A grid density optimization method based on flow field physical information

Abstract

The application relates to a grid density optimization method based on flow field physical information, and belongs to the field of fluid mechanics simulation and simulation, and comprises the following steps: step one: generating an initial grid for a fluid in a fluid mechanics problem numerical simulation system, and giving the initial physical quantity distribution on a flow field; step two: calculating the characteristic physical quantity gradient of an internal edge in the grid system; step three: adjusting the grid based on the distribution of the characteristic physical quantity gradient, and calculating the displacement of each internal node; and step four: updating the grid according to the displacement vector of the internal node, and iteratively executing steps two to four until the characteristic physical quantity gradient variance of the grid meets a convergence condition, and outputting the optimized grid. The application can be simultaneously applied to two-dimensional and three-dimensional grids, and compared with the grid before optimization, the calculation precision can be improved under the condition that the calculation time length is basically unchanged; especially when the grid quantity is relatively small, the comparison result is more obvious.

Description

Technical Field

[0001] This invention belongs to the field of fluid dynamics simulation and relates to a grid density optimization method based on flow field physical information. Background Technology

[0002] Computational fluid mechanics (CFD) is an interdisciplinary field that emerged with the development of computers, integrating mathematics, fluid mechanics, and computer science. Its main research content is to use numerical methods (such as the finite volume method and the finite element method) to solve fluid control equations and simulate and analyze fluid mechanics problems.

[0003] In simulating and analyzing fluid dynamics problems, it is necessary to mesh the simulated fluid domain. The mesh generation and optimization techniques have a crucial impact on the accuracy and solution efficiency of CFD numerical simulations. Overly dense meshes lead to excessively long solution times, while overly sparse meshes result in significant errors in the calculation results. Therefore, researching relatively efficient mesh generation and optimization techniques that meet accuracy requirements is a significant challenge. To date, the scientific community has proposed various mesh generation and optimization methods based on different mesh quality metrics. Some methods excel in mesh quality but are too time-consuming, such as radial basis function interpolation; others have shorter computation times but lower accuracy, failing to meet engineering requirements. A mesh deformation method that simultaneously achieves high computational accuracy and low computation time presents a significant challenge for CFD numerical simulations.

[0004] The computation time of CFD numerical simulations largely depends on the number and quality of the mesh. When the mesh is severely distorted, both computational efficiency and accuracy decrease significantly, and it may even prevent the calculation from proceeding. Large mesh deformation problems, such as aspect ratio misalignment, distortion, and other distortions, all affect the accuracy and time of numerical calculations. Therefore, it is necessary to conduct in-depth and systematic research on mesh technology in conjunction with practical problems, and to design efficient and reasonable mesh adjustment methods to improve the efficiency and accuracy of numerical calculations. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a grid density optimization method based on flow field physical information, which is used to optimize the grid for fluid division in the simulation analysis of fluid dynamics problems, so as to make the grid point distribution more reasonable and thus improve the calculation accuracy of numerical simulation in CFD.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A grid density optimization method based on flow field physical information includes the following steps:

[0008] Step 1: In the numerical simulation system for fluid mechanics problems, generate an initial mesh for the fluid and give the initial distribution of physical quantities in the flow field;

[0009] Step 2: Calculate the gradient of characteristic physical quantities of the internal edges in the mesh system;

[0010] Step 3: Adjust the mesh based on the distribution of the characteristic physical quantity gradient, and calculate the displacement of each internal node;

[0011] Step 4: Update the mesh based on the displacement vectors of the internal nodes, and iterate through steps 2 to 4 until the gradient method of the characteristic physical quantities of the mesh satisfies the convergence condition, and output the optimized mesh.

[0012] Furthermore, the characteristic physical quantity gradient of the internal edges in the computational grid system described in step two specifically includes: the gradient of the grid M generated in the k-th iteration. k For each internal grid point m, a polyhedral cavity subsystem is constructed, and the gradients of characteristic physical quantities on the edges formed by the internal grid point m and its neighboring grid points n are calculated.

[0013] Furthermore, the gradient of the characteristic physical quantity mentioned in step two The calculation formula is as follows:

[0014]

[0015] In the formula, Φ m , Φ n d represents the characteristic physical quantity at grid point m and its adjacent grid point n, respectively; mn This represents the distance between grid point m and grid point n; This represents the gradient of a characteristic physical quantity between grid point m and grid point n.

