Method for generating a grid of a rocket aerodynamic structure

Abstract

The present application belongs to the field of aerospace technology, and particularly relates to a kind of spinning body rocket aerodynamic structure grid generation method. It aims to solve the problems of complex and time-consuming generation process of traditional three-dimensional structured grid, and the problems of overall asymmetry of generated grid, large amount of grid and slow convergence of calculation of unstructured grid. The present application generates high-quality structured grid in the two-dimensional plane of the symmetry axis by utilizing the geometric symmetry of the spinning body, and then efficiently assembles the complete three-dimensional structured grid by rotating the structured grid as a template around the symmetry axis through geometric operation. While ensuring high quality and high orthogonality of the grid, the generation efficiency is greatly improved. Furthermore, the present application realizes accurate control of grid density through parameterization, and improves the reliability of high-precision numerical simulation of aerodynamic characteristics of the spinning body.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a method for generating aerodynamic structure meshes for spinning rockets. Background Technology

[0002] Aircraft fluid dynamics computation is a crucial aspect of modern aerospace engineering design, with its computational accuracy and reliability highly dependent on the quality of the fluid dynamics computational mesh generated during the preprocessing stage. Based on mesh cell type, computational meshes are mainly divided into two major systems: structured meshes and unstructured meshes. For aircraft with spinning body characteristics, such as rockets and missiles, aerodynamic characteristic analysis requires generating high-quality computational meshes that match their complex shapes. Spinning body shapes possess unique geometric symmetries, providing special optimization conditions for mesh generation; however, existing mesh generation techniques still face significant technical challenges in balancing computational efficiency and numerical accuracy.

[0003] Currently, aerodynamic calculations of spinning bodies are mainly based on the two types of meshes mentioned above to generate computational meshes. Specifically, structured mesh methods can generate high-quality orthogonal meshes by establishing regular mesh topologies. However, when dealing with complex three-dimensional shapes, the mesh generation process requires a large amount of manual intervention, is complex and time-consuming, and it is difficult to guarantee the symmetry distribution of the mesh. On the other hand, unstructured mesh methods, although highly automated and faster in generation, generate meshes mainly composed of tetrahedral elements, which are difficult to maintain in practical applications, leading to non-physical deviations in the flow field calculation results. At the same time, the number of elements in unstructured meshes is usually too large, greatly increasing the consumption of computational resources. In addition, the inconsistent mesh quality can also lead to slow convergence speed of numerical calculations, affecting the iterative efficiency of engineering design.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] One objective of this invention is to solve the problems of complex and time-consuming traditional three-dimensional structured mesh generation processes, as well as the problems of overall asymmetry, large mesh size, and slow computational convergence in unstructured meshes.

[0006] To achieve the above objectives, the present invention provides a method for generating aerodynamic structure meshes for spinning rockets, comprising:

[0007] In the Oxy plane of the global coordinate system Oxyz, construct and discretize the boundary of the 1 / 2 symmetry plane computational region of the spinning rocket;

[0008] Based on the boundary of the computational region of the 1 / 2 symmetry plane, a planar structure mesh of the 1 / 2 symmetry plane is generated in the Oxy plane;

[0009] The 1 / 2 symmetry plane mesh is rotated around the symmetry axis of the solid rocket to generate a full-domain three-dimensional structure mesh.

[0010] Further, the step of constructing and discretizing the boundary of the 1 / 2 symmetry plane calculation region of the spinning rocket in the Oxy plane of the global coordinate system Oxyz includes: extracting the intersection line of the spinning rocket's shape and the Oxy plane as the generatrix, and extracting the intersection line of the outer boundary of the calculation region and the Oxy plane as the upper contour of the outer boundary, and discretizing the generatrix and the upper contour of the outer boundary into I+1 coordinate points respectively; connecting the endpoints of the generatrix at the head and tail to the corresponding points of the upper contour of the outer boundary to form the right boundary and left boundary of the calculation region, and discretizing the two sides into J+1 coordinate points respectively; the generatrix, the upper contour of the outer boundary, the right boundary and the left boundary together enclose and form the closed boundary of the 1 / 2 symmetry plane calculation region.

[0011] Furthermore, the step of generating a 1 / 2 symmetry plane structure mesh in the Oxy plane includes: generating an initial structure mesh within the boundary of the 1 / 2 symmetry plane computational region using an overlimit interpolation method based on the coordinates of all boundary points obtained by discretization; and iteratively solving the mesh using a mesh smoothing method based on elliptic partial differential equations, starting from the initial structure mesh, to optimize the distribution of mesh points and obtain a 1 / 2 symmetry plane structure mesh.

[0012] Furthermore, the transfinite interpolation method is a linear transfinite interpolation method, and the interpolation process is defined by a vector function of Boolean form.

