Accelerated analysis method for aerodynamic characteristics of free molecular flow of aircraft

Abstract

The invention discloses an accelerated analysis method for aerodynamic characteristics of a free molecular flow of an aircraft, belongs to the field of numerical simulation of rarefied gas dynamics, and aims to solve the problem of low shadow analysis calculation efficiency of a ray tracing surface element method in aerodynamic analysis of an extremely low earth orbit aircraft. The method comprises the following steps of: initializing parameters and reading a surface grid; establishing a uniform background grid as a spatial index, and quickly associating surface triangular surface elements to corresponding sub-grids; an OpenMP parallel instruction is adopted, and ray tracing-based shielding judgment is executed on a large number of surface elements at the same time; and calculating the aerodynamic contribution of the unshielded surface element according to the free molecular flow theory, and integrating to obtain the overall aerodynamic force. According to the method, the calculation complexity of shadow analysis is remarkably reduced from O (N) through cooperation of spatial index and parallel calculation, and efficient and high-precision prediction of the aerodynamic characteristics of the extremely-low-orbit aircraft is achieved on the premise that precision is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation of rarefied gas dynamics, and more specifically, to an accelerated analysis method for the aerodynamic characteristics of free molecular flow in aircraft. Background Technology

[0002] At altitudes above approximately 130 km, the mean free path of gas molecules can exceed 10 m. For most aircraft, the flow around them falls into the category of free molecular flow. In this flow region, collisions between gas molecules are negligible, while collisions between gas molecules and the aircraft surface dominate. The force coefficients depend on the gas-surface interaction model. Theoretical studies of free molecular flow can provide analytical expressions for the pressure, friction, and heat flux of local surfaces with simple shapes, mainly related to the inflow velocity ratio, inflow temperature, wall temperature, the angle between the inflow velocity and the surface normal, and the gas-surface interaction model. For more complex shapes, numerical methods are required, mainly four methods: the element method, the ray-traced element method, the Test-Particle Monte Carlo (TPMC) method, and the Direct Simulation Monte Carlo (DSMC) method.

[0003] The design of very low Earth orbit vehicles requires accurate and efficient numerical prediction of aerodynamic characteristics. Existing prediction methods struggle to achieve a balance between efficiency and accuracy.

[0004] The element-counting method discretizes the aircraft surface into grid cells. Based on the analytical formulas for pressure and friction on a flat plate, the local pressure and friction distribution of each cell can be calculated. Integrating along the surface yields the overall aerodynamic characteristics. The element-counting method is simple and efficient, but only applicable to convex bodies. When the geometry has cavities or mutual occlusion, the element-counting method cannot account for shadowing and multiple reflection effects. The ray-tracing element-counting method, building upon the element-counting method, considers possible shadowing effects between geometric shapes through ray tracing, achieving higher computational accuracy than the element-counting method, but it does not consider multiple reflection effects between particles on walls. The TPMC method simulates gas flow by tracking the trajectories of test particles within the computational domain. Each test particle represents a large number of real gas molecules, whose trajectories can be accurately calculated. Ignoring collisions between molecules, only the particles whose trajectories collide with the aircraft surface need to be considered and statistically analyzed. Macroscopic aerodynamic and thermal information can be obtained by averaging surface statistics. In the DSMC method, simulated molecules represent a large number of gas molecules that can collide and move. The computational domain is divided into grids, and collision pairs are selected within them. Collision calculations are then performed according to different collision models. The macroscopic properties of the gas, such as pressure, temperature, density, and velocity, are obtained by sampling the microscopic information of the simulated molecules.

[0005] Among these methods, the DSMC method has the highest accuracy, but its computational cost is high. The TPMC method has comparable accuracy to DSMC in the free molecular flow region, and although its cost is lower than DSMC, it is still much higher than the panel method. In the preliminary design stage of very low Earth orbit satellites, considering both computational accuracy and cost, the ray tracing panel method is more suitable.

[0006] Ray tracing surface element method needs to consider the possible shadowing effect between geometric shapes, and the brute-force search algorithm has a complexity of O(N). 2 When the shape of the aircraft is complex and the number of surface units is large, the computational efficiency is extremely low.

