Coarse and fine mesh interpolation method and system for wall turbulence calculation

Abstract

The invention relates to a thick and thin grid fast interpolation technology for wall turbulence calculation, and aims to solve the problems of large calculation amount and complex implementation process of an existing interpolation method. Half of the minimum grid spacing of the fine grids is used as a judgment standard, and interpolation modes are intelligently switched. For each fine grid point, when the distance between the fine grid point and the nearest coarse grid point is smaller than the standard, the physical value of the nearest coarse grid point is directly given to the fine grid point; otherwise, if the distance is greater than or equal to the standard, interpolation is carried out by adopting an inverse distance weighted average method. According to the method, half of the minimum fine grid scale is defined to serve as a standard for judging whether the fine grid point is directly assigned by the physical quantity on the nearest coarse grid amplitude point or not, and on the premise that it is ensured that physical information is not distorted, the complex calculation problem is simplified. The tedious calculation process in a traditional method is avoided, the algorithm complexity is effectively reduced, and the interpolation calculation speed and efficiency are remarkably improved.

Description

Technical Field

[0001] This application relates to the field of turbulence computation, and in particular to a coarse-fine grid interpolation method, system, computer device, and computer-readable storage medium for wall turbulence computation. Background Technology

[0002] In computational fluid dynamics, especially in numerical calculations of turbulent fields with flow control (such as applying air blowing or suction to the wall), researchers often need to prepare multiple sets of meshes with different resolutions. Typically, when calculating the basic uncontrolled flow condition, a coarse mesh with fewer grid points and larger grid spacing can be used. When it is necessary to study the details of the flow after control is applied, a fine mesh with refined meshing in the control region or region of interest must be used.

[0003] In numerical calculations, the development of flow from a transitional state to a fully developed turbulent state consumes a significant amount of computation time. To improve computational efficiency, a common practice is to use the fully developed turbulent field calculated on a coarse grid and interpolate it as the initial flow field for calculations on a fine grid. This method can significantly shorten the computation time for turbulent development under each operating condition, thereby effectively reducing the overall computational cost. However, since the number and spatial location of grid points in coarse and fine grids are usually different, and the nodes of the two grids almost do not overlap in physical space, an accurate and efficient grid interpolation technique must be employed to convey the flow field information.

[0004] The flow field is physically continuous (ignoring discontinuities such as shock waves), therefore, the values ​​of physical quantities (such as velocity and pressure) at adjacent grid points usually transition smoothly. Some simple grid interpolation techniques, such as directly assigning the physical quantity of the nearest coarse grid point to a fine grid point, while simple to implement, have significant drawbacks. If multiple fine grid points surround a coarse grid point, this method will cause these adjacent fine grid points to acquire identical physical quantity values, resulting in a stepped distribution on the fine grid that does not conform to physical laws, causing physical distortion.

[0005] To address the aforementioned issues, several high-accuracy interpolation methods have been proposed in related technologies. For example, some interpolation methods based on unstructured meshes or complex interpolation algorithms for structured meshes can achieve high interpolation accuracy. However, these methods typically require selecting a large number of mesh points around the target point for interpolation calculations, leading to complex implementation processes and high computational costs. In scenarios where only a reasonable initial field is needed for subsequent calculations, and the interpolation accuracy requirement is not extreme, these complex methods are insufficient in terms of computational efficiency and implementation complexity. Summary of the Invention

[0006] This application provides a method, system, computer device, and computer-readable storage medium for coarse-fine grid interpolation for wall turbulence calculation, in order to at least solve the problem of low interpolation accuracy in related technologies.

[0007] In a first aspect, embodiments of this application provide a coarse-fine grid interpolation method for wall turbulence calculation, used to interpolate the physical information of grid points between coarse and fine grids during wall turbulence calculation. The method includes: Obtain the target grid point in the fine grid, determine multiple neighboring grid points of the target grid point in the coarse grid, and calculate the relative distance between the target grid point and each of the neighboring grid points; The minimum distance is obtained among multiple relative distances, and the minimum distance is compared with half of the minimum scale of the fine mesh, wherein the minimum scale is the smallest scale among all flow and spanwise spacing of the fine mesh; Based on the comparison results, physical information is configured for the target grid points using a preset hybrid interpolation strategy.