[0016] Furthermore, the step three, which involves adjusting the distribution mesh based on the gradient of the characteristic physical quantity and calculating the displacement of each internal node, specifically includes: adjusting the mesh based on the gradient of the characteristic physical quantity. Calculate the displacement vector of each internal grid point m in the k-th iteration.

[0017]

[0018] In the formula, and The grid M in the k-th iteration is respectively k The displacement vector of grid point m and the k-th iteration grid M k The displacement vector of grid point n on the grid; R represents the number of grid points adjacent to grid point m.

[0019] Furthermore, in the k-th iteration, the coordinates of grid point m are:

[0020]

[0021] Among them, V m,k V represents the coordinates of grid point m in the k-th iteration. m,k-1 This represents the coordinates of grid point m in the (k-1)th iteration. For the grid M in the k-th iteration k The displacement vector of grid point m on the grid.

[0022] Furthermore, in step four, the mesh M k The formula for calculating the ratio of the characteristic physical quantity gradient at the geometric center of the grid cell in the i-th grid cavity to the volume of that grid cell, GVR, is as follows:

[0023]

[0024] In the formula, grad(Φ) represents the gradient of the characteristic physical quantity Φ, and V represents the volume of the mesh cell.

[0025] The variance of GVR represents the degree of optimization of the mesh cells based on the gradient of the characteristic physical quantity, and it is defined as follows:

[0026]

[0027] In the formula, σ 2 (GVR) represents the variance of GVR. This represents the average GVR of the grid, where N represents the number of grid cells;

[0028] Furthermore, in step four, after updating the mesh, based on the mesh M before the update... k The distribution of physical quantities f on k (M k Interpolation calculation of the updated mesh M k+1 The distribution of physical quantities f on k+1 (M k+1 ); Computational grid M k+1 The gradient variance σ of the flow characteristic physical quantity 2 (GVR) k+1 Determine if the mesh meets the termination condition. If it does, output mesh M according to the termination condition. * =M k Or M * =M k+1 and flow field distribution f * (M * )=f k (M k ) or f * (M *)=f k+1 (M k+1 If the iteration count is not found, stop the iteration; otherwise, increment the iteration count by 1 and return to step two.

[0029] Furthermore, in step four, the step of updating the mesh M before the update... k The distribution of physical quantities f on k (M k Interpolation calculation of the updated mesh M k+1 The distribution of physical quantities f on k+1 (M k+1 For grid M k For grid point m, there are three possible cases:

[0030] (4) If grid M k+1 Point m on the line is exactly opposite to M k If grid points n on the grid coincide, then:

[0031] f k+1 (m)=f k (n)

[0032] In the formula, f k+1 (m), f k (n) represent the grid M respectively. k+1 Grid point m and grid M k The physical quantity at grid point n on the grid;

[0033] (5) If grid M k+1 Point m on the grid exactly falls on grid M k grid edges Above, where a and b are grids M k+1 For two adjacent grid points, there are two possible scenarios:

[0034] a) If the grid edge There is a suspended node, and the physical quantity f at point m is... k+1 The formula for calculating (m) is:

[0035]

[0036] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n on the grid; n represents the grid point in the two grids excluding the grid points on the common edge, and the grid points on both sides of the grid point m on the common edge that are closest to m; N represents the grid edge. The number of grid points in the two grids to which they belong;

[0037] Wherein, the weight w of the weighted average mn The calculation formula is:

[0038]

[0039] In the formula, d mn This represents the distance between grid point m and grid point n;

[0040] b) If the grid edge If there are no dangling nodes, then:

[0041]

[0042] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n; n represents the grid edge. Grid points on the two grids; N represents the grid edge. The number of grid points in the two grids to which they belong;

[0043] Wherein, the weight w of the weighted average mn The calculation formula is:

[0044]

[0045] In the formula, d mn This represents the distance between grid point m and grid point n;

[0046] (6) If grid point m falls on M k Within a certain mesh cavity, then:

[0047]

[0048] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n on M; n represents the position of grid point m on M. k The grid point to which grid point m belongs; N indicates that grid point m is in grid M. k The number of grid points in the grid to which it belongs;

[0049] Wherein, the weight w of the weighted average mn The calculation formula is:

[0050]

[0051] In the formula, d mn This represents the distance between grid point m and grid point n;

[0052] After interpolation calculation of M k+1 After adding all grid points, we get M.k+1 The distribution of physical quantities f on k+1 (M k+1 ).