[0007] Therefore, existing technologies face a core contradiction in the aerodynamic characteristic analysis of very low orbit vehicles: high-efficiency methods (basic element method) lack accuracy, while high-precision methods (ray tracing element method, Monte Carlo method) are inefficient. Summary of the Invention

[0008] This invention proposes a method based on uniform grid spatial partitioning and OpenMP parallelism, which can accelerate the shadow analysis process of the ray-tracing surface element method, greatly improve the computational efficiency of the method, and support the efficient and high-precision prediction of the aerodynamic characteristics of free molecular flow of ultra-low orbit spacecraft.

[0009] To achieve the above-mentioned objective, this invention provides an accelerated analysis method for the aerodynamic characteristics of free molecular flow in aircraft, the method comprising:

[0010] Step 1: Parameter initialization processing includes: reading in the parameter file, obtaining flow parameters including the path of the aircraft surface mesh file, incoming flow velocity, angle of attack, sideslip angle, incoming flow temperature and wall temperature, as well as spatial segmentation resolution parameters;

[0011] Step 2: Surface mesh processing includes: reading in the aircraft surface mesh file, obtaining the aircraft surface geometry represented by multiple discretized facets; calculating the unit normal vector and area of ​​each facet.

[0012] Step 3: Parallel shadow analysis processing includes:

[0013] Construct a spatial index grid: Determine the spatial bounding box based on the vertex coordinates of all face elements. Based on the spatial segmentation resolution parameters, establish a uniform background grid within the spatial bounding box. This background grid consists of multiple sub-grids. Index each face element to one or more of the sub-grids' belonging lists according to its spatial position.

[0014] Parallel occlusion detection: For each face element used as the current test face element, perform the following operations:

[0015] a. Emit a ray from the vertex of the current test element in a direction opposite to the direction of the incoming flow velocity;

[0016] b. Based on the starting point and direction of the ray and the structure of the background grid, calculate and generate a sequence of sub-grids that the ray passes through in sequence;

[0017] c. Query the ownership list of each sub-grid in the sequence in turn, and determine whether the ray intersects with any other surface element in the ownership list of the sub-grid; if they intersect, it is determined that the current test surface element is occluded;

[0018] Among them, the process of traversing all face elements and performing operations from a to c is executed in parallel by multiple threads;

[0019] Step 4: Aerodynamic calculation includes: based on the occlusion judgment result, for unoccluded surface elements, calculate their aerodynamic contribution based on the flow parameters and the unit normal vector and area of ​​each surface element; for occluded surface elements, their aerodynamic contribution is set to zero; integrate the aerodynamic contributions of all surface elements to obtain the overall aerodynamic force and moment coefficient of the aircraft.

[0020] Step 5: Output the results.

[0021] This method introduces a uniform background grid as a spatial index, dividing the entire computational space into regular sub-grids. Each sub-grid stores only a few surface elements within its spatial range. This fundamentally changes the inefficient traditional brute-force search (O(N²)) model, which requires traversing all N surface elements to determine the occlusion of a single element. The result is that when a ray is emitted from a surface element, only a small number of sub-grids through which the ray passes need to be calculated sequentially, and intersection detection is performed only on surface elements belonging to the list of these sub-grids. This reduces the computational complexity from being related to the square of the total number of surface elements N to being related to the number of sub-grids K through which the ray passes, achieving a significant leap in efficiency. Furthermore, based on the substantial reduction in computational cost per surface element through spatial indexing, this method employs the OpenMP parallel programming model, automatically allocating the loop task of traversing all surface elements for shadow determination to multiple threads on a multi-core CPU for simultaneous execution. This solves the bottleneck that even with faster individual tasks, thousands of tasks still need to be processed sequentially, fully utilizing the multi-core computing power of modern processors. It achieves an almost linear decrease in computation time as the number of CPU cores increases, resulting in a second efficiency improvement on a multiple level.

[0022] This method significantly improves computational efficiency: through innovative algorithm design, the computational complexity of shadow analysis in the ray tracing panel method is effectively reduced from O(N²), enabling its application to complex shapes in large-scale meshes. It maintains computational accuracy: while achieving acceleration, the original physical accuracy of the ray tracing panel method is not sacrificed, ensuring the reliability of aerodynamic property predictions.

