically, a set of conservation-type information transfer and numerical flux calculation methods were designed for the special interfaces generated between different levels of the cross-tree mesh, to ensure the strict conservation of physical quantities and the accuracy and stability of calculations when crossing the interface between coarse and fine meshes.

[0039] After reconstructing the flow field state variables on both sides of the interface, the Riemann approximation solver is used to calculate the interface flux. For each surface, its convective flux needs to be calculated. and viscous flux .

[0040] Step 6: Based on the interface flux and conserved variables, solve the control equations using a time format, update the flow field state variables, and continue to step 4 to continue the calculation until the preset termination condition is met, thus obtaining the flow field calculation results of the complex microscale structure of the aircraft.

[0041] Specifically, after obtaining the interface flux, the ordinary differential equations are solved using a time-space format to update the flow field state variables and obtain the flow field at the next time step. The system then checks if the calculation is complete; if so, the result is output; otherwise, the loop continues.

[0042] This method enables efficient numerical solutions for anisotropic adaptive cross-tree meshes grown from orthogonal fields, solving the problem that traditional solvers cannot be directly applied to such meshes.

[0043] The aforementioned adaptive cross-tree mesh computation method for complex microscale structures is applicable to efficient numerical solutions in automatically generated cross-tree meshes for complex micro-surfaces. Addressing the challenges of large local geometric scales, complex microstructure surface morphology, difficulty in generating high-quality meshes near boundaries, and insufficient adaptability of traditional solvers to special meshes in complex microscale aircraft scenarios, this invention constructs an adaptive cross-tree mesh computation method for complex microscale structures. By combining the adaptive cross-tree mesh with a flux-solving algorithm, stable and efficient numerical solutions for flow fields of complex shapes can be achieved, thereby improving the flexibility of mesh generation, flow field resolution, and overall computational efficiency under complex configuration conditions.

[0044] While ensuring the solution of the aforementioned special meshes, this method's core algorithm is also compatible with traditional structured and unstructured meshes, achieving a universal solution capability of "one algorithm for multiple types of meshes".

[0045] In one embodiment, step 2 includes: creating an array to centrally store the node information of all grid cells, and storing the node information of all grid cells in the array, the array having a dimension of 8 × the total number of cells; calculating the area and centroid of each grid cell using the shoelace formula based on the node information of each grid cell; the formula for calculating the area and centroid of a grid cell is: ; in, S and( C x , C y ) represent the area and centroid coordinates of the mesh cell, respectively. x j , y j )express n The first polygon j The coordinates of each vertex, and have .

[0046] Construct a unified in-memory data structure; the in-memory data structure is used to store the area, centroid, face normal, face area and adjacency relationship of grid cells.

[0047] Specifically, in terms of geometric quantity calculation, to accommodate potential dangling nodes and achieve unified processing for all element types, this method uses the shoelace formula to calculate the area and centroid of each element. This method has the advantages of uniformity of form and applicability to arbitrarily simple polygons. Its specific calculation expression is shown in the formulas for calculating the area and centroid of the mesh element mentioned above. A unified memory data structure is constructed, and the system stores key information such as element area, centroid, face normal vector, face area, and adjacency relationships, providing fast access support for subsequent throughput calculation and gradient reconstruction.

[0048] In one embodiment, the flow field state quantities in step 3 include: temperature, velocity, pressure, and density.

[0049] In one embodiment, step 4 includes: performing calculations using a spatial second-order precision scheme, and reconstructing the flow field state variables on the left and right sides of the interface using a reconstruction formula; the reconstruction formula is: ; in, , These represent the flow field state variables on the left and right sides of the interface obtained through the reconstruction formula, respectively. , These represent adjacent grid cells on both sides of the interface. i and grid cells j The flow field state at the center of the unit; yes In grid cells i The gradient at the center, , Represents grid cells i Limiter function, yes In grid cells j The gradient at the center, Represents grid cells j Limiter function, and These represent the vectors pointing from the centroids of the left and right grid cells to the face center, respectively. The linear reconstruction of the lattice center scheme in the two-dimensional case is as follows: Figure 5 As shown.