[0013] Further, the step of generating the initial structural mesh within the boundary of the 1 / 2 symmetry plane computational region using the trans-limit interpolation method includes: defining a vector mapping function from the regular parameter space to the physical computational region; constructing interpolation functions along two coordinate axes in the parameter space based on the coordinates of discrete points on the boundary of the computational region; combining the interpolation functions in the two directions using a Boolean sum to obtain the vector mapping function; according to the Boolean sum mapping function, the set of coordinate points corresponding to the regular grid points in the parameter space in the physical space constitutes the initial value of the 1 / 2 symmetry plane mesh; and generating the initial structural mesh within the boundary of the 1 / 2 symmetry plane computational region based on the initial value of the 1 / 2 symmetry plane mesh.

[0014] Further, the step of defining the vector mapping function from the regular parameter space to the physical computation region includes: defining the vector mapping function from the parameter space (ξ,η) to the physical space (x,y) as follows: : The range of values ​​for parameter ξ is as follows: The range of values ​​for parameter η is: The four boundaries of the computational region are respectively mapped to the four boundaries of the parameter space.

[0015] Further, the step of constructing interpolation functions along two coordinate axes of the parameter space based on the coordinates of discrete points on the boundary of the computational region, and combining the interpolation functions in the two directions using Boolean sums to obtain the vector mapping function, includes: based on positive integer indices... and Generate regular grid points in the parameter space ( , The expression is as follows:

[0016] ;

[0017] Based on the coordinates of discrete points on the boundary of the computational region, interpolation functions U and V are constructed along the ξ and η directions, respectively:

[0018] ;

[0019] in, Let L be the interpolation basis function in the ξ direction; L be the number of basis functions in the ξ direction; P be the highest order of the summation in the ξ direction; and n be the order of the partial derivative (0 ≤ n ≤ P). yes Partial derivative with respect to the direction of ξ; Let M be the interpolation basis function in the η direction; M be the number of basis functions in the η direction; Q be the highest order of the summation in the η direction; and m be the order of the partial derivative (0 ≤ m ≤ Q). yes The partial derivatives with respect to η; where, when linear interpolation is used, the parameters are P=Q=0, L=M=2, then the interpolation basis function is:

[0020] ;

[0021] The interpolation function and The vector mapping function is obtained by combining Boolean and formal methods. The expression for (ξ,η):

[0022] Among them, the product term The expression for (ξ,η) is:

[0023] .

[0024] Furthermore, the mesh smoothing method for the elliptic partial differential equation adopts the Laplace equation and is solved discretly using the finite difference method.

[0025] Furthermore, the step of iteratively solving the grid using a mesh smoothing method based on elliptic partial differential equations to optimize the distribution of grid points and obtain a 1 / 2 symmetry plane structure grid includes: establishing the Laplace equation based on the elliptic partial differential equations in physical space; transforming the governing equations from physical coordinates to parametric coordinates through coordinate transformation to obtain a set of grid generation equations; discretizing the set of grid generation equations on a regular grid in parametric space using a numerical discretization method, transforming it into a set of nonlinear algebraic equations on discrete grid points; and iteratively solving the initial grid's physical... The coordinates are used as the initial values ​​for iterative calculations and are iterated multiple times. In each iteration, the internal grid points of the parameter space are traversed, and the latest known coordinate values ​​adjacent to the current grid point are substituted into the discretized algebraic equation system to solve and update the coordinate estimate of the current grid point. Throughout the iteration process, the coordinates of the grid points on the boundary of the computational domain remain unchanged. When the preset iteration termination condition is met, the iteration process is terminated, and the finally updated physical coordinates are used as the optimized 1 / 2 symmetry plane structure grid coordinates. A 1 / 2 symmetry plane structure grid is generated based on the optimized 1 / 2 symmetry plane structure grid coordinates.

[0026] Furthermore, the step of rotating the 1 / 2 symmetry plane mesh around the symmetry axis of the spinning rocket to generate a three-dimensional structure mesh covering the entire flow domain includes: obtaining the node coordinate set of the two-dimensional plane structure mesh representing the 1 / 2 symmetry profile of the spinning rocket; dividing the entire 360-degree circumferential domain of the rocket into equal-angle discretizations; performing a spatial rotation transformation on the node coordinate set of the two-dimensional plane structure mesh around the symmetry axis of the rocket at a corresponding angle to generate a series of two-dimensional mesh profiles uniformly distributed in the circumferential direction; and connecting the mesh points in all the two-dimensional mesh profiles obtained after the circumferential transformation in three-dimensional space according to their inherent topological relationships to assemble a three-dimensional structure mesh covering the entire flow domain.