[0023] Preferably, step 4 specifically includes:

[0024] Based on the occlusion determination results, for unoccupied surface elements, the pressure coefficient and friction coefficient of the surface element are calculated according to the angle between its unit normal vector and the direction of the incoming flow velocity, combined with the incoming flow temperature and wall temperature in the flow parameters; the aerodynamic contribution vector of the surface element is calculated by combining the area of ​​the surface element with the incoming flow velocity and atmospheric density in the flow parameters; for occupied surface elements, their aerodynamic contribution is set to zero; the aerodynamic contribution vectors of all surface elements are summed and integrated to obtain the overall aerodynamic force and moment coefficients of the aircraft.

[0025] Preferably, the spatial bounding box is determined by the minimum and maximum values ​​of the coordinates of all facet vertices in the X, Y, and Z directions; the number of sub-mesh in the X, Y, and Z directions of the background mesh is defined by the spatial segmentation resolution parameter.

[0026] Specifically, a uniform background mesh is automatically and standardizedly generated based on the axial bounding box of the surface mesh and a preset resolution. This solves the problem of how the background mesh can adaptively match the specific shape of the aircraft, avoiding the inaccuracies and inefficiencies of manual settings. It ensures the universal applicability and standardized construction of the spatial indexing structure, which is the foundation for subsequent acceleration.

[0027] Preferably, the specific method for indexing face elements to sub-grids in the construction of the spatial index grid is as follows: calculate the center point coordinates of the face element, determine the number of one or more sub-grids to which it belongs by rounding up the starting coordinates of the background grid and the size of the sub-grid, and store the index of the face element in the corresponding sub-grid's belonging list.

[0028] This method calculates the geometric relationship between the center coordinates of surface elements and the background mesh, and uses rounding operations to quickly map surface elements to sub-mesh. It solves the key problem of how to efficiently organize thousands of unordered surface elements into a spatial index structure. It achieves O(N) complexity in spatial index creation, laying the foundation for subsequent O(1) or O(k) complexity fast queries (where k is the number of sub-mesh traversed by the ray).

[0029] Preferably, a ray-triangle intersection algorithm is used to determine whether the ray intersects with any other face element in the subgrid's belonging list.

[0030] Preferably, the ray-triangle intersection algorithm is the Möller-Trumbore algorithm. This algorithm ensures the accuracy and reliability of the core geometric operation of shadow detection. In the accelerated overall process, it guarantees the accuracy of the lowest-level geometric operations, which is the cornerstone of the accurate final result.

[0031] Preferably, multi-threaded parallel execution is achieved through the OpenMP parallel programming interface. This enables thread-level parallel acceleration, allowing computation time to decrease approximately linearly with the increase in the number of CPU cores, and is a direct means to achieve ultimate ultra-high-speed computing performance.

[0032] Preferably, the specific way to achieve multi-threaded parallel execution through OpenMP is as follows: at the loop structure that traverses all face elements, add OpenMP standard parallel loop compilation directives to instruct the compiler to automatically allocate the loop iterations to multiple threads for execution.

[0033] Preferably, the face element is a triangular face element.

[0034] Preferably, the spacecraft is a very low Earth orbit spacecraft. The application scenario is a very low Earth orbit above 130 kilometers, where the atmosphere above this altitude enters a free molecular flow state.

[0035] One or more technical solutions provided by this invention have at least the following technical effects or advantages:

[0036] This method can improve computational efficiency while maintaining computational accuracy. Attached Figure Description

[0037] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0038] Figure 1 This is a flowchart illustrating an accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft.

[0039] Figure 2 Schematic diagram of the space shuttle surface mesh and background sub-mesh;

[0040] Figure 3 This is a schematic diagram of the pressure coefficient distribution on the surface of the space shuttle. Detailed Implementation

[0041] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0042] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0043] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0044] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0045] Example 1;

[0046] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating an accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft. The method includes:

[0047] Step 1, Initialization. Read in the parameter file, including information such as mesh file name, inflow velocity, angle of attack, sideslip angle, gas constant, specific heat ratio, inflow temperature, wall temperature, reflectivity, scale conversion factor, reference length, reference area, reference point, spatial partitioning resolution, etc.

[0048] Step 2, Mesh Import. A triangular unstructured mesh is used, and the mesh file is in .obj format. The aircraft surface mesh is imported to obtain information such as the number of nodes, the number of facets, the nodes that make up the facets, and the node coordinates. Based on the geometric information, the unit normal vector, unit tangential vector, and area of ​​each facet are calculated.