[0050] Specifically, spatial second-order accuracy means that the error of the numerical solution in the spatial direction is proportional to the square of the grid size. In the boundary cell method, achieving spatial second-order accuracy means ensuring that the difference between the numerical solution and the actual physical quantity at the boundary decreases at a faster rate as the grid size decreases.

[0051] In one embodiment, the calculation process for flux in step 5 includes: setting the conservation variable W in the 3D case as: ; in, W As a conserved variable, For density, u , v , w They are respectively x , y , z Directional velocity, E For total energy.

[0052] Based on density, velocity, total enthalpy, and pressure, the flow rate is determined as follows: ; in, To control the circulation volume, p For pressure, H For total enthalpy, V Perpendicular to surface element d S Inverter speed, V Defined as velocity vector ( u , v , w ) and unit normal vector ( , , The scalar product of ), i.e.: .

[0053] In one embodiment, the calculation process of viscous flux in step 5 includes: determining the viscous flux as follows based on the stress tensor: ; in, For viscous flux, , and Representing stress tensors respectively exist x , y , z Normal stress in the direction, , and Representing stress tensors respectively exist x , y , z Tangential stress in the direction; , and for: ; in, u , v , w They are respectively x , y , z Directional velocity, The thermal conductivity coefficient, For temperature, To act perpendicular to x The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft x directional components, To act perpendicular to z The stress in the plane of the shaft x directional components, To act perpendicular to x The stress in the plane of the shaft z directional components, To act perpendicular to z The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft z The directional component. A schematic diagram of flux calculation in the two-dimensional case is shown below. Figure 6 As shown.

[0054] In one embodiment, the governing equation in step 6 is: ; in, W As a conserved variable, For viscous flux, To control the circulation volume, It is a control volume within a two-dimensional computational domain. For the source term vector, t For time, The boundary of the control body.

[0055] In a verification embodiment, the method has been successfully applied to a flow simulation around a cylinder, where the cylinder radius is... Mach number unit Reynolds number , static temperature The cylindrical wall is subjected to no-slip isothermal conditions, and the wall temperature is... Trump's number Numerical simulations were performed using a structured grid with 16,000 grid elements and a cross-tree grid with 36,476 grid elements. The grids are as follows: Figure 7 As shown, where Figure 7 (a) is a schematic diagram of the structural mesh. Figure 7Figure (b) shows a schematic diagram of the cross-tree mesh. The structured mesh uses an implicit LU-SGS time-progression scheme, with second-order spatial reconstruction. The reconstruction limiter is the van Albada limiter, and the flux discretization uses the HLLE scheme. The cross-tree mesh uses an explicit second-order Runge-Kutta time-progression scheme, with second-order spatial reconstruction combined with the Venkatakrishnan limiter, and the flux discretization uses the HLLE scheme. The flow simulation pressure contour plot is shown below. Figure 8 As shown, the structural mesh calculation results are displayed in the form of cloud maps, and the cross-tree mesh calculation results are displayed in the form of contour lines. The results show good agreement in both the overall flow field structure and local feature locations.

[0056] In the Mach number of the flow In this case, the empirical formula for the shock wave separation distance can be used to calculate the shock wave separation distance. : ; The theoretical shock wave detachment distance was calculated. The shock wave detachment distance obtained from numerical simulation results is approximately... The relative error is approximately 3.62%. Since the above formula applies to the adiabatic wall assumption, the shock wave detachment distance will be slightly reduced for isothermal cold walls, while the actual... Less than the theoretical value The results are as expected. The above results demonstrate that the proposed cross-tree grid calculation method has good computational accuracy.