[0008] In some embodiments, based on the comparison results, the physical information of the target grid points includes, through an interpolation strategy: When the minimum distance is less than half the minimum scale of the fine grid, the physical information of the neighboring grid point with the smallest relative distance to the target grid point is assigned to the target grid point; When the minimum distance is greater than or equal to half the minimum scale of the fine grid, the physical information of the target grid point is calculated based on the relative distance using an inverse distance weighted interpolation algorithm.

[0009] In some embodiments, based on the distance, an inverse distance weighted interpolation algorithm is used to calculate the physical information of the target grid point, including: The interpolation weights for each neighboring grid point are calculated, specifically by obtaining the reciprocal of the square of the relative distance between each neighboring grid point and the target grid point, which is used as the distance influence value for each neighboring grid point. The total influence value is obtained by summing the distance influence values ​​of all neighboring grid points. The normalized interpolation weight of a neighboring grid point is obtained by dividing the distance influence value of any neighboring grid point by the total influence value. Based on the normalized interpolation weights, the physical information of multiple neighboring grid points is weighted and summed to obtain the physical information of the target grid point.

[0010] In some embodiments, before obtaining the target mesh points of the fine mesh, the method further includes: Configure coarse and fine grids for interpolation, wherein the coarse and fine grids are structured grids in a Cartesian coordinate system. The coarse and fine grids have the same number and distribution of grid points in the normal direction, and are used to perform interpolation on multiple two-dimensional planes perpendicular to the normal direction during the process of configuring physical information for the target grid points.

[0011] In some embodiments, determining the target grid point's multiple neighboring grid points in the coarse grid includes: Obtain the coordinates of the target grid point on the two-dimensional plane; Obtain the grid spacing of the coarse grid in the flow direction and the spanning direction; Based on the coordinates of the target grid point and the grid spacing, a grid cell consisting of four initial coarse grid points is determined to surround the target grid point, and the four initial coarse grid points are designated as the neighboring grid points.

[0012] In some embodiments, the coarse grid is a uniformly distributed grid in the flow and span directions and a non-uniformly distributed grid in the normal direction, while the fine grid is a uniformly distributed grid or a non-uniformly distributed grid in the flow, normal, and span directions.

[0013] In some embodiments, the method further includes: After all target grid points on a two-dimensional plane have been configured with physical information, the coarse and fine grid interpolation method described above for wall turbulence calculation is repeated on other two-dimensional planes perpendicular to the normal until all fine grid points have been configured with physical information.

[0014] Secondly, embodiments of this application provide a coarse-fine grid interpolation system for wall turbulence calculation, used to interpolate the physical information of grid points between coarse and fine grids during wall turbulence calculation. The system includes: The acquisition module acquires the target grid point in the fine grid, determines multiple neighboring grid points of the target grid point in the coarse grid, and calculates the relative distance between the target grid point and each of the neighboring grid points; The judgment module obtains the minimum distance among multiple relative distances and compares the minimum distance with half of the minimum scale of the fine mesh, wherein the minimum scale is the smallest scale among all flow direction and spanwise spacing of the fine mesh; The difference processing module configures physical information for the target grid points based on the comparison results using a preset hybrid interpolation strategy.

[0015] Thirdly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in the first aspect above.

[0016] Fourthly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect above.

[0017] Compared to related technologies, this application provides a fast coarse-fine grid interpolation technique for wall turbulence calculation, aiming to solve the problems of high computational load and complex implementation process in existing interpolation methods. It uses half the minimum grid spacing of the fine grid as a criterion to intelligently switch interpolation methods. For each fine grid point, if the distance between it and the nearest coarse grid point is less than this criterion, the physical value of the nearest coarse grid point is directly assigned to the fine grid point; otherwise, if the distance is greater than or equal to the criterion, an inverse distance-weighted average method is used for interpolation. This method simplifies complex calculations by clearly defining half the minimum fine grid scale as the standard for determining whether a fine grid point is directly assigned a physical value from the nearest coarse grid amplitude point, while ensuring that physical information is not distorted. It avoids the cumbersome calculation process in traditional methods, effectively reduces algorithm complexity, and significantly improves the speed and efficiency of interpolation calculations. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of this application; Figure 2 This is a schematic diagram of a grid interpolation according to an embodiment of this application; Figure 3 This is a schematic diagram of the distribution of coarse grid points according to an embodiment of this application; Figure 4 This is a schematic diagram of the fine mesh point distribution according to an embodiment of this application; Figure 5 This is a partial schematic diagram of the flow field before interpolation according to an embodiment of this application; Figure 6 This is a partial schematic diagram of the flow field after interpolation according to an embodiment of this application; Figure 7 This is a structural block diagram of a coarse-fine grid interpolation system for wall turbulence calculation according to an embodiment of the application; Figure 8This is a flowchart of another coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of this application; Figure 9 This is a schematic diagram of the internal structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the application is described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0020] Obviously, the accompanying drawings described below are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar scenarios based on these drawings without any inventive effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, any changes to design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as insufficient disclosure of the content of this application.