[0049] Step 3, Shadow Analysis. First, based on the spatial range of the surface mesh (Xmin, Ymin, Zmin, Xmax, Ymax, Zmax), a uniform background mesh is established, numbered (I, J, K), where I = 1~Nx, J = 1~Ny, K = 1~Nz. Nx, Ny, and Nz represent the resolution of the background mesh. Xmin, Xmax, Ymax, Ymin, Zmax, and Zmin are the maximum and minimum values ​​in the X, Y, and Z directions, respectively. I, J, and K are the sub-mesh indices of the background mesh in the X, Y, and Z coordinate axes, respectively. Nx, Ny, and Nz are the number of sub-mesh in the X, Y, and Z directions of the background mesh, set according to the spatial segmentation resolution parameters, i.e., the resolution. Then, the nodes of each facet are sequentially checked. If the node coordinates are located within a certain background sub-mesh, the facet is added to the list belonging to that sub-mesh. After the background mesh is established, all facets are iterated again. Rays are emitted sequentially from the three nodes of each facet, with the ray direction exactly opposite to the flow direction vector. The Möller-Trumbore ray triangulation algorithm is used to determine whether the ray intersects with a certain background sub-mesh. If they do not intersect, they are skipped; if they intersect, the facets within that sub-mesh are further checked to see if they intersect with the ray (based on the facet numbers within the sub-mesh, checked sequentially. The check also uses the Möller-Trumbore ray triangulation algorithm). If there is an intersection, the facet is determined to be occluded. To further improve the efficiency of shadow analysis, the main loop can be parallelized using OpenMP. To simplify the process, only the main shadow analysis loop can be parallelized, or adjustments can be made according to actual needs.

[0050] Step 4, Aerodynamic Characteristic Calculation. For all unobstructed surface elements, calculate the pressure coefficient and friction coefficient using the free molecular flow theory. For obstructed surface elements, the pressure coefficient and friction coefficient are zero. Integrate over all surface elements to calculate the overall aerodynamic forces and moments of the aircraft.

[0051] Step 5, Output Results. Output the aerodynamic coefficient calculation results and the physical quantity distribution file of the aircraft wall.

[0052] Step 3 specifically includes:

[0053] Construct a spatial index grid: Determine the spatial bounding box based on the vertex coordinates of all face elements. Based on the spatial segmentation resolution parameters, establish a uniform background grid within the spatial bounding box. This background grid consists of multiple sub-grids. Index each face element to one or more of the sub-grids' belonging lists according to its spatial position.

[0054] Parallel occlusion detection: For each face element used as the current test face element, perform the following operations:

[0055] a. Emit a ray from the vertex of the current test element in a direction opposite to the direction of the incoming flow velocity;

[0056] b. Based on the starting point and direction of the ray and the structure of the background grid, calculate and generate a sequence of subgrids through which the ray passes in sequence; step b can be based on the implementation of the classic Digital Differential Analyzer (DDA) algorithm or its variants (such as the Amanatides & Woo algorithm) in computer graphics. Specific implementations may include: S1: Determine the initial subgrid where the ray's starting point is located, S2: Calculate the step direction and initial exit distance, S3: Iterate stepping and generate the sequence. Specific implementations will not be elaborated upon in this embodiment of the invention.

[0057] c. Query the ownership list of each sub-grid in the sequence in turn, and determine whether the ray intersects with any other surface element in the ownership list of the sub-grid; if they intersect, it is determined that the current test surface element is occluded;

[0058] Among them, the process of traversing all face elements and performing operations from a to c is executed in parallel by multiple threads;

[0059] Among these advantages, using triangular unstructured meshes has the benefits of universality and computational simplicity.

[0060] OpenMP is a preferred embodiment of the present invention. In specific embodiments, other parallel processing methods can be used instead, such as Intel Threading Building Blocks (TBB), C++11 / 14 / 17 standard thread library, CUDA or OpenCL, etc.

[0061] Step 4 specifically includes:

[0062] Aerodynamic calculation: Based on the results of the occlusion determination,

[0063] For unoccluded triangular face elements, execute:

[0064] (4a) Based on the angle between the unit normal vector of the triangular surface element and the direction of the incoming flow velocity, and according to the incoming flow temperature and wall temperature in the flow parameters, the pressure coefficient and friction coefficient of the surface element are calculated using the free molecular flow theory formula.