[0027] Based on the foregoing description, those skilled in the art will understand that this invention utilizes the geometric symmetry of the rotating body to generate a high-quality structured mesh in a two-dimensional plane along the axis of symmetry. The structured mesh is then used as a template for geometric operations involving rotation around the axis of symmetry, efficiently assembling into a complete three-dimensional structured mesh. This effectively solves the problems of complex and time-consuming generation processes in traditional three-dimensional structured meshes, as well as the high numerical dissipation and difficulty in ensuring symmetry in unstructured meshes. While ensuring high mesh quality and high orthogonality, it significantly improves generation efficiency and achieves precise control of mesh density through parameterization, thereby enhancing the reliability of high-precision numerical simulations of the aerodynamic characteristics of rotating bodies. Attached Figure Description

[0028] The accompanying drawings, as part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation of the invention. Obviously, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without creative effort. In the drawings:

[0029] Figure 1 This is a flowchart illustrating the steps of the method for generating aerodynamic structure mesh for a spinning rocket in some embodiments of the present invention;

[0030] Figure 2 This is a schematic diagram of the first partial structure of a 1 / 2 symmetry plane structure mesh in some embodiments of the present invention;

[0031] Figure 3 This is a schematic diagram of the second partial structure of a 1 / 2 symmetry plane structure mesh in some embodiments of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0033] Those skilled in the art should understand that the embodiments described below are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. These partial embodiments are intended to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention. Based on the embodiments provided by the present invention, all other embodiments obtained by those skilled in the art without creative effort should still fall within the scope of protection of the present invention.

[0034] The following reference Figures 1 to 3 This document will provide a detailed description of the method for generating aerodynamic structure meshes for spinning rockets in some embodiments of the present invention. Figure 1 This is a flowchart illustrating the steps of the method for generating aerodynamic structure mesh for a spinning rocket in some embodiments of the present invention; Figure 2 This is a schematic diagram of the first partial structure of a 1 / 2 symmetry plane structure mesh in some embodiments of the present invention; Figure 3 This is a schematic diagram of the second partial structure of a 1 / 2 symmetry plane structure mesh in some embodiments of the present invention.

[0035] In some embodiments of this invention, a method for generating aerodynamic structure meshes for spinning-body rockets is provided. First, leveraging the symmetry of the spinning-body, mesh generation is performed only within a two-dimensional plane of one symmetrical section (1 / 2 symmetry plane), reducing the three-dimensional problem to a two-dimensional one, significantly simplifying the process. Then, the generated high-quality two-dimensional mesh is rotated and copied around an axis of symmetry, quickly and accurately assembling it into a three-dimensional mesh. This decomposes the complex global three-dimensional mesh generation into simple two-dimensional mesh generation and efficient geometric transformation. Compared to traditional unstructured mesh generation methods for spinning-body rockets, this method effectively solves the problems of large mesh size, high numerical dissipation, difficulty in ensuring symmetry, and low efficiency in manually generating high-quality structured meshes. This method for generating aerodynamic structure meshes for spinning-body rockets is applicable to the pre-processing stage of numerical simulation (CFD calculation) of aerodynamic characteristics for spinning-body aircraft such as rockets and missiles.

[0036] like Figure 1 As shown, the method for generating aerodynamic structure meshes for spinning rockets utilizes the fact that the shape of spinning bodies such as rockets and missiles is formed by rotating a planar generatrix around an axis of symmetry. This means that the complete three-dimensional aerodynamic characteristics can be fully characterized by the characteristics of a two-dimensional cross-section (1 / 2 symmetry plane) passing through the axis of symmetry. Generating meshes in three-dimensional space is complex, while processing them in a two-dimensional plane is several orders of magnitude simpler. This invention utilizes the geometric symmetry of spinning bodies to decompose the full-domain mesh generation process in three-dimensional space into two core stages: two-dimensional planar mesh generation and spatial rotational replication. The specific method includes:

[0037] Step S100: In the Oxy plane of the global coordinate system Oxyz, construct and discretize the boundary of the 1 / 2 symmetry plane computational region of the spinning rocket, and generate a high-quality 1 / 2 symmetry plane structure mesh in the Oxy plane.

[0038] Any numerical simulation, such as computational fluid dynamics (CFD), requires a defined computational domain. This invention constructs a clear and closed computational domain in a two-dimensional plane through the steps of extraction (generatrix, outer contour) → connection (left and right boundaries) → closure. Specifically, step S100 includes:

[0039] Step S110, the boundary partitioning step of the 1 / 2 symmetry plane computational region, involves constructing and discretizing the boundary of the 1 / 2 symmetry plane computational region of the rotating rocket within the Oxy plane of the global coordinate system Oxyz. Specifically:

[0040] First, geometric elements are extracted and discretized. The actual shape of a rocket is a continuous, smooth curve, while computers can only process discrete data. Through discretization, the continuous boundary lines are represented by a finite number of points (I+1 and J+1), transforming the continuous geometric problem into a discrete numerical problem. This is a prerequisite for subsequent numerical methods (such as finite difference and transfinite interpolation). Specifically, the intersection of the rotating rocket's shape with the Oxy plane is extracted as the generatrix, and the intersection of the outer boundary of the computational domain with the Oxy plane is extracted as the upper contour of the outer boundary. The generatrix and the upper contour of the outer boundary are then discretized into I+1 coordinate points.

[0041] Among them, parameter I is the key control parameter for grid resolution. The value of I determines the number of grid points along the rocket's axis, thereby controlling the accuracy of the geometric fitting of the rocket's shape (such as the nose cone, column segments, and tail skirt). The larger the value of I, the more accurate the description, but the greater the computational cost. Specifically, I represents the number of segments / grid points along the axial direction of the computational region of the closed 1 / 2 symmetry plane.