[0021] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that is mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0022] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms “a,” “an,” “an,” “the,” and similar words used in this application do not indicate quantity limitation and may indicate singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units not listed, or may include other steps or units inherent to these processes, methods, products, or devices. The terms “connected,” “linked,” “coupled,” and similar words used in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. “Multiple” used in this application refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following objects are in an "or" relationship. The terms "first," "second," and "third" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects.

[0023] The method provided in this application can be applied to multiple fields of computational fluid dynamics (CFD), such as turbulence research, aircraft aerodynamic design, and aerodynamic analysis. In these fields, structured meshes are widely used due to their regularity in topology, particularly in direct numerical simulation (DNS) and large eddy simulation (LES) of wall turbulence. The interpolation method proposed in this application aims to provide a fast and efficient way to generate a fine-mesh initial field from coarse-mesh calculation results for such computational scenarios.

[0024] Figure 1 This is a flowchart of a coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of this application, as shown below. Figure 1 As shown, the process includes the following steps: Step S101: Obtain the target grid point in the fine grid, determine multiple neighboring grid points of the target grid point in the coarse grid, and calculate the relative distance between the target grid point and each neighboring grid point; specifically including:

[0025] S1 configures the coarse and fine meshes for interpolation. Both meshes are structured meshes in a Cartesian coordinate system, typically defined with the flow direction as the x-axis, the normal as the y-axis, and the span as the z-axis. The number and distribution of mesh points in the normal direction must be consistent between the coarse and fine meshes. This constraint allows for dimensionality reduction in the 3D interpolation problem, i.e., interpolation is performed sequentially on multiple 2D planes perpendicular to the normal (e.g., the XZ plane), significantly simplifying the computation process.

[0026] In this step, two sets of meshes are first needed for interpolation calculations: a source mesh (coarse mesh) and a target mesh (fine mesh). Both meshes are structured meshes in a three-dimensional Cartesian coordinate system. In wall turbulence calculations, the three directions of the coordinate system are usually defined as the streamwise direction. (representation), normal (wall-normal, using) (representation) and spanwise (using) express).

[0027] The coarse and fine meshes must satisfy a key constraint: both must be in the normal direction ( The number and distribution of grid points in the direction are consistent. This constraint simplifies the 3D interpolation problem to independent 2D interpolation on a series of 2D planes perpendicular to the normal, reducing the implementation complexity and computational cost of the algorithm.

[0028] In one specific embodiment, the flow direction, normal direction, and span direction of the coordinate system are represented by x, y, and z, respectively. The mesh computational domain is a cube, with lengths of x, y, and z in the flow direction, normal direction, and span direction, respectively. The number of grid points in the flow direction, normal direction, and span direction of the coarse grid are respectively... The grid distribution must be uniform in both the flow direction and spanwise direction (i.e., the spacing between adjacent grid points in the flow direction is 1). The spacing between adjacent grid points in the span is The normal direction allows for non-uniform mesh distribution; the number of mesh points in the flow direction, normal direction, and span direction of the coarse mesh are respectively... Coarse meshes allow for non-uniform distribution of meshes in the flow direction, normal direction, and span direction, but require that the distribution and number of points of the normal direction in the fine mesh be the same as those in the coarse mesh (i.e., Generally speaking, , .

[0029] This step defines the basic framework and constraints for interpolation calculations. By forcing normal mesh consistency, it reduces the dimensionality of complex three-dimensional problems, laying the foundation for subsequent efficient and accurate two-dimensional interpolation.

[0030] S2, after the mesh configuration is completed, reads the coordinate information of all grid points in the coarse mesh and the physical information stored thereon (such as velocity, pressure, etc.), as well as the coordinate information of all grid points in the fine mesh.