[0053] Furthermore, the convergence condition described in step four is:

[0054] (σ 2 (GVR) k+1 ≥σ 2 (GVR) k &&σ 2 (GVR) k+1 -σ 2 (GVR) k ≤ε q )V(σ 2 (GVR) k+1 <σ 2 (GVR) k )

[0055] In the formula, ε q Given a tolerance; when the convergence condition σ is satisfied 2 (GVR) k+1 <σ 2 (GVR) k When the iteration stops, let M * =M k f * (M * )=f k (M k When the convergence condition (σ) is satisfied... 2 (GVR) k+1 ≥σ 2 (GVR) k &&σ 2 (GVR) k+1 -σ 2 (GVR) k ≤ε q When the iteration stops, then M * =M k+1 f * (M * )=f k+1 (M k+1 M * For the optimized mesh.

[0056] The beneficial effects of this invention are as follows: By optimizing the distribution of grid points, this invention further improves the computational accuracy of numerical analysis of fluid mechanics problems; this invention adjusts the grid based on the gradient of characteristic physical quantities in the flow field, making the grid distribution in the flow field more reasonable, striving to distribute the error evenly across each grid; this invention can reduce the variance of the gradient of characteristic physical quantities of the grid while keeping the number of grids and the grid topology unchanged; the computation time of CFD numerical simulation mainly depends on the number and quality of grids, therefore, this invention can improve the computational accuracy of CFD numerical simulation by making the grid more consistent with the actual application of computational fluid dynamics while keeping the computation time basically unchanged. This invention can be applied to both two-dimensional and three-dimensional grids, and can improve the computational accuracy while keeping the computation time basically unchanged compared with the grid before optimization.

[0057] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0059] Figure 1 This is a flowchart of the mesh density optimization method based on flow field physical information described in this invention;

[0060] Figure 2 This is a schematic diagram illustrating the interpolation method of physical quantities before and after grid update in the grid density optimization method based on flow field physical information described in this invention.

[0061] Figure 3 This is a schematic diagram illustrating the steps of the mesh density optimization method based on flow field physical information described in this invention, where there are suspended nodes on the common edges.

[0062] Figure 4 Spatial pressure distribution diagram of an embodiment of the present invention; Detailed Implementation

[0063] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0064] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0065] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present 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 terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0066] Example: In this example, the methane combustion case from the OpenFOAM open-source CFD numerical simulation software is used. This example simulates the methane combustion process. Based on this example, the mesh quality, computation time, and computational accuracy of the mesh density optimization method based on flow field physical information proposed in this invention are explained. The case directory is tutorials\incompressible\simpleFoam\smallPoolFire.

[0067] In this embodiment, snappyHexMesh is used to generate an initial mesh M0, with approximately 22,000 meshes generated. The initial σ 2 The (GVR) value is 2.41 × 10 8 The mesh M0 is optimized using the mesh optimization method based on flow field physical information proposed in this invention, resulting in the optimized mesh M. * .

[0068] like Figure 1As shown, this embodiment utilizes a grid density optimization method based on flow field physical information to optimize M0, mainly including the following steps:

[0069] Step 1: Given the initial grid M0 and flow field f0(M0) for the smallPoolFire case, the number of grid cells is approximately 22,000, σ 2 The (GVR) value is 2.41 × 10 8 The temperature field in the smallPoolFire case is as follows: Figure 4 As shown;

[0070] Step 2: Calculate the gradient variance of the characteristic physical quantity of the initial mesh M0. The gradient variance (gradient to volume ratio) represents the ratio of the gradient of the characteristic physical quantity at the geometric center of the mesh cell to the volume of that mesh cell. k The gradient of the characteristic physical quantity of the i-th mesh cavity The calculation formula is:

[0071]

[0072] In the formula, grad(Φ) represents the gradient of the characteristic physical quantity Φ, and V represents the volume of the mesh cell.

[0073] The variance of GVR represents the degree of optimization of the mesh cells based on the gradient of the characteristic physical quantity, and it is defined as follows:

[0074]

[0075] In the formula, σ 2 (GVR) represents the variance of GVR. This represents the average GVR of the grid, and N represents the number of grid cells.

[0076] In this embodiment, the variance σ of the characteristic physical quantity of grid M0 2 The calculated (GVR) result is 1.72 × 10⁻⁶. 6 .