[0042] Then, the computational domain is closed to form a topologically complete parameter space that can be used to generate structured meshes. By adding left and right boundaries, an open region is transformed into a closed "quadrilateral" region, and only closed regions can be used to apply subsequent structured mesh generation algorithms (such as transboundary interpolation). Specifically, the right and left boundaries of the computational domain are formed by connecting the endpoints of the generatrix at the head and tail to the corresponding points on the outer boundary profile, and these two boundaries are discretized into J+1 coordinate points respectively.

[0043] The parameter J controls the number of grid layers from the rocket surface (high gradient region) to the far field (uniform flow region). For fluid dynamics CFD, a very dense grid is required near the rocket surface to resolve the boundary layer, and the value of J directly affects the ability to capture such physical phenomena. Specifically, J represents the number of segments of the closed 1 / 2 symmetry plane computational region boundary / the number of vertical grid layers.

[0044] Finally, a closed region is formed, which generates a two-dimensional computational domain object with discrete boundaries and a well-defined range. This closed region forms the basis for subsequent mapping and mesh generation. Specifically, the boundary of the closed 1 / 2 symmetry plane computational region is formed by the generatrix, the outer boundary contour, the right boundary, and the left boundary.

[0045] Based on the above steps, the complex computational domain boundary is decomposed into four distinct components: the rocket generatrix (inner boundary), the outer boundary contour, the right boundary, and the left boundary. By discretizing these four boundary lines (approximating them with a series of points), a closed, discrete boundary is formed, establishing geometric constraints for the next step of filling the region with grid points. This clarifies the geometric domain for grid generation and effectively avoids problems such as grid generation failure or poor quality caused by unclear region definition.

[0046] Step S120, Planar Structured Mesh Generation Step: Calculate the region boundary based on the discretized 1 / 2 symmetry plane, and generate a high-quality 1 / 2 symmetry plane structured mesh in the Oxy plane.

[0047] Due to the inherent trade-off between efficiency and quality in single mesh generation methods (e.g., algebraic methods are fast but of poor quality, while differential methods offer high quality but are slow and sensitive to initial values), this invention employs a hybrid strategy of TFI initial generation combined with elliptic smoothing optimization. First, a topologically correct but potentially low-quality initial mesh is quickly generated using Transfinite Interpolation (TFI). Then, starting from this initial mesh, iterative optimization is performed using a smoothing method based on elliptic partial differential equations to smooth and orthogonalize the mesh lines, thereby obtaining a high-quality final mesh. Specifically, step S120 includes:

[0048] Step S121, Rapid Generation of Initial Mesh: Based on the coordinates of all boundary points obtained through discretization, an initial structural mesh within the boundary of the 1 / 2 symmetry plane computational region is generated using trans-interpolation. The trans-interpolation method is a linear trans-interpolation method, and its interpolation process is defined by a vector function in Boolean sum form. A mapping relationship r(ξ,η)=[x(ξ,η), y(ξ,η)] is established from the regular rectangular parameter space (ξ, η) to the irregular physical computational region (x, y). Then, interpolation construction is performed, constructing interpolation functions along the ξ and η directions of the parameter space, considering function values ​​and even derivatives at the boundaries. The interpolation results in the two directions are then combined using Boolean sum operations to ensure accurate matching of the given boundary conditions on all boundaries. Finally, by taking values ​​on the regular parameter space mesh and using the above mapping function, the corresponding physical space coordinates are calculated, thereby quickly filling the entire region and generating the initial mesh.

[0049] Step S121, which involves generating the initial structured mesh within the boundary of the 1 / 2 symmetry plane computational domain using trans-limit interpolation, includes:

[0050] Step S1211: Define a vector mapping function from the rule parameter space to the physical computation region.

[0051] Specifically, the vector mapping function from the parameter space (ξ,η) to the physical space (x,y) is defined as follows: :

[0052] ;

[0053] The range of values ​​for parameter ξ is as follows: The range of values ​​for parameter η is: The four boundaries of the computational domain are mapped to the four boundaries of the parameter space.

[0054] Step S1212: Based on the known coordinates of discrete points on the boundary of the computational region, construct interpolation functions along the two coordinate axes of the parameter space respectively; combine the interpolation functions in the two directions using Boolean sum form to obtain the complete expression of the vector mapping function.

[0055] Specifically, based on positive integer indexes and Generate regular grid points in the parameter space ( , The expression is as follows:

[0056] ;

[0057] Based on the coordinates of discrete points on the boundary of the computational domain, interpolation functions U and V are constructed along the ξ and η directions, respectively:

[0058] ;

[0059] in, Let L be the interpolation basis function in the ξ direction; L be the number of basis functions in the ξ direction; P be the highest order of the summation in the ξ direction; and n be the order of the partial derivative (0 ≤ n ≤ P). yes Partial derivative with respect to the direction of ξ; Let M be the interpolation basis function in the η direction; M be the number of basis functions in the η direction; Q be the highest order of the summation in the η direction; and m be the order of the partial derivative (0 ≤ m ≤ Q). yes Partial derivative with respect to η.