[0031] Subsequently, all fine grid points on a given two-dimensional plane are traversed, and one of these points is designated as the target grid point P0. Based on the coordinates of the target grid point on this two-dimensional plane, and the grid spacing of the coarse grid in the flow and span directions, a grid cell consisting of four initial coarse grid points is determined to enclose the target grid point. These four initial coarse grid points are then identified as neighboring grid points. Due to the uniformity of the coarse grid, these four points can be quickly located using integer division operations.

[0032] In one specific embodiment, the x, y, and z coordinates of all grid points of the coarse grid are read in and denoted as... , , And the physical information (such as velocity u, pressure p, etc.) at all grid points of the coarse grid, which is uniformly represented in this embodiment. Indicated, denoted as Read in the coordinates of all grid points in the fine grid, and denote them as follows: , , Obviously, since the number and distribution of grid points are consistent in the normal direction for both sets of meshes, we have... Therefore, all that is needed next is to perform interpolation on the XZ plane (i.e., the wall, j=1).

[0033] Step S2 is the data preparation stage, loading all the basic data required for subsequent calculations. By reading the coordinate information of the coarse and fine grids, as well as the existing physical quantity data on the coarse grid, input is provided for the interpolation calculation. Simultaneously, based on the premise of normal grid consistency, a calculation strategy for interpolation on a per-two-dimensional plane basis is determined.

[0034] S3, determine the multiple neighboring grid points of the target grid point in the coarse grid; In one specific embodiment, the four nearest coarse grid points are found based on the x and z coordinates of the fine grid. Figure 2 This is a schematic diagram of a grid interpolation according to an embodiment of this application, such as... As shown, the black dashed lines represent a coarse grid, and the red solid lines represent a fine grid. The specific implementation method is as follows: for coordinates in the XZ plane... The four nearest coarse grid points to the fine grid point P0 are: P1 , P2 , P3 and P4 .

[0035] in, , Here, " " indicates integer division, and the result will be the largest integer not greater than the quotient. For example, , If it is a boundary point, that is... (or ), then let , (or , ).

[0036] Step S3 is the positioning stage of the interpolation calculation. Utilizing the uniformity of the coarse grid on a specific plane, positioning can be efficiently completed through simple integer division operations, determining the precise coordinates of the four neighboring points. This operation provides the foundation for subsequent distance calculations and weighted interpolation.

[0037] S4. After determining the four neighboring grid points, further calculate the relative distance between the target grid point and each neighboring grid point.

[0038] In one specific embodiment, the distances from fine-mesh point P0 to P1, P2, P3, and P4 are calculated. Let the distances from fine-mesh point P0 to P1, P2, P3, and P4 be respectively... , , and Taking P1 as an example, the distance is calculated using the Pythagorean theorem. , .

[0039] Understandable. , and and The calculation method is similar and will not be described again in this embodiment.

[0040] Through step S101 above, the target grid point in the fine grid is obtained, multiple neighboring grid points of the target grid point in the coarse grid are determined, and the relative distance between the target grid point and each neighboring grid point is calculated. By calculating the Euclidean distance, the geometric distance is converted into a specific numerical value, providing a data foundation for subsequent interpolation algorithms. These distance values ​​are key parameters for determining which interpolation strategy to use and for calculating the weighting coefficients.

[0041] S102, obtain the minimum distance among multiple relative distances, and compare the minimum distance with half of the minimum scale of the fine mesh, where the minimum scale is the smallest scale among all flow and spanwise spacings of the fine mesh; specifically including:

[0042] S1. Find the minimum value among the four distances calculated in the above steps. Simultaneously, it is necessary to obtain the minimum scale of the fine mesh in both the flow and spanwise directions. This minimum scale is defined as the minimum value among all flow and spanwise spacings of the fine mesh. It should be noted that, since the fine mesh may be non-uniform, it is necessary to traverse all fine mesh cells to determine this value.

[0043] In one specific embodiment, find , , and The minimum value and the minimum scale of the fine mesh can be found using the bubble sort algorithm or built-in functions in the program. , , and The minimum value is denoted as , The smallest scale of the fine mesh is read in, denoted as... Here, "minimum scale" refers to the smallest spacing in all flow directions and spanwise directions within the fine mesh, which can be expressed as...

[0044] S2, by comparing the minimum distance with the size of the finer grid, determines which interpolation strategy to use. This step is crucial for ensuring the accuracy and feasibility of the interpolation algorithm.