[0065] (4b) Combining the area of ​​the triangular element with the incoming flow velocity and atmospheric density in the flow parameters, the pressure coefficient and friction coefficient are converted into the aerodynamic contribution vector of the element.

[0066] For the occluded triangular surface element, its aerodynamic contribution vector is set to zero;

[0067] Finally, the aerodynamic contribution vectors of all triangular surface elements are summed and integrated to obtain the overall aerodynamic force and moment coefficients of the aircraft.

[0068] In this embodiment of the invention, in step (4a), when calculating the pressure coefficient and friction coefficient based on the free molecular flow theory formula, the gas-surface interaction model used is either a completely diffuse reflection model or a hybrid model including specular reflection components. The free molecular flow theory formula can employ either a completely diffuse reflection model or a hybrid reflection model.

[0069] In this embodiment of the invention, the spatial segmentation resolution parameter is adaptively set based on the total number of triangular facets and available computing memory. The density of the background mesh is dynamically determined according to the mesh size and hardware memory to balance indexing efficiency and memory overhead.

[0070] In this embodiment of the invention, the aircraft surface mesh file is a .obj format file containing triangular element information. .obj is a widely used, simple 3D model format that is easy to read, write, and interact with.

[0071] This invention provides a method based on a combination of uniform grid spatial partitioning and OpenMP parallelism to accelerate the shadow analysis process of the ray-tracing surface element method, greatly improve the computational efficiency of the method, and support the efficient and high-precision prediction of the aerodynamic characteristics of free molecular flow in ultra-low orbit vehicles.

[0072] This invention accelerates the ray-tracing surface element method for shadow analysis based on uniform grid spatial partitioning and the OpenMP parallel method. Compared with brute-force search methods, the computational efficiency is improved by 1 to 2 orders of magnitude, greatly enhancing the applicability of this method and supporting efficient and high-precision prediction of the aerodynamic characteristics of free molecular flows in ultra-low orbit vehicles.

[0073] Example 2;

[0074] Based on Embodiment 1, Embodiment 2 of the present invention provides specific implementation examples to more clearly illustrate the specific implementation schemes of the present invention. These examples are only used to explain and describe the present invention and are not intended to limit the scope of the invention.

[0075] The data structure of the storage node is as follows:

[0076] The system uses a custom type defined in the Fortran language, named node, which is a one-dimensional dynamic array that can be allocated memory. Each element of the array contains three floating-point numbers x, y, and z, representing the three-dimensional spatial coordinates of the node.

[0077] The data structure for storing face cells is as follows:

[0078] The face is defined using a custom type in Fortran, named face. It is a one-dimensional dynamic array that can be allocated memory. Each element of the array contains the node number of the face element (node(3) - a one-dimensional integer array of size 3), the unit normal direction of the face element (normal(3) - a one-dimensional floating-point array of size 3), the unit tangent direction of the face element (tangent(2,3) - a two-dimensional floating-point array of size 2×3), the area of ​​the face element (area - floating-point number), the center coordinates of the face element (center(3) - a one-dimensional floating-point array of size 3), and whether it will be occluded (integer), etc.

[0079] The data structure for storing a uniform background grid is as follows:

[0080] The system uses a custom type defined in the Fortran language, named grid, which contains information about the aircraft surface grid within each background subgrid (a four-dimensional dynamic integer array cells that can be allocated memory), the minimum and maximum spatial range of the background grid (one-dimensional floating-point arrays min_bound and max_bound, both of size 3), and the resolution of the background grid (a one-dimensional integer array resolution, of size 3).

[0081] cell_size represents the spatial extent of each background subgrid:

[0082] cell_size = (grid%max_bound - grid%min_bound) / grid%resolution. grid%max_bound represents the maximum spatial coordinates of the background sub-grid, grid%min_bound represents the minimum spatial coordinates of the background sub-grid, and grid%resolution represents the spatial resolution of the background sub-grid. The surface grid is assigned to a specific background sub-grid by comparing the coordinates; the specific calculation method is as follows.