[0057] It should be understood that, although the above Figure 2 The steps are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated in this document, there is no strict order in which these steps are executed; they can be performed in other orders. Furthermore, the above... Figure 2 At least some of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0058] In one embodiment, an adaptive cross-tree grid computing device for complex microscale structures is also provided, including: The adaptive cross-tree mesh generation module is used to obtain the geometric description of the complex micro-scale structure of the aircraft, establish the spatial index of the computational domain, construct the initial uniform cross-tree mesh, and then generate the adaptive cross-tree mesh of the complex micro-scale structure of the aircraft through orthogonal field alignment and geometric boundary processing.

[0059] The grid cell abstraction module is used to abstract all cell types in the adaptive cross-tree grid into generalized polygons, calculate the area and centroid of each grid cell using the shoelace formula, and construct a unified memory data structure.

[0060] The flow field initialization module is used to initialize the flow field state variables for each grid cell.

[0061] The flow field reconstruction module is used to reconstruct the flow field state variables on the left and right sides of the interface using a spatial second-order precision format.

[0062] The interface flux calculation module is used to calculate the interface flux using a Riemann approximation solver based on the flow field state quantities on both sides of the reconstructed interface. The interface flux includes convective flux and viscous flux.

[0063] The flow field calculation module is used to solve the control equations in a time format based on the interface flux and conserved variables, update the flow field state variables, and then transfer to the flow field reconstruction module to continue the calculation until the preset termination condition is met, so as to obtain the flow field calculation results of the complex microscale structure of the aircraft.

[0064] In one embodiment, the grid cell abstraction processing module is further configured to create an array for centrally storing the node information of all grid cells, and store the node information of all grid cells in the array, the array having a dimension of 8 × the total number of cells; based on the node information of each grid cell, the area and centroid of each grid cell are calculated using the shoelace formula; the formula for calculating the area and centroid of a grid cell is: ; in, S and( C x , C y ) represent the area and centroid coordinates of the mesh cell, respectively. x j , y j )express n The first polygon j The coordinates of each vertex, and have .

[0065] Construct a unified in-memory data structure; the in-memory data structure is used to store the area, centroid, face normal, face area and adjacency relationship of grid cells.

[0066] In one embodiment, the flow field reconstruction module is further configured to perform calculations using a second-order spatial precision format, and reconstruct the flow field state variables on the left and right sides of the interface using a reconstruction formula; the reconstruction formula is: ; in, , These represent the flow field state variables on the left and right sides of the interface obtained through the reconstruction formula, respectively. , These represent adjacent grid cells on both sides of the interface. i and grid cells j The flow field state at the center of the unit; express In grid cells i The gradient at the center, , Represents grid cells i Limiter function, yes In grid cells j The gradient at the center, Represents grid cells j Limiter function, and These represent the vectors pointing from the centroid of the left and right grid cells to the center of the face, respectively.

[0067] In one embodiment, the flux calculation process in the interface flux calculation module includes: setting the conservation variable W in the 3D case as: ; in, W As a conserved variable, For density, u , v , w They are respectively x , y , z Directional velocity, E For total energy.

[0068] Based on density, velocity, total enthalpy, and pressure, the flow rate is determined as follows: ; in, To control the circulation volume, p For pressure, H For total enthalpy, V Perpendicular to surface element d S Inverter speed, V Defined as velocity vector ( u , v , w ) and unit normal vector ( , , ) scalar product.

[0069] In one embodiment, the calculation process of viscous flux in the interface flux calculation module includes: determining the viscous flux as follows based on the stress tensor: ; in, For viscous flux, , and Representing stress tensors respectively exist x , y , z Normal stress in the direction, , and Representing stress tensors respectively exist x , y , z Tangential stress in the direction; , and for: ; in, u , v , w They are respectively x , y , z Directional velocity, The thermal conductivity coefficient, For temperature, To act perpendicular to x The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft x directional components, To act perpendicular to z The stress in the plane of the shaft x directional components, To act perpendicular to x The stress in the plane of the shaft z directional components, To act perpendicular to z The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft z The directional component.

