A radial basis function interpolation mesh deformation method supporting radius adaptation

Abstract

The application provides a radial basis function interpolation grid deformation method supporting radius self-adaption, and belongs to the technical field of flow field grid deformation, which comprises the following steps: determining a grid boundary needing deformation, performing grid point extraction on the grid boundary to form a set of deformation boundary grid points; determining an increment step of a support radius of a given RBF interpolation model, selecting a plurality of grid points as initial control points to construct the RBF interpolation model; calculating a fitting error of the grid points based on the current RBF interpolation model, adding the grid point corresponding to the maximum fitting error to the initial control points and reconstructing the RBF interpolation model if the fitting error does not meet the requirement; performing a deformation operation on all the grid points according to the RBF interpolation model meeting the requirement, calculating the quality of the deformed grid, and sequentially increasing the support radius based on the increment step and reconstructing the RBF interpolation model if the grid quality does not meet the requirement, until the grid quality meets the requirement or the grid quality no longer improves after the support radius is increased.

Description

Technical Field

[0001] This application belongs to the field of flow field mesh deformation technology, and specifically relates to a radial basis function interpolation mesh deformation method that supports radius adaptation. Background Technology

[0002] Mesh deformation refers to adjusting the mesh node coordinates to adapt the mesh to the movement or deformation of geometric boundaries without changing the mesh topology (i.e., keeping the element connections unchanged), thereby satisfying changes in physical interfaces (such as free liquid surfaces and fluid-solid interfaces). It has wide applications in fluid mechanics and solid mechanics calculations. Radial basis function (RBF) interpolation is one of the commonly used mesh deformation methods. It is suitable for conditions requiring high accuracy and large deformation, but it lacks adaptive characteristics. If the support radius is not properly selected, the mesh deformation quality will significantly decrease.

[0003] Therefore, a radius-adaptive RBF interpolation mesh deformation method is needed to automatically find the optimal support radius under large deformation conditions, thereby improving the mesh deformation quality. Summary of the Invention

[0004] The purpose of this application is to provide a radial basis function interpolation mesh deformation method that supports radius adaptation, in order to solve or mitigate at least one of the problems in the prior art.

[0005] The technical solution of this application is: a radial basis function interpolation mesh deformation method that supports radius adaptation, comprising:

[0006] Step S1: Determine the mesh boundary that needs to be deformed, and extract mesh points on the mesh boundary to form a set of deformable boundary mesh points;

[0007] Step S2: Given an initial value for the support radius of the RBF interpolation model, determine the incremental step size of the support radius;

[0008] Step S3: Select several grid points from the set of deformable boundary grid points as initial control points, and construct an RBF interpolation model based on the initial control points;

[0009] Step S4: Calculate the fitting error of all deformable boundary grid points based on the current RBF interpolation model, and determine whether the fitting error meets the requirements. If it does, proceed to the next step; if it does not meet the requirements, add the deformable boundary grid point corresponding to the maximum fitting error to the initial control points and reconstruct the RBF interpolation model.

[0010] Step S5: Perform deformation operations on all deformable boundary grid points according to the current RBF interpolation model that meets the requirements, obtain the displacement of all deformable boundary grid points, update the geometric data of all deformable boundary grid points according to the displacement, calculate the quality of the deformed mesh according to the geometric data, and output the current mesh if the mesh quality meets the requirements; if the mesh quality does not meet the requirements, increase the support radius sequentially based on the incremental step size and reconstruct the RBF interpolation model until the mesh quality meets the requirements or the mesh quality no longer improves after increasing the support radius, and then output the mesh under the currently found optimal support radius.

[0011] In a preferred embodiment of the present invention, the characteristic dimensions of the deformable object are used as the initial value of the support radius of the BRF interpolation model.

[0012] In a preferred embodiment of the present invention, a predetermined ratio of the difference between the farthest distance from the mesh deformation boundary to the mesh point and the initial value of the support radius is used as the incremental step size of the support radius.

[0013] In a preferred embodiment of the present invention, the predetermined ratio is from one-thousandth to one-hundredth.

[0014] In a preferred embodiment of the present invention, the RBF interpolation model constructed based on the initial control points is as follows:

[0015] ;

[0016] In the formula, It is the basis function matrix calculated based on N grid points selected on the current deformed mesh boundary points. , It is the weight coefficient vector along the k-direction. , It is the displacement vector of the grid point in the k direction. , , , These are the elements of the basis function matrix, the weight coefficient vector, and the displacement vector, respectively.