[0045] Step S102 prepares for subsequent strategy selection. By finding the distance (dmin) between the target point and its closest neighbor, and determining a feature length (δ) that represents the fine mesh resolution, two core parameters are established to determine the relative proximity of the two points. dmin reflects the specific location characteristics of the current point, while δ provides a global scale reference. The comparison between the two is the basis for subsequent selection of interpolation strategies.

[0046] S103. Based on the comparison results, physical information is configured for the target grid points using a preset hybrid interpolation strategy.

[0047] This step is the core of this technical solution. It employs a hybrid interpolation strategy, selecting different interpolation methods based on the relative distance between the target grid point and the nearest coarse grid point to balance computational accuracy, robustness, and efficiency. The comparison is based on comparing the minimum distance dmin with half of the minimum scale of the fine grid (δ / 2).

[0048] When dmin < δ / 2, a direct assignment strategy is adopted. If the distance between the target grid point P0 and a certain coarse grid point is too small, inverse distance weighted interpolation may cause problems. This is because in the inverse distance weighted algorithm, the weight is inversely proportional to the square of the distance; a very small distance will cause its corresponding weight to become extremely large, thus introducing instability or even floating-point overflow errors in numerical calculations. Furthermore, if multiple neighboring fine grid points are interpolated from the same few coarse grid points using a weighted method, their interpolation results will be very similar when they are all very close to a certain coarse grid point, potentially losing physical details.

[0049] To avoid these problems, this invention proposes that when the minimum distance dmin is less than half of the minimum scale δ of the fine grid, the physical information of the neighboring grid point with the smallest relative distance to the target grid point P0 is directly folded and assigned to the target grid point P0.

[0050] In this embodiment, using a threshold δ / 2 ensures that the physical quantity of any coarse grid point will be directly assigned to at most one fine grid point. When dmin < δ / 2, at most only one fine grid point will be directly assigned a physical quantity from a coarse grid point. This is because the distance between any two different fine grid points is at least δ. If two different fine grid points P0 and P0' are both directly assigned by the same coarse grid point Pc, then dist(P0,Pc) < δ / 2 and dist(P0′,Pc) < δ / 2. According to the triangle inequality, dist(P0,P0′) ≤ dist(P0,Pc) + dist(P0′,Pc) < δ / 2 + δ / 2 = δ. This contradicts the premise that the minimum distance between fine grid points is δ. Therefore, this strategy effectively avoids physical distortion.

[0051] When dmin ≥ δ / 2, an inverse distance weighted interpolation strategy is adopted. When the target grid point P0 is relatively far from all four neighboring coarse grid points, it indicates that P0 is located inside the coarse grid cell, and in this case, the inverse distance weighted (IDW) interpolation algorithm is used. This algorithm assumes that the closer the neighboring point is to the target point, the greater the influence of its physical information on the target point.

[0052] First, calculate the interpolation weights for each neighboring grid point. Specifically, obtain the reciprocal of the square of the relative distance between each neighboring grid point and the target grid point, and use it as the distance influence value for each neighboring grid point.

[0053] Then, the distance influence values ​​of all neighboring grid points are summed to obtain the total influence value. The normalized interpolation weight of any neighboring grid point is obtained by dividing the distance influence value of any neighboring grid point by the total influence value. Finally, based on the normalized interpolation weight, the physical information of the four neighboring grid points is weighted and summed to obtain the physical information of the target grid point.

[0054] In one specific embodiment, when dmin > δ / 2, it indicates that the distance between points P0 in the coarse and fine grids is not too small, and therefore, an inverse distance-weighted average is used for P0 interpolation. The calculation method is as follows: .in The interpolation weights are expressed as follows: .

[0055] After all target mesh points on a two-dimensional plane (e.g., the wall at j=1) have been configured with physical information, the process moves to the next two-dimensional plane with a normal height (e.g., j=2) and repeats the above steps to interpolate all fine mesh points on that plane. This process continues until all fine mesh points on all normal planes (j=1 to Ny) have been configured with physical information, thus completing the interpolation of the entire three-dimensional fine mesh.

[0056] Step S103 proposes a hybrid interpolation strategy that switches between "direct assignment" and "inverse distance weighting" methods by comparing the distance between the target point and the nearest coarse grid point with the scale of the fine grid itself. This design can avoid numerical instability and physical distortion caused by excessively close distances through direct assignment, while ensuring the smoothness and accuracy of interpolation when the point is located inside the grid through inverse distance weighting, thus achieving a balance between robustness and accuracy.