[0070] In one embodiment, the governing equations in the flow field calculation module are: ; in,W As a conserved variable, For viscous flux, To control the circulation volume, It is a control volume within a two-dimensional computational domain. For the source term vector, t For time, The boundary of the control body.

[0071] It is understood that for a detailed explanation of the adaptive cross-tree grid computing device for complex microscale structures, please refer to the corresponding explanations of the various embodiments of the adaptive cross-tree grid computing method for complex microscale structures above, and will not be repeated here. Each module in the aforementioned adaptive cross-tree grid computing device for complex microscale structures can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of a device with data processing capabilities, or stored in software in the memory of the aforementioned device, so that the processor can call and execute the operations corresponding to each module. The aforementioned device can be, but is not limited to, various types of data processing computer devices already existing in the art.

[0072] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0073] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and all such modifications and improvements fall within the scope of protection of this application.

Claims

1. An adaptive cross-tree mesh computation method for complex microscale structures, characterized in that, Including the following steps: Step 1: Obtain the geometric description of the complex microscale structure of the aircraft, establish the spatial index of the computational domain, construct an initial uniform cross-tree mesh, and then generate an adaptive cross-tree mesh of the complex microscale structure of the aircraft through orthogonal field alignment and geometric boundary processing. Step 2: Abstract all cell types in the adaptive cross-tree mesh into generalized polygons, calculate the area and centroid of each mesh cell using the shoelace formula, and construct a unified memory data structure; Step 3: Initialize the flow field state variables for each grid cell; Step 4: Reconstruct the flow field state variables on the left and right sides of the interface using a spatial second-order precision scheme; Step 5: Based on the flow field state variables on both sides of the reconstructed interface, calculate the interface flux using the Riemann approximation solver; the interface flux includes: convective flux and viscous flux. Step 6: Based on the interface flux and conserved variables, solve the governing equations using a time-based format to update the flow field state variables. Proceed back to Step 4 for further calculations until the preset termination condition is met, obtaining the flow field calculation results for the complex microscale structure of the aircraft. The governing equations are: in, W As a conserved variable, For viscous flux, To control the circulation volume, It is a control volume within a two-dimensional computational domain. For the source term vector, t For time, The boundary of the control body Step 4 includes: performing calculations using a second-order spatial precision scheme, and reconstructing the flow field state variables on the left and right sides of the interface using a reconstruction formula; the reconstruction formula is: in, , These represent the flow field state variables on the left and right sides of the interface obtained through the reconstruction formula, respectively. , These represent adjacent grid cells on both sides of the interface. i and grid cells j The flow field state at the center of the unit; yes In grid cells i The gradient at the center, , Represents grid cells i Limiter function, yes In grid cells j The gradient at the center, Represents grid cells j Limiter function, and These represent the vectors pointing from the centroid of the left and right grid cells to the center of the face, respectively.

2. The adaptive cross-tree mesh computation method for complex microscale structures according to claim 1, characterized in that, Step 2 includes: Create an array to centrally store the node information of all grid cells, and store the node information of all grid cells in the array. The dimension of the array is 8 × the total number of cells. Based on the node information of each grid cell, the area and centroid of each grid cell are calculated using the shoelace formula; the formulas for calculating the area and centroid of a grid cell are as follows: in, S and( C x , C y ) represent the area and centroid coordinates of the mesh cell, respectively. x j , y j )express n The first polygon j The coordinates of each vertex, and have ; Construct a unified memory data structure; the memory data structure is used to store the area, centroid, face normal vector, face area and adjacency relationship of grid cells.

3. The adaptive cross-tree mesh computation method for complex microscale structures according to claim 1, characterized in that, The flow field state quantities mentioned in step 3 include: temperature, velocity, pressure, and density.