[0083] ix = floor((node(face(i)%node(1))%x - grid%min_bound(1)) / cell_size(1)) + 1;

[0084] iy = floor((node(face(i)%node(1))%y - grid%min_bound(2)) / cell_size(2)) + 1;

[0085] iz = floor((node(face(i)%node(1))%z - grid%min_bound(3)) / cell_size(3)) + 1;

[0086] `face(i)%node(1)` represents the first node of face element `i`, `node(face(i)%node(1))%x` represents the x-coordinate of this node, `node(face(i)%node(1))%y` represents the y-coordinate of this node, `node(face(i)%node(1))%z` represents the z-coordinate of this node, `grid%min_bound(1)` represents the minimum coordinate of the background subgrid in the x-direction, `grid%min_bound(2)` represents the minimum coordinate of the background subgrid in the y-direction, `grid%min_bound(3)` represents the minimum coordinate of the background subgrid in the z-direction, and `ix`, `iy`, and `iz` represent the index of the current point's subgrid along the X-axis, Y-axis, and Z-axis in the background grid, respectively. `floor()` is the floor function in programming and mathematics, and `node(1)` refers to the first vertex of the face element.

[0087] Since each face of the background sub-mesh is parallel to the coordinate axes, if a ray intersects the background sub-mesh, the ray must first intersect one of the three nearest faces. Therefore, we can check whether they intersect in turn.

[0088] step:

[0089] 1. Determine if the starting point is inside the intersection; if it is, they must intersect; otherwise, they will intersect.

[0090] 2. Traverse each axis and find the intersection points with the nearest plane;

[0091] 3. Determine whether the intersection point is inside the bounding box.

[0092] The Möller-Trumbore algorithm is used to determine whether a point is inside a triangle element.

[0093] Figure 2 A schematic diagram of the space shuttle surface mesh and background sub-mesh is provided. The background mesh divides the space, which can reduce invalid judgments in shadow analysis and improve computational efficiency.

[0094] Enabling OpenMP acceleration for the main loops in the analysis section can further improve computational efficiency. This is mainly achieved by adding OMP parallel loop compilation directives outside the loops. The specific OpenMP parallel acceleration method is as follows:

[0095] Iterate through all wall elements;

[0096] If the current wall element is occluded, skip it;

[0097] Set the spatial coordinates of the center of the wall unit;

[0098] Define the spatial coordinates of the three nodes of the wall unit;

[0099] Iterate through all background subgrids in sequence;

[0100] Skip if the background submesh does not contain wall elements;

[0101] Rays are emitted from the three nodes of the wall element in the opposite direction to the incoming flow direction. It is checked whether the ray intersects with a background sub-mesh (first, the intersection points of the particle trajectory and each surface of the sub-mesh are calculated, then the intersection points are checked to see if they are within the sub-mesh's boundaries). If any ray intersects with the background sub-mesh, the wall elements belonging to that background sub-mesh are iterated, and the Möller-Trumbore ray triangulation algorithm is used to determine which wall element the ray intersects with. If a wall element can be found, the current wall element is determined to be occluded.

[0102] The wall unit cycle has ended;

[0103] The accuracy of the method proposed in this invention was verified using both flat and spherical shapes.

[0104] Table 1 Calculation of Flat Plate Resistance

[0105]

[0106] Tables 1 and 2 show the comparison between the calculated results and theoretical values ​​of free molecular flow for flat plates and spheres, respectively. The calculated values ​​and theoretical solutions agree well.

[0107] Table 2 Calculation of Sphere Resistance

[0108]

[0109] The space shuttle shape was used as a complex example to verify the proposed acceleration algorithm. The altitude was 170 km, and the surface mesh number was 215,880. Table 3 shows the time comparison under different operating conditions. Without shading analysis, the computation time is approximately 3.72 seconds; with shading analysis enabled but without acceleration techniques, the computation time increases significantly, by about 165 times; using only spatial partitioning acceleration can improve efficiency by about 90%; using spatial partitioning + OpenMP acceleration can further improve efficiency by about 80%. It is evident that the computation method proposed in this invention has a significant acceleration effect.

[0110] Table 3 Comparison of Space Shuttle Calculation Time

[0111]

[0112] Figure 3The pressure coefficient distribution on the surface of the space shuttle is given.

[0113] As can be seen from the preceding description, this method not only achieves improvements in efficiency and accuracy, but also realizes a synergistic effect—architectural optimization produces a 1+1 greater than 2 effect.

[0114] Spatial indexing is a prerequisite for efficient parallelism. Because the background mesh organizes data (cells) locally according to their spatial location, the probability of overlapping and conflicting data (sub-mesh ownership lists) that different threads need to access when processing spatially distant cells is extremely low. This significantly reduces time-consuming data contention and cache synchronization overhead in parallel computing.