[0060] When linear interpolation is used, with parameters P=Q=0 and L=M=2, the interpolation basis function is:

[0061] .

[0062] interpolation function and By combining Boolean and formal methods, we obtain the vector mapping function. The expression for (ξ,η):

[0063] ;

[0064] Among them, the product term The expression for (ξ,η) is:

[0065] .

[0066] Step S1213: Based on the Boolean mapping function, calculate the set of coordinate points corresponding to the regular grid points in the parameter space in the physical space, which constitutes the initial value of the 1 / 2 symmetry plane mesh; generate the initial structure mesh within the boundary of the 1 / 2 symmetry plane computational domain based on the initial value of the 1 / 2 symmetry plane mesh. Specifically, based on the Boolean mapping function... (ξ,η), generating regular grid points (ξ) in the parameter space by traversing positive integer indices i and j. i ,η j ), and then calculate its corresponding coordinates (x) in physical space. i ,y j This process generates a set of coordinate points from all coordinate points, which serves as the initial values ​​for the 1 / 2 symmetry plane mesh. Finally, based on the initial values ​​of the 1 / 2 symmetry plane mesh, an initial structural mesh is generated within the boundary of the 1 / 2 symmetry plane computational domain.

[0067] In some specific embodiments, the step of generating an initial structured mesh within the boundary of the 1 / 2 symmetry plane computational domain based on the initial values ​​of the 1 / 2 symmetry plane mesh includes:

[0068] Node data is associated with the topology index: the initial values ​​of the 1 / 2 symmetry plane mesh are defined as the coordinate dataset of all mesh nodes in physical space [(x i y j ]; where each node coordinate is established in a one-to-one correspondence with the index (i, j) of the parameter space regular grid, i is the node index along the ξ direction (1 ≤ i ≤ I+1), and j is the node index along the η direction (1 ≤ j ≤ J+1).

[0069] Automatic mesh cell generation: Traverse all rectangular cells in the parameter space regular mesh that consist of four adjacent nodes [(i, j), (i+1, j), (i+1, j+1), (i, j+1)]; map each parameter space cell to physical space, generating cells with corresponding node coordinates (x, y, y)... i y j ), (x i+1 y j ), (x i+1， y j+1 ), (x i y j+1The quadrilateral mesh elements formed are connected sequentially; by traversing i from 1 to I and j from 1 to J, I × J quadrilateral mesh elements covering the entire computational domain are generated.

[0070] Computational region boundary identification: Based on the value of node index (i, j), the grid nodes located on the boundary of the computational region are automatically identified and marked; among them, the node set with index j=1 is identified as the boundary of the rotating rocket generatrix, the node set with index j=J+1 is identified as the far-field outer boundary, and the node sets with indices i=1 and i=I+1 are identified as the left and right boundaries of the computational region, respectively.

[0071] Initial structure mesh data assembly: Integrate the node coordinate dataset, mesh cell connection relationship dataset, and boundary identification information to assemble a complete initial structure mesh within the boundary of the 1 / 2 symmetry plane computational domain, which can be used for numerical calculations.

[0072] Step S122, Mesh Quality Iterative Optimization: Starting with the initial structure mesh, an iterative solution is performed using a mesh smoothing method based on elliptic partial differential equations to optimize the distribution of mesh points, resulting in a high-quality, highly orthogonal final planar structure mesh. The elliptic partial differential equation mesh smoothing method employs the Laplace equation and uses the finite difference method for discretization. To address potential issues such as mesh line distortion and poor orthogonality in the initial algebraic mesh and to meet the stringent mesh quality requirements of CFD calculations, this invention uses elliptic equations such as the Laplace equation as the governing equations. The solutions of these equations exhibit smoothness, enabling smooth distribution of mesh lines within the region. The equations are then transformed from physical space to parameter space to obtain the generating equations. These are then discretized into a system of nonlinear algebraic equations about the coordinates of the mesh points using the finite difference method. Finally, an iterative solution is performed, starting with the initial mesh and solving the system of equations using an iterative method (such as the Gauss-Seidel method). In each iteration, the position of the current point is updated based on the latest positions of neighboring points, and the initial mesh is smoothed and its quality optimized, ultimately resulting in a smooth, high-quality planar mesh. Specifically, step S122 includes:

[0073] Step S1221: Based on the elliptic partial differential equations in physical space, establish the Laplace equations; through coordinate transformation, transform the governing equations from physical coordinates to parametric coordinates to obtain the mesh generation equation set.

[0074] Specifically, based on the physical space (x,y), the Laplace equation is established, with the following expression:

[0075] ;

[0076] The Laplace equation is transformed from physical coordinates (x, y) to parametric coordinates (ξ, η), as shown in the following expression:

[0077] ;

[0078] Step S1222: On the regular grid in the parameter space, the grid generation equations are discretized using a numerical discretization method, transforming them into a set of nonlinear algebraic equations at discrete grid points. Specifically, on the regular grid in the parameter space, the grid generation equations for each grid are discretized using a numerical discretization method, and each is transformed into a set of nonlinear algebraic equations at discrete grid points, generating a set of all nonlinear algebraic equations.