[0057] Through the steps S101 to S103 described above, this application provides a fast coarse-fine grid interpolation technique for wall turbulence calculation. This scheme aims to solve the problems of large computational load and complex implementation process in existing grid interpolation techniques while ensuring high accuracy. By introducing a judgment step, namely comparing the relationship between the distance between a fine grid point and the nearest coarse grid point and the minimum scale of the fine grid, the interpolation method is switched between "direct assignment" and "inverse distance weighting". Ultimately, while ensuring that the interpolation results can better maintain the physical information of the flow field, the complexity of the interpolation algorithm is effectively reduced, and the calculation speed and efficiency are significantly improved.

[0058] To illustrate the technical effects of the method of the present invention more specifically, a calculation example of flat plate turbulence is presented below.

[0059] Since the Mach number , incoming Reynolds number The effect of this interpolation method is demonstrated using a flat plate turbulent flow as an example. The computational domain size is... . Figure 3 This is a schematic diagram of the coarse grid point distribution according to an embodiment of this application, such as... As shown, the coarse mesh is uniformly distributed in the flow and spanwise directions, with the number of mesh points in the three directions being [number missing]. . Figure 4 This is a schematic diagram of the fine mesh point distribution according to an embodiment of this application, such as... As shown, the fine mesh is The area is encrypted, with the number of grid points in the three directions being [number missing]. Both coarse and fine meshes employ hyperbolic tangent functions to refine the wall surface along the normal direction, and the two meshes have the same distribution along the normal direction.

[0060] Figure 5 This is a partial schematic diagram of the flow field before interpolation according to an embodiment of this application. Figure 6 This is a partial schematic diagram of the flow field after interpolation according to an embodiment of this application. Figure 5 and Present flow velocity u-contour plots before and after interpolation for a local flow field with a normal height of y = 0.01750821 inches. Compare... and It can be observed that this interpolation method can well preserve the physical information of the coarse-grid flow field and provide a flow field that is close to the real physical situation for the fine-grid.

[0061] This embodiment uses a specific case of flat-plate turbulence calculation to intuitively demonstrate the practical application effect of the proposed method. By comparing the flow field contour maps before and after interpolation, it is proven that the method can successfully preserve the key physical flow structure when transferring information from a coarse grid to a locally refined fine grid, and the results are smooth and reasonable. This strongly demonstrates the effectiveness and practical value of the present invention in providing high-quality initial fields.

[0062] Secondly, embodiments of this application also provide a coarse-fine grid interpolation system for wall turbulence calculation. This system is used to perform interpolation calculations of grid point information between coarse and fine grids during wall turbulence calculations. Figure 7 This is a structural block diagram of a coarse-fine grid interpolation system for wall turbulence calculation according to an embodiment of the application, such as... Figure 7 As shown, the system includes: The acquisition module 70 is used to acquire the target grid point in the fine grid, determine the multiple neighboring grid points of the target grid point in the coarse grid, and calculate the relative distance between the target grid point and each neighboring grid point; The judgment module 71 is used to obtain the minimum distance among multiple relative distances and compare the minimum distance with half of the minimum scale of the fine mesh, where the minimum scale is the smallest scale among all flow direction and spanwise spacing of the fine mesh;

[0063] The interpolation processing module 72 is used to configure physical information for the target grid points based on the comparison results and a preset interpolation strategy.

[0064] The functions of each module in the above system correspond to the corresponding steps in the aforementioned method embodiments, and will not be repeated here. Furthermore, Figure 8 This is a flowchart of another coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of this application.

[0065] This application provides a fast coarse-fine grid interpolation system for wall turbulence calculations. This system aims to address the problems of high computational complexity and cumbersome implementation in existing grid interpolation techniques while maintaining high accuracy. By introducing a judgment step—comparing the distance between a fine grid point and the nearest coarse grid point with the smallest scale of the fine grid—the interpolation method is switched between "direct assignment" and "inverse distance weighting." Ultimately, while ensuring that the interpolation results retain good flow field physical information, the complexity of the interpolation algorithm is effectively reduced, significantly improving computational speed and efficiency.