[0077] Step 3: Starting from k=0, let M be... k Each internal grid point establishes a polyhedral cavity subsystem. The polyhedral cavity system constructed by the grid points refers to a system including grid M. k The subsystem consists of the target grid point m and all grid points n adjacent to it. This subsystem is used to determine the formula... Calculate the pressure gradient on each edge Construct a pressure gradient field; where P m P n d represents the pressure at grid point m and its adjacent grid point n, respectively;mn This represents the distance between grid point m and grid point n; This represents the pressure gradient between grid point m and grid point n.

[0078] Step 4: In this embodiment, the number of internal grid points is approximately 22,000, according to the formula... Calculate the displacement vector of each internal grid point In the formula, and The grid M in the k-th iteration is respectively k The displacement vector of grid point m and the k-th iteration grid M k The displacement vector of grid point n on the grid; R represents the number of grid points adjacent to grid point m. Therefore, in the k-th iteration, the coordinates of grid point m are:

[0079]

[0080] Among them, V m,k V represents the coordinates of grid point m in the k-th iteration. m,k-1 This represents the coordinates of grid point m in the (k-1)th iteration. For the grid M in the k-th iteration k The displacement vector of grid point m on the grid.

[0081] Step 5: Based on the results of Step 4, update the mesh to obtain mesh M. k+1 ;

[0082] Step Six: Based on the mesh M before the update k The distribution of physical quantities f on k (M k Interpolation calculation of the updated mesh M k+1 The distribution of physical quantities f on k+1 (M k+1 Computational grid M k+1 The characteristic physical quantity gradient variance σ 2 (GVR) k+1 Determine if the mesh meets the termination condition. If it does, output mesh M according to the termination condition. * =M k Or M * =M k+1 and flow field distribution f * (M * )=f k (M k ) or f * (M * )=f k+1 (M k+1 If the iteration stops, stop; otherwise, let k = k + 1 and jump to step three.

[0083] The convergence condition is as follows:

[0084] (σ 2 (GVR) k+1 ≥σ 2 (GVR) k &&σ 2 (GVR) k+1 -σ 2 (GVR) k ≤ε q )∨(σ 2 (GVR) k+1 <σ 2 (GVR) k )

[0085] In the formula, ε q Given a tolerance; when the convergence condition σ is satisfied 2 (GVR) k+1 <σ 2 (GVR) k When the iteration stops, let M * =M k f * (M * )=f k (M k When the convergence condition (σ) is satisfied... 2 (GVR) k+1 ≥σ 2 (GVR) k &&σ 2 (GVR) k+1 -σ 2 (GVR) k ≤ε q )∨(σ 2 (GVR) k+1 When the iteration stops, then M * =M k+1 f * (M * )=f k+1 (M k+1 M * For the optimized mesh.

[0086] Grid M k and the distribution of physical quantities f on its grid k (M k To interpolate and calculate the updated mesh M k+1 The distribution of physical quantities f on k+1 (M k+1 For grid M k Grid point m on, such as Figure 2 As shown, there are three possible scenarios:

[0087] (1) If grid M k+1 Point m on the line is exactly opposite to M k If grid points n on the grid coincide, then:

[0088] f k+1 (m)=f k (n)

[0089] In the formula, f k+1 (m), f k (n) represent the grid M respectively. k+1 Grid point m and grid M k The physical quantity at grid point n.

[0090] (2) If grid M k+1 Point m on the grid exactly falls on grid M k grid edges Above, where a and b are grids M k+1 For two adjacent grid points, there are two possible scenarios:

[0091] a) If the grid edge There are dangling nodes. A dangling node is a point located on the edge of the mesh. Figure 3 Several cases for suspended nodes. The physical quantity f at point m. k+1 The formula for calculating (m) is:

[0092]

[0093] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n on the grid; n represents the grid point in the two grids excluding the grid points on the common edge, and the grid points on both sides of the grid point m on the common edge that are closest to m; N represents the grid edge. The number of grid points in the two grids to which it belongs.

[0094] Wherein, the weight w of the weighted average mn The calculation formula is:

[0095]

[0096] In the formula, d mn This represents the distance between grid point m and grid point n.

[0097] b) If the grid edge If there are no dangling nodes, then:

[0098]

[0099] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n; n represents the grid edge. Grid points on the two grids; N represents the grid edge. The number of grid points in the two grids to which it belongs.

[0100] Wherein, the weight w of the weighted average mn The calculation formula is:

[0101]

[0102] In the formula, d mn This represents the distance between grid point m and grid point n.