[0079] In some specific embodiments, the process of generating the nonlinear algebraic equations includes: in the parameter space (ξ,η), based on the given grid density parameters I and J, generating a regular rectangular computational grid consisting of (I+1)*(J+1) grid points; wherein each internal grid point is identified by a unique index (i,j), and its parametric coordinates are (ξ,η). i η j For all partial derivative terms appearing in the generating equations, a central difference scheme is used for numerical approximation; each partial derivative term is expressed as a linear combination of the physical coordinates of the grid point and its neighboring grid points. The expression obtained after the finite difference approximation is substituted back into the generating equations, thus transforming the partial differential equations into a nonlinear algebraic equation system. All internal grid points are traversed, and their values ​​are substituted into the aforementioned nonlinear algebraic equation system to obtain a corresponding equation system for each internal point (i, j). All these equation systems are then combined into a single set of nonlinear algebraic equations with the physical coordinates of all internal grid points as unknowns.

[0080] In some specific examples, the nonlinear algebraic equations described in the above specific embodiments are expressed as follows:

[0081] At the internal grid point (i, j), the discretized system of algebraic equations contains equations of the following form:

[0082] A i,j (x i+1,j - 2x i,j +x i-1,j )+B i,j (x i,j+1 -2x i,j +x i,j-1 )+...+D i,j (y i+1,j -y i-1,j )(y i,j+1 -y i,j-1 )=0;

[0083] E i,j (y i+1,j -2y i,j +y i-1,j )+F i,j (y i,j+1 -2y i,j +y i,j-1 )+...+H i,j (x i+1,j -x i-1,j (x) i,j+1 -x i,j-1 )=0;

[0084] Where, x i,j The x-coordinate of grid point (i, j) in physical space; x i+1,j x i-1,j x i,j+1 x i,j-1 Let x and y represent the x-coordinates of adjacent grid points surrounding the center point (i, j); i,j This represents the Y-coordinate of grid point (i, j) in physical space; y i+1,j y i-1,j y i,j+1 y i,j-1 These represent the Y coordinates of adjacent grid points around the center point (i, j); coefficient A i,j B i,j H i,j The variables are the coordinates of the grid points, and the equations contain cross-product terms of unknown coordinates, thus ensuring that the generated system of algebraic equations is nonlinear.

[0085] Step S1223, Iterative solution: The physical coordinates of the initial grid are used as the initial values ​​for iterative calculation and the process is repeated multiple times. In each iteration, the internal grid points in the parameter space are traversed, and the latest known coordinate values ​​adjacent to the current grid point are substituted into the discretized algebraic equation system to solve and update the coordinate estimate of the current grid point.

[0086] Specifically, after obtaining the set of nonlinear algebraic equations at discrete grid points, iterative solutions and grid point updates are performed:

[0087] Initialization: Set the physical coordinates x(ξ, η) of the initial mesh generated by the TFI method. 0 and y(ξ,η) 0 As the initial value for iteration; where the subscript... 0 This represents the initial value for the iteration.

[0088] Iterative loop: Based on the set of nonlinear algebraic equations, perform K iterations, where K is a preset positive integer; for the (k+1)th iteration (k≥0), traverse each internal grid point (i,j) in the parameter space:

[0089] In the discretized set of nonlinear algebraic equations, excluding the unknown coordinates of the current point (i, j) in the (k+1)th iteration... , Except for the other terms, the coordinates of the adjacent points in the latest known iteration step are substituted into the equations.

[0090] Solve the set of nonlinear algebraic equations and update the coordinate estimates of the current grid points.

[0091] Boundary condition handling: When constructing the set of algebraic equations, the physical coordinates of all grid points located on the boundary of the computational domain are treated as known constants and remain unchanged throughout the entire iteration process.

[0092] Step S1224: When the preset iteration termination condition is met, the iteration process is terminated, and the finally updated physical coordinates are used as the optimized 1 / 2 symmetry plane structure mesh coordinates, that is, the physical coordinates obtained from the last iteration update. and The optimized coordinates of the 1 / 2 symmetry plane structure mesh are used as the reference, and a 1 / 2 symmetry plane structure mesh is generated based on the optimized coordinates of the 1 / 2 symmetry plane structure mesh. Figure 2 and Figure 3 As shown.

[0093] The preset iteration termination condition is that the iteration process terminates when the preset number of iterations K is reached.

[0094] In some specific embodiments, the preset number of iterations K can be set to 8 to 15 times, and preferably the preset number of iterations K is set to 10 times.