[0017] In a preferred embodiment of the present invention, the fitting error is the error between the interpolation result of the current RBF interpolation model after interpolating the deformation boundary grid points and the actual deformation displacement.

[0018] In a preferred embodiment of the present invention, the mesh quality includes orthogonality, aspect ratio, and volume ratio.

[0019] The method of this invention adds an automatic adjustment strategy for the support radius to the original RBF interpolation method for mesh deformation calculation, and sets two mesh deformation convergence conditions: the current deformed mesh quality reaches the minimum requirement or the deformed mesh quality no longer improves with the increase of the support radius. These settings automatically adjust the size of the support radius in the RBF interpolation method without manual setting, thereby reducing the workload of manual operation in mesh deformation calculation. Simultaneously, the method of this invention can guarantee that the mesh deformation quality meets the given minimum requirement, or, if the minimum requirement cannot be met, achieve optimal mesh quality. The method of this invention is versatile and suitable for different types of mesh deformation calculations. Attached Figure Description

[0020] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0021] Figure 1 This is a schematic diagram of the radial basis function interpolation mesh deformation method supporting radius adaptation according to the present invention.

[0022] Figure 2 This is a schematic diagram of a deformable boundary mesh according to an embodiment of the present invention.

[0023] Figure 3 This is a schematic diagram of wingtip deformation according to an embodiment of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0025] This application provides a radial basis function interpolation mesh deformation method that supports radius adaptation. During the mesh deformation calculation process, the support radius can be automatically adjusted to the optimal state, thereby ensuring the quality of the deformed mesh during large mesh deformation using the RBF interpolation method.

[0026] like Figure 1 As shown, the radial basis function interpolation mesh deformation method with adaptive radius provided in this application includes the following steps:

[0027] Step S1: Determine the mesh boundary that needs to be deformed, and extract mesh points on the mesh boundary to form a set of deformable boundary mesh points.

[0028] like Figure 2 The diagram shown is a schematic diagram of a deformable mesh interface in the wingtip structure of an airfoil according to an embodiment of the present invention. The mesh needs to be deformed at the mesh boundary. The set of deformable boundary mesh points is formed by extracting the mesh nodes at the deformable interface.

[0029] Step S2: Given the initial value of the support radius of the RBF interpolation model, determine the incremental step size of the support radius.

[0030] In this invention, the characteristic length of the deformable object is generally selected as the initial value of the support radius of the RBF interpolation model. For example, in this embodiment of the invention, the deformable object is an airfoil, and the average aerodynamic chord length of the airfoil is generally selected as its characteristic length. Further, in this invention, the farthest distance from the mesh deformation boundary to a mesh point is calculated, and a predetermined proportion of the difference between this farthest distance and the initial value of the support radius is used as the increment step size of the support radius. Typically, this predetermined proportion is between one-thousandth (1‰) and one-hundredth (1%). For example, in this embodiment of the invention, 1 / 1000 of the difference between the farthest distance from the mesh deformation boundary to a mesh point and the initial value of the support radius is used as the increment step size of the support radius.

[0031] Step S3: Select several grid points from the set of deformable boundary grid points as initial control points, and construct an RBF interpolation model based on the initial control points.

[0032] The RBF interpolation method calculates the deformation displacement of all grid points using a certain number of control points. For displacement calculation in a specific coordinate direction, the expression is:

[0033] (1)

[0034] In the formula, For any coordinate point in space The deformation displacement; k represents the direction of the coordinate, k=0 / 1 / 2 represent the x / y / z directions respectively; N represents the number of control points, i represents the control point number; This represents the weighting coefficient of the i-th control point in the k-th direction; As basis functions, , where r is the dimensionless normalized radius. R is the support radius.

[0035] After selecting N control points, the solution equation can be written in the form shown in Equation 2:

[0036] (2)

[0037] , , ;

[0038] In the formula, It is the basis function matrix calculated based on N grid points selected on the current deformed mesh boundary points. It is the weight coefficient vector along the k-direction. It is the displacement vector of the grid point in the k direction. , , These are the elements of the basis function matrix, the weight coefficient vector, and the displacement vector, respectively.

[0039] By selecting N control points, the basis function matrix Φ and the displacement vector can be completed. The construction of the RBF interpolation model is completed by obtaining the weight coefficient vector by giving the weight coefficients.