[0103] (3) If grid point m falls on M k Within a certain mesh cavity, then:

[0104]

[0105] In the formula, w mn f represents the weights in the weighted average; k (n) represents the grid M k The physical quantity at grid point n on M; n represents the position of grid point m on M. k The grid point to which grid point m belongs; N indicates that grid point m is in grid M. k The number of grid points in the grid to which it belongs.

[0106] Wherein, the weight w of the weighted average mn The calculation formula is:

[0107]

[0108] In the formula, d mn This represents the distance between grid point m and grid point n.

[0109] After interpolation calculation of M k+1 After adding all grid points, we get M. k+1 The distribution of physical quantities f on k+1 (M k+1 ).

[0110] In this embodiment, there are no suspended nodes, and the flow field distribution f on the previous grid is used. k (M k Interpolation calculation of the updated flow field distribution f on the mesh k+1 (M k+1 ), computational grid M k+1 The characteristic physical quantity gradient variance σ2 (GVR) k+1 Determine if the mesh meets the convergence condition. If it does, output mesh M according to the termination condition. * and f * (M * If the iteration stops, stop; otherwise, let k = k + 1 and jump to step three.

[0111] After 212 iterations, the program satisfies the convergence condition σ. 2 (GVR) k+1 ≥σ 2 (GVR) k &&σ 2 (GVR) k+1 -σ 2 (GVR) k ≤10 -8 The resulting mesh M * =M k+1 Its characteristic physical quantity variance is 1.72 × 10⁻⁶. 6 Since this embodiment lacks analytical solutions and physical experimental results, the calculation results with a finer mesh are used as the reference standard. Fine meshes have a larger number of grids and higher calculation accuracy, but the disadvantage is a longer computation time. This embodiment uses the calculation results with a finer mesh as the reference standard, comparing the calculation results of the meshes before and after optimization with the calculation results of the finer mesh for the smallPoolFire embodiment. A set of refined meshes with 820,000 grids is obtained using the area method mapping, and the calculation results of this mesh are used as the reference standard; based on the mesh M0 before optimization and the mesh M0 after optimization respectively... * The flow field distribution is calculated using a fine mesh and the simpleFoam solver. These three meshes are used for the implementation calculation.

[0112] The computation time of this embodiment is shown in Table 1. According to the calculation results, the computation time of the initial mesh is 45.2 seconds, the computation time of the refined mesh is 231.2 seconds, and the computation time of the optimized mesh is 484.8 seconds. The average temperature error before and after optimization is 178.2K and 11.84K, respectively, and the average velocity error before and after optimization is 6.66m / s and 1.56m / s, respectively. This shows that the method of the present invention has a significant improvement on the computational accuracy of the embodiment. The mesh quality change of this embodiment is shown in Table 2. It can be seen that the method of the present invention has little impact on the mesh quality. This indicates that the optimization method of the present invention can improve the accuracy of numerical simulation without significantly affecting the mesh quality.

[0113] Table 1

[0114] Initial grid This article's method Encrypted Grid Number of grid cells Approximately 22,000 Approximately 22,000 Approximately 23.6 Mesh generation time (seconds / s) 12.1 178.7 129.8 Calculation time (seconds / s) 33.1 52.5 355 Total time (seconds / s) 45.2 231.2 484.8 Average temperature error (k) 178.2 11.84 0 Average velocity error (m / s) 6.66 1.56 0

[0115] Table 2

[0116] Nonorthogonality Twist Non-uniformity Initial grid 7.68 0.28 0.43 Optimized mesh 7.32 0.31 0.35

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A grid density optimization method based on flow field physical information, characterized in that, Includes the following steps: Step 1: In the numerical simulation system for fluid mechanics problems, generate an initial mesh for the fluid and give the initial distribution of physical quantities in the flow field; Step 2: Calculate the gradient of characteristic physical quantities of the internal edges in the mesh system; Step 3: Adjust the mesh based on the distribution of the characteristic physical quantity gradient, and calculate the displacement of each internal node; Step 4: Update the mesh based on the displacement vectors of the internal nodes, and iterate through steps 2 to 4 until the gradient variance of the characteristic physical quantities of the mesh satisfies the convergence condition, and output the optimized mesh. The step of calculating the gradient of the characteristic physical quantity of the internal edge in the grid system in the second step specifically comprises: constructing a polyhedral envelope subsystem for each internal grid point m of the grid generated in the kth iteration and calculating the gradient of the characteristic physical quantity on the edge composed of the internal grid point m and its adjacent grid point n . The characteristic physical quantity gradient in step two The calculation formula is as follows: wherein, , respectively represent the characteristic physical quantity at the grid point m and its neighboring grid point n; represents the distance between the grid point m and the grid point n; represents the gradient of the characteristic physical quantity between the grid point m and the grid point n; Step three, which involves adjusting the distribution mesh based on the gradient of the characteristic physical quantity and calculating the displacement of each internal node, specifically includes: adjusting the mesh based on the gradient of the characteristic physical quantity. Calculate the displacement vector of each internal grid point m in the k-th iteration. : In the formula, and The grids for the k-th iteration are respectively The displacement vectors of grid point m and grid point n are given; R represents the number of grid points adjacent to grid point m.