[0066] In one embodiment, Figure 9 This is a schematic diagram of the internal structure of an electronic device according to an embodiment of this application, such as... Figure 9 As shown, an electronic device is provided, which can be a server, and its internal structure diagram can be as follows. Figure 9 As shown, the electronic device includes a processor, a network interface, internal memory, and non-volatile memory connected via an internal bus. The non-volatile memory stores the operating system, computer programs, and a database. The processor provides computational and control capabilities, the network interface communicates with external terminals via a network connection, the internal memory provides the environment for the operating system, the computer programs are executed by the processor to implement a coarse-fine mesh interpolation method for wall turbulence calculations, and the database stores data.

[0067] Those skilled in the art will understand that Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the electronic device to which the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0068] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by hardware related to computer program instructions. This computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0069] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A coarse-fine grid interpolation method for wall turbulence calculation, characterized in that, The method for interpolating the physical information of grid points between coarse and fine grids during wall turbulence calculations includes: Obtain the target grid point in the fine grid, determine multiple neighboring grid points of the target grid point in the coarse grid, and calculate the relative distance between the target grid point and each of the neighboring grid points; The minimum distance among multiple relative distances is obtained, and the minimum distance is compared with half of the minimum scale of the fine mesh, wherein the minimum scale is the smallest scale among all flow and spanwise spacing of the fine mesh; Based on the comparison results, physical information is configured for the target grid points using a preset hybrid interpolation strategy.

2. The method according to claim 1, characterized in that, Based on the comparison results, the physical information of the target grid points includes, through a preset hybrid interpolation strategy: When the minimum distance is less than half the minimum scale of the fine grid, the physical information of the neighboring grid point with the smallest relative distance to the target grid point is assigned to the target grid point; When the minimum distance is greater than or equal to half the minimum scale of the fine grid, the physical information of the target grid point is calculated based on the relative distance using an inverse distance weighted interpolation algorithm.

3. The method according to claim 2, characterized in that, Based on the distance, the physical information of the target grid point is calculated using an inverse distance weighted interpolation algorithm, including: The interpolation weights for each neighboring grid point are calculated, specifically by obtaining the reciprocal of the square of the relative distance between each neighboring grid point and the target grid point, which is used as the distance influence value for each neighboring grid point. The total influence value is obtained by summing the distance influence values ​​of all neighboring grid points. The normalized interpolation weight of a neighboring grid point is obtained by dividing the distance influence value of any neighboring grid point by the total influence value. Based on the normalized interpolation weights, the physical information of multiple neighboring grid points is weighted and summed to obtain the physical information of the target grid point.

4. The method according to claim 1, characterized in that, Before obtaining the target grid points of the fine grid, the method further includes: Configure coarse and fine grids for interpolation, wherein the coarse and fine grids are structured grids in a Cartesian coordinate system. The coarse and fine grids have the same number and distribution of grid points in the normal direction, and are used to perform interpolation on multiple two-dimensional planes perpendicular to the normal direction during the process of configuring physical information for the target grid points.

5. The method according to claim 4, characterized in that, Determining the target grid point's multiple neighboring grid points in the coarse grid includes: Obtain the coordinates of the target grid point on the two-dimensional plane; Obtain the grid spacing of the coarse grid in the flow direction and the spanning direction; Based on the coordinates of the target grid point and the grid spacing, a grid cell consisting of four initial coarse grid points is determined to surround the target grid point, and the four initial coarse grid points are designated as the neighboring grid points.

6. The method according to claim 4, characterized in that, The coarse grid is uniformly distributed in the flow and span directions, and non-uniformly distributed in the normal direction. The fine grid is either uniformly distributed or non-uniformly distributed in the flow, normal, and span directions.

7. The method according to claim 1, characterized in that, The method further includes: After all target mesh points on a two-dimensional plane have been configured with physical information, the method described in any one of claims 1 to 6 is repeated on other two-dimensional planes perpendicular to the normal until all fine mesh points have been configured with physical information.

8. A coarse-fine grid interpolation system for wall turbulence calculation, characterized in that, The system is used to interpolate the physical information of grid points between coarse and fine grids during wall turbulence calculations. The system includes: The acquisition module acquires the target grid point in the fine grid, determines multiple neighboring grid points of the target grid point in the coarse grid, and calculates the relative distance between the target grid point and each of the neighboring grid points; The judgment module obtains the minimum distance among multiple relative distances and compares the minimum distance with half of the minimum scale of the fine mesh, wherein the minimum scale is the smallest scale among all flow direction and spanwise spacing of the fine mesh; The difference processing module configures physical information for the target grid points based on the comparison results using a preset hybrid interpolation strategy.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 7.

Images