[0095] Step S200 involves reconstructing the 3D spatial mesh, which expands the high-quality 2D profile mesh into a 3D global mesh. Specifically, the 1 / 2 symmetry plane mesh is rotated around the symmetry axis of the rocket to generate the final full-domain 3D structural mesh. By treating the 2D profile mesh as a "template," the rocket is divided circumferentially, and the template mesh is rotated around the symmetry axis at each division angle. Coordinate transformation is then used to generate the 3D mesh profile at that angle. Finally, these 3D profile mesh points are assembled according to their inherent topological connections (inherited from the 2D mesh) to form a complete, high-quality 3D structural mesh, effectively ensuring the strict symmetry and high quality of the 3D mesh. Step S200 specifically includes:

[0096] Step S210: Obtain the node coordinate set of the two-dimensional planar structure mesh representing the 1 / 2 symmetric section of the spinning rocket.

[0097] The 1 / 2 planar mesh mentioned above is a mesh in the z=0 plane. Therefore, the node coordinates of the 1 / 2 symmetry plane mesh are represented as (x... i y j ,0), the node coordinates (x, 0) of the 1 / 2 symmetry plane mesh i y j ,0) serves as the initial dataset for the rotation operation, i.e., the set of node coordinates of the two-dimensional planar mesh. ; , .

[0098] Step S220: The rocket's 360-degree circumferential domain is discretized at equal angles. The coordinate set of the nodes of the two-dimensional planar structure mesh is transformed by a corresponding angle around the rocket's axis of symmetry to generate a series of two-dimensional mesh profiles that are uniformly distributed in the circumferential direction.

[0099] Specifically, the initial dataset is rotated around the x-axis. A new mesh surface will be obtained at a certain degree, with coordinates as follows: Divide the rocket's circumference into Z equal parts (360 degrees). Rotate the initial dataset around the x-axis Z times, with each rotation being an angle θ. z =2πz / Z (where z is an integer from 1 to Z), the expression for generating the coordinates of grid points on Z planes of revolution is:

[0100] .

[0101] In some specific embodiments, the value of Z can be set to 100 to 140, and preferably, the value of Z is set to 120.

[0102] Step S230 involves connecting the grid points in all the two-dimensional grid profiles obtained after the circumferential transformation in three-dimensional space according to their inherent topological relationships, assembling them into a complete three-dimensional structural grid covering the entire watershed. Specifically, all grid points generated on the Z rotation surfaces are connected according to topological relationships to assemble a complete three-dimensional structural grid covering the entire watershed.

[0103] Those skilled in the art will understand that this invention utilizes the geometric symmetry of the rotating body to generate a high-quality structured mesh in a two-dimensional plane along the axis of symmetry. The structured mesh is then used as a template for geometrical operations involving rotation around the axis of symmetry, efficiently assembling into a complete three-dimensional structured mesh. This effectively solves the problems of complex and time-consuming generation processes in traditional three-dimensional structured mesh generation, as well as the high numerical dissipation and difficulty in ensuring symmetry in unstructured meshes. While ensuring high mesh quality and high orthogonality, it significantly improves generation efficiency and achieves precise control of mesh density through parameterization, thereby enhancing the reliability of high-precision numerical simulations of the aerodynamic characteristics of rotating bodies.

[0104] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the claims, any of the claimed embodiments can be used in any combination.

[0105] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for generating aerodynamic structure meshes for a spinning rocket, characterized in that, include: In the Oxy plane of the global coordinate system Oxyz, construct and discretize the boundary of the 1 / 2 symmetry plane computational region of the spinning rocket; Based on the boundary of the computational region of the 1 / 2 symmetry plane, a planar structure mesh of the 1 / 2 symmetry plane is generated in the Oxy plane; The 1 / 2 symmetry plane mesh is rotated around the symmetry axis of the solid rocket to generate a full-domain three-dimensional structure mesh.

2. The method according to claim 1, characterized in that, The step of constructing and discretizing the boundary of the 1 / 2 symmetry plane computational region of the spinning rocket in the Oxy plane of the global coordinate system Oxyz includes: The intersection of the shape of the spinning rocket and the Oxy plane is extracted as the generatrix, and the intersection of the outer boundary of the calculation region and the Oxy plane is extracted as the upper contour of the outer boundary. The generatrix and the upper contour of the outer boundary are discretized into I+1 coordinate points respectively. Connect the endpoints of the busbar at the head and tail to the corresponding points on the outer boundary contour to form the right and left boundaries of the calculation area, and discretize the two boundaries into J+1 coordinate points respectively; The boundary of the 1 / 2 symmetry plane calculation region is formed by the combination of the generatrix, the outer boundary contour, the right boundary, and the left boundary.

3. The method according to claim 2, characterized in that, The step of generating a planar structured mesh with a 1 / 2 symmetry plane in the Oxy plane based on the boundary of the computational region using the 1 / 2 symmetry plane includes: Based on the coordinates of all boundary points obtained by discretization, the initial structural mesh within the boundary of the computational region of the 1 / 2 symmetry plane is generated using the trans-limit interpolation method. Starting from the initial structure mesh, the mesh smoothing method based on elliptic partial differential equations is used for iterative solution to optimize the distribution of mesh points and obtain a 1 / 2 symmetry plane structure mesh.