2. The grid density optimization method based on flow field physical information according to claim 1, characterized in that: In the k-th iteration, the coordinates of grid point m are: in, This represents the coordinates of grid point m in the k-th iteration. This represents the coordinates of grid point m in the (k-1)th iteration. For the grid in the k-th iteration The displacement vector of grid point m on the grid.

3. The grid density optimization method based on flow field physical information according to claim 1, characterized in that: In step four, the mesh The formula for calculating the ratio of the characteristic physical quantity gradient at the geometric center of the grid cell in the i-th grid cavity to the volume of that grid cell, GVR, is as follows: In the formula, Representing characteristic physical quantities gradient, Indicates the volume of a grid cell; The variance of GVR represents the degree of optimization of the mesh cells based on the gradient of the characteristic physical quantity, and it is defined as follows: In the formula, This represents the variance of GVR. This represents the average GVR of the grid, and N represents the number of grid cells.

4. The grid density optimization method based on flow field physical information according to claim 1, characterized in that: In step four, after updating the mesh, the mesh is compared with the mesh before the update. Distribution of physical quantities on Interpolation calculation of the updated mesh Distribution of physical quantities on Computational grid gradient variance of flow characteristic physical quantities Determine if the mesh meets the termination condition; if so, output the mesh according to the termination condition. or and flow field distribution or If the iteration stops, stop the iteration; otherwise, increment the iteration count by 1 and return to step two.

5. The grid density optimization method based on flow field physical information according to claim 4, characterized in that: In step four, the mesh before the update is used... Distribution of physical quantities on Interpolation calculation of the updated mesh Distribution of physical quantities on For grid For grid point m, there are three possible cases: (1) If the grid Point m on the line is exactly the same as If grid points n on the grid coincide, then: In the formula, , Representing grids respectively Grid point m and grid The physical quantity at grid point n on the grid; (2) If the grid Point m on the grid falls exactly on the grid. grid edges Above, where a and b are grids. For two adjacent grid points, the following two cases exist: a) If the grid edge There is a suspended node on the surface, and the physical quantity at point m... The calculation formula is: In the formula, Indicates the weights of the weighted average; Represents a grid The physical quantity at grid point n on the grid; n represents the grid point in the two grids excluding the grid points on the common edge, and the grid points on both sides of the grid point m on the common edge that are closest to m; N represents the grid edge. The number of grid points in the two grids to which they belong; Among them, the weights of the weighted average The calculation formula is: In the formula, This represents the distance between grid point m and grid point n; b) If the grid edge If there are no dangling nodes, then: In the formula, Indicates the weights of the weighted average; Represents a grid The physical quantity at grid point n; n represents the grid edge. Grid points on the two grids; N represents the grid edge. The number of grid points in the two grids to which they belong; Among them, the weights of the weighted average The calculation formula is: In the formula, This represents the distance between grid point m and grid point n; (3) If grid point m falls on Within a certain mesh cavity, then: In the formula, Indicates the weights of the weighted average; Represents a grid The physical quantity at grid point n on the grid; n represents the position of grid point m. The grid point to which grid point m belongs; N represents the grid point m in the grid. The number of grid points in the grid to which it belongs; Among them, the weights of the weighted average The calculation formula is: In the formula, This represents the distance between grid point m and grid point n; Interpolation calculation completed After adding all grid points, we get Distribution of physical quantities on .

6. The grid density optimization method based on flow field physical information according to claim 1, characterized in that: The convergence condition described in step four is: In the formula, Given a tolerance; when the convergence condition is met When the iteration stops, let , When the convergence condition is met When the iteration stops, , , For the optimized mesh.

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