[0115] As shown in Table 3, the speedup of spatial partitioning alone is approximately 90%, while the total speedup of spatial partitioning combined with parallelism exceeds 96%. The additional benefits of parallelism are achieved on top of the already highly optimized serial algorithm, demonstrating that the combination of the two techniques produces a synergistic speedup effect that goes beyond simple superposition.

[0116] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0117] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for accelerating the analysis of aerodynamic characteristics of free molecular flow in an aircraft, characterized in that, The method includes: Step 1: Parameter initialization processing includes: reading in the parameter file, obtaining flow parameters including the path of the aircraft surface mesh file, incoming flow velocity, angle of attack, sideslip angle, incoming flow temperature and wall temperature, as well as spatial segmentation resolution parameters; Step 2: Surface mesh processing includes: reading in the aircraft surface mesh file, obtaining the aircraft surface geometry represented by multiple discretized facets; calculating the unit normal vector and area of ​​each facet. Step 3: Parallel shadow analysis processing includes: Construct a spatial index grid: Determine the spatial bounding box based on the vertex coordinates of all face elements. Based on the spatial segmentation resolution parameters, establish a uniform background grid within the spatial bounding box. This background grid consists of multiple sub-grids. Index each face element to one or more of the sub-grids' belonging lists according to its spatial position. Parallel occlusion detection: For each face element used as the current test face element, perform the following operations: a. Emit a ray from the vertex of the current test element in a direction opposite to the direction of the incoming flow velocity; b. Based on the starting point and direction of the ray and the structure of the background grid, calculate and generate a sequence of sub-grids that the ray passes through in sequence; c. Query the ownership list of each sub-grid in the sequence in turn, and determine whether the ray intersects with any other surface element in the ownership list of the sub-grid; if they intersect, it is determined that the current test surface element is occluded; Among them, the process of traversing all face elements and performing operations from a to c is executed in parallel by multiple threads; Step 4: Aerodynamic calculation includes: based on the occlusion judgment result, for unoccluded surface elements, calculate their aerodynamic contribution based on the flow parameters and the unit normal vector and area of ​​each surface element; for occluded surface elements, their aerodynamic contribution is set to zero; integrate the aerodynamic contributions of all surface elements to obtain the overall aerodynamic force and moment coefficient of the aircraft. Step 5: Output the results.

2. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, Step 4 specifically includes: Based on the occlusion determination results, for unoccupied surface elements, the pressure coefficient and friction coefficient of the surface element are calculated according to the angle between its unit normal vector and the direction of the incoming flow velocity, combined with the incoming flow temperature and wall temperature in the flow parameters; the aerodynamic contribution vector of the surface element is calculated by combining the area of ​​the surface element with the incoming flow velocity and atmospheric density in the flow parameters; for occupied surface elements, their aerodynamic contribution is set to zero; the aerodynamic contribution vectors of all surface elements are summed and integrated to obtain the overall aerodynamic force and moment coefficients of the aircraft.

3. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, The spatial bounding box is determined by the minimum and maximum values ​​of the coordinates of all face vertexes in the X, Y, and Z directions; the number of sub-mesh in the X, Y, and Z directions of the background mesh is defined by the spatial segmentation resolution parameter.

4. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, The specific method for indexing face elements to sub-grids in the construction of the spatial index grid is as follows: calculate the center point coordinates of the face element, determine the number of one or more sub-grids to which it belongs by rounding operation based on the starting coordinates of the background grid and the size of the sub-grid, and store the index of the face element in the corresponding sub-grid's belonging list.

5. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, The ray-triangle intersection algorithm is used to determine whether the ray intersects with any other face element in the subgrid's ownership list.

6. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 6, characterized in that, The ray-triangle intersection algorithm is the Möller-Trumbore algorithm.

7. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, Multi-threaded parallel execution is achieved through the OpenMP parallel programming interface.

8. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 7, characterized in that, The specific way to achieve multi-threaded parallel execution using OpenMP is to add OpenMP standard parallel loop compilation directives at the loop structure that traverses all face elements, instructing the compiler to automatically distribute the loop iterations to multiple threads for execution.

9. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, The surface element is a triangular surface element.

10. The accelerated analysis method for the aerodynamic characteristics of free molecular flow in an aircraft according to claim 1, characterized in that, The spacecraft is a very low Earth orbit spacecraft.

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