4. The method according to claim 3, characterized in that, The transfinite interpolation method is a linear transfinite interpolation method, and the interpolation process is defined by a vector function of Boolean form.

5. The method according to claim 4, characterized in that, The step of generating the initial structure mesh within the boundary of the 1 / 2 symmetry plane computational region using the trans-limit interpolation method includes: Define a vector mapping function from the rule parameter space to the physical computation domain; Based on the coordinates of discrete points on the boundary of the computational region, interpolation functions are constructed along the two coordinate axes of the parameter space; and the interpolation functions in the two directions are combined in Boolean form to obtain the vector mapping function. Based on the Boolean mapping function, the set of coordinate points corresponding to the regular grid points in the parameter space in the physical space is calculated, which constitutes the initial value of the 1 / 2 symmetry plane grid; based on the initial value of the 1 / 2 symmetry plane grid, the initial structural grid within the boundary of the 1 / 2 symmetry plane computational region is generated.

6. The method according to claim 5, characterized in that, The steps of defining the vector mapping function from the rule parameter space to the physical computation region include: The steps of defining the vector mapping function from the rule parameter space to the physical computation region include: Define the vector mapping function from the parameter space (ξ,η) to the physical space (x,y) as follows: : ； The range of values ​​for parameter ξ is as follows: The range of values ​​for parameter η is: The four boundaries of the computational region are respectively mapped to the four boundaries of the parameter space.

7. The method according to claim 5, characterized in that, The steps of constructing interpolation functions along two coordinate axes of the parameter space based on the coordinates of discrete points on the boundary of the computational region, and combining the interpolation functions in the two directions using Boolean sums to obtain the vector mapping function, include: Based on positive integer index and Generate regular grid points in the parameter space ( , The expression is as follows: ； Based on the coordinates of discrete points on the boundary of the computational region, interpolation functions U and V are constructed along the ξ and η directions, respectively: ； in, Let L be the interpolation basis function in the ξ direction; L be the number of basis functions in the ξ direction; P be the highest order of the summation in the ξ direction; and n be the order of the partial derivative (0 ≤ n ≤ P). yes Partial derivative with respect to the direction of ξ; Let M be the interpolation basis function in the η direction; M be the number of basis functions in the η direction; Q be the highest order of the summation in the η direction; and m be the order of the partial derivative (0 ≤ m ≤ Q). yes Partial derivative with respect to the direction of η; When linear interpolation is used, with parameters P=Q=0 and L=M=2, the interpolation basis function is: ； The interpolation function and The vector mapping function is obtained by combining Boolean and formal methods. The expression for (ξ,η): ； Among them, the product term The expression for (ξ,η) is: 。 8. The method for generating aerodynamic structure mesh for a spinning rocket according to claim 3, characterized in that, The mesh smoothing method for the elliptic partial differential equations uses the Laplace equations and employs the finite difference method for discrete solution.

9. The method for generating aerodynamic structure mesh for a spinning rocket according to claim 8, characterized in that, The steps of iteratively solving the problem using a mesh smoothing method based on elliptic partial differential equations to optimize the distribution of mesh points and obtain a 1 / 2 symmetry plane structure mesh include: Based on the elliptic partial differential equations in physical space, the Laplace equations are established; through coordinate transformation, the governing equations are transformed from physical coordinates to parametric coordinates to obtain the mesh generation equation set. On a regular grid in the parameter space, the grid generation equations are discretized using a numerical discretization method, transforming them into a set of nonlinear algebraic equations on discrete grid points. Iterative solution: The physical coordinates of the initial grid are used as the initial values ​​for iterative calculation and the process is repeated multiple times. In each iteration, the internal grid points in the parameter space are traversed and the latest known coordinate values ​​adjacent to the current grid point are substituted into the discretized algebraic equation system to solve and update the coordinate estimate of the current grid point. Throughout the entire iteration process, the coordinates of the grid points on the boundary of the computational domain remain unchanged; When the preset iteration termination condition is met, the iteration process is terminated, and the finally updated physical coordinates are used as the coordinates of the optimized 1 / 2 symmetry plane structure mesh; and a 1 / 2 symmetry plane structure mesh is generated based on the optimized 1 / 2 symmetry plane structure mesh coordinates.

10. The method according to claim 1, characterized in that, The step of rotating the 1 / 2 symmetry plane mesh around the symmetry axis of the solid rocket to generate a full-domain three-dimensional structure mesh includes: Obtain the node coordinate set of a two-dimensional planar structure mesh representing a half-symmetric section of a spinning rocket; The rocket's 360-degree circumference is discretized at equal angles; the coordinate set of the nodes of the two-dimensional planar structure mesh is transformed by a corresponding angle around the rocket's axis of symmetry to generate a series of two-dimensional mesh profiles that are uniformly distributed in the circumference. The grid points in all the two-dimensional grid profiles obtained after circumferential transformation are connected in three-dimensional space according to their inherent topological relationships, and assembled into a three-dimensional structural grid covering the entire watershed.

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