[0040] Step S4: Calculate the fitting error of all deformation boundary grid points based on the current RBF interpolation model, and determine whether the fitting error meets the requirements. If it does, proceed to the next step; if it does not meet the requirements, add the deformation boundary grid point with the maximum fitting error to the initial control points and reconstruct the RBF interpolation model.

[0041] In this invention, the fitting error of the deformation boundary grid points is the error between the interpolation result of the current RBF interpolation model after interpolating the deformation boundary grid points and the actual deformation displacement.

[0042] Step S5: Perform deformation operations on all deformation boundary grid points according to the current RBF interpolation model that meets the requirements, obtain the displacement of all deformation boundary grid points, update the geometric data of all deformation boundary grid points according to the displacement, calculate the quality of the deformed mesh according to the geometric data, if the mesh quality meets the requirements, output the current mesh, if the mesh quality does not meet the requirements, increase the support radius sequentially based on the incremental step size and reconstruct the RBF interpolation model until the mesh quality meets the requirements or the mesh quality no longer improves after increasing the support radius, then output the mesh under the currently found optimal support radius.

[0043] In this application, mesh quality includes orthogonality, aspect ratio, volume ratio, etc.

[0044] like Figure 3 The diagram shown is a schematic of the wingtip deformation calculated using the method of the present invention in this embodiment. The method of the present invention can accurately calculate the wingtip deformation mesh, so that the mesh quality reaches the optimal level.

[0045] This invention adds an automatic support radius adjustment strategy to the original RBF interpolation method for mesh deformation calculation, and sets two mesh deformation convergence conditions: the current deformed mesh quality reaches the minimum requirement or the deformed mesh quality no longer improves with the increase of the support radius. These settings automatically adjust the size of the support radius in the RBF interpolation method without manual setting, thus reducing the workload of manual operation in mesh deformation calculation. Furthermore, the method of this invention can guarantee that the mesh deformation quality meets the given minimum requirement, or, if the minimum requirement cannot be met, achieve optimal mesh quality. The method of this invention is versatile and suitable for different types of mesh deformation calculations.

[0046] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A radial basis function interpolation mesh deformation method supporting radius adaptation, characterized in that, include: Step S1: Determine the mesh boundary that needs to be deformed, and extract mesh points on the mesh boundary to form a set of deformable boundary mesh points; Step S2: Given an initial value for the support radius of the RBF interpolation model, determine the incremental step size of the support radius; Step S3: Select several grid points from the set of deformable boundary grid points as initial control points, and construct an RBF interpolation model based on the initial control points; Step S4: Calculate the fitting error of all deformable boundary grid points based on the current RBF interpolation model, and determine whether the fitting error meets the requirements. If it does, proceed to the next step; if it does not meet the requirements, add the deformable boundary grid point corresponding to the maximum fitting error to the initial control points and reconstruct the RBF interpolation model. Step S5: Perform deformation operations on all deformation boundary grid points according to the current RBF interpolation model that meets the requirements, obtain the displacement of all deformation boundary grid points, update the geometric data of all deformation boundary grid points according to the displacement, calculate the quality of the deformed mesh according to the geometric data, and output the current mesh if the mesh quality meets the requirements. If the mesh quality does not meet the requirements, the support radius is increased sequentially based on the incremental step size, and the RBF interpolation model is reconstructed until the mesh quality meets the requirements or the mesh quality no longer improves after increasing the support radius. Then, the mesh with the currently found optimal support radius is output.

2. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 1, characterized in that, The feature dimensions of the deformable object are used as the initial support radius of the BRF interpolation model.

3. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 2, characterized in that, The incremental step size of the support radius is a predetermined proportion of the difference between the farthest distance from the mesh deformation boundary to the mesh point and the initial value of the support radius.

4. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 3, characterized in that, The predetermined ratio is from one in a thousand to one in a hundred.

5. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 4, characterized in that, The RBF interpolation model constructed based on the initial control points is as follows: ； In the formula, It is the basis function matrix calculated based on N grid points selected on the current deformed mesh boundary points. , It is the weight coefficient vector along the k-direction. , It is the displacement vector of the grid point in the k direction. , , , These are the elements of the basis function matrix, the weight coefficient vector, and the displacement vector, respectively.

6. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 5, characterized in that, The fitting error is the error between the interpolation result calculated by the current RBF interpolation model for the deformation boundary grid points and the actual deformation displacement.

7. The radial basis function interpolation mesh deformation method supporting radius adaptation as described in claim 6, characterized in that, The mesh quality includes orthogonality, aspect ratio, and volume ratio.

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