4. The adaptive cross-tree mesh computation method for complex microscale structures according to claim 1, characterized in that, Step 5, the calculation process for the flow rate, includes: In the 3D case, the conserved variable W is set as follows: in, W As a conserved variable, For density, u , v , w They are respectively x , y , z Directional velocity, E For total energy; Based on density, velocity, total enthalpy, and pressure, the flow rate is determined as follows: in, To control the circulation volume, p For pressure, H For total enthalpy, V Perpendicular to surface element d S Inverter speed, V Defined as velocity vector ( u , v , w ) and unit normal vector ( , , ) scalar product.

5. The adaptive cross-tree mesh computation method for complex microscale structures according to claim 1, characterized in that, The calculation process for viscous flux in step 5 includes: Based on the stress tensor, the viscous flux is determined as follows: in, For viscous flux, , and Representing stress tensors respectively exist x , y , z Normal stress in the direction, , and Representing stress tensors respectively exist x , y , z Tangential stress in the direction; , and for: in, u , v , w They are respectively x , y , z Directional velocity, k The thermal conductivity coefficient, T For temperature, To act perpendicular to x The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft x directional components, To act perpendicular to z The stress in the plane of the shaft x directional components, To act perpendicular to x The stress in the plane of the shaft z directional components, To act perpendicular to z The stress in the plane of the shaft y directional components, To act perpendicular to y The stress in the plane of the shaft z The directional component.

6. An adaptive cross-tree grid computing device for complex microscale structures, characterized in that, include: The adaptive cross-tree mesh generation module is used to obtain the geometric description of the complex micro-scale structure of the aircraft, establish the spatial index of the computational domain, construct the initial uniform cross-tree mesh, and then generate the adaptive cross-tree mesh of the complex micro-scale structure of the aircraft through orthogonal field alignment and geometric boundary processing. The grid cell abstraction processing module is used to abstract all cell types in the adaptive cross-tree grid into generalized polygons, calculate the area and centroid of each grid cell using the shoelace formula, and construct a unified memory data structure. The flow field initialization module is used to initialize the flow field state variables for each grid cell. The flow field reconstruction module is used to reconstruct the flow field state variables on the left and right sides of the interface using a second-order spatial precision format. Specifically, it includes: calculating using a second-order spatial precision format and reconstructing the flow field state variables on the left and right sides of the interface using a reconstruction formula; the reconstruction formula is: in, , These represent the flow field state variables on the left and right sides of the interface obtained through the reconstruction formula, respectively. , These represent adjacent grid cells on both sides of the interface. i and grid cells j The flow field state at the center of the unit; yes In grid cells i The gradient at the center, , Represents grid cells i Limiter function, yes In grid cells j The gradient at the center, Represents grid cells j Limiter function, and These represent the vectors pointing from the centroid of the left and right grid cells to the face center, respectively. The interface flux calculation module is used to calculate the interface flux using a Riemann approximation solver based on the flow field state variables on both sides of the reconstructed interface; the interface flux includes convective flux and viscous flux. The flow field calculation module is used to solve the governing equations using a time format based on the interface flux and conserved variables, update the flow field state variables, and then transfer the calculation to the flow field reconstruction module to continue the calculation until a preset termination condition is met, thereby obtaining the flow field calculation results of the complex microscale structure of the aircraft; wherein the governing equations are: in, W As a conserved variable, For viscous flux, To control the circulation volume, It is a control volume within a two-dimensional computational domain. For the source term vector, t For time, The boundary of the control body.

7. The adaptive cross-tree grid computing device for complex microscale structures according to claim 6, characterized in that, The grid cell abstraction module is also used to create an array for centrally storing the node information of all grid cells, and to store the node information of all grid cells in the array, the array having a dimension of 8 × the total number of cells; based on the node information of each grid cell, the area and centroid of each grid cell are calculated using the shoelace formula; the formula for calculating the area and centroid of a grid cell is: in, S and( C x , C y ) represent the area and centroid coordinates of the mesh cell, respectively. x j , y j )express n The first polygon j The coordinates of each vertex, and have ; Construct a unified memory data structure; the memory data structure is used to store the area, centroid, face normal vector, face area and adjacency relationship of grid cells.

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