A coarse-fine grid interpolation method and system for wall turbulence calculations

Abstract

The application relates to a coarse-fine grid fast interpolation technology for wall turbulence calculation, aiming at solving the problems of large calculation amount and complex implementation process of an existing interpolation method. Half of the minimum grid spacing of a fine grid is used as a judgment standard to intelligently switch the interpolation mode. For each fine grid point, when the distance between the fine grid point and the nearest coarse grid point is less than the standard, 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 standard, the inverse distance weighted average method is used for interpolation. The method simplifies the complex calculation problem by taking half of the minimum fine grid size as the standard for judging whether the fine grid point is directly assigned by the physical quantity on the nearest coarse grid value point, under the premise of ensuring the distortionlessness of physical information. The method avoids the complicated calculation process in the traditional method, effectively reduces the algorithm complexity, and significantly improves the speed and efficiency of the interpolation calculation.

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] Embodiments of the present application provide a coarse-fine grid interpolation method, system, computer device and computer readable storage medium for wall turbulence calculation, to at least solve the problem of low interpolation accuracy in the related art.

[0007] In a first aspect, the embodiments of the present application provide a coarse-fine grid interpolation method for wall turbulence calculation, for realizing interpolation of grid point physical information between coarse grids and fine grids in a wall turbulence calculation process, the method comprising:

[0008] obtaining a target grid point of a fine grid, determining a plurality of adjacent grid points of the target grid point in a coarse grid, and calculating relative distances between the target grid point and each of the adjacent grid points;

[0009] obtaining a minimum distance from the plurality of relative distances, and comparing the minimum distance with half of a minimum scale of the fine grid, wherein the minimum scale is the smallest scale among all streamwise and spanwise pitches of the fine grid;

[0010] according to the comparison result, configuring physical information of the target grid point by a preset hybrid interpolation strategy.

[0011] In some embodiments, the physical information of the target grid point according to the comparison result by the interpolation strategy comprises:

[0012] when the minimum distance is smaller than half of the minimum scale of the fine grid, assigning physical information of the adjacent grid point with the smallest relative distance to the target grid point to the target grid point;

[0013] when the minimum distance is greater than or equal to half of the minimum scale of the fine grid, calculating physical information of the target grid point by an inverse distance weighted interpolation algorithm based on the relative distances.

[0014] In some embodiments, the calculation of the physical information of the target grid point by the inverse distance weighted interpolation algorithm based on the distances comprises:

[0015] calculating an interpolation weight of each adjacent grid point, specifically comprising obtaining a square reciprocal of a relative distance between each adjacent grid point and the target grid point as a distance influence value of each adjacent grid point,

[0016] summing up the distance influence values of all adjacent grid points to obtain a total influence value, and obtaining a normalized interpolation weight of any adjacent grid point by dividing the distance influence value corresponding to the adjacent grid point by the total influence value;

[0017] based on the normalized interpolation weights, respectively weighting and summing up physical information of a plurality of the adjacent grid points to obtain physical information of the target grid point.

[0018] In some embodiments, before obtaining the target grid point of the fine grid, the method further comprises:

[0019] configuring a coarse grid and a fine grid for interpolation, wherein the coarse grid and the fine grid are Cartesian coordinate system structured grids,

[0020] the number and distribution of grid points of the coarse grid and the fine grid in the normal direction are consistent, and interpolation is performed on a plurality of two-dimensional planes perpendicular to the normal direction in the process of configuring physical information for the target grid point.

[0021] In some embodiments, determining the plurality of adjacent grid points of the target grid point in the coarse grid comprises:

[0022] obtaining the coordinates of the target grid point in the two-dimensional plane;

[0023] obtaining the grid spacing of the coarse grid in the streamwise direction and the spanwise direction;

[0024] determining a grid cell that encloses the target grid point and is composed of four initial coarse grid points as the adjacent grid points according to the coordinates of the target grid point and the grid spacing.

[0025] In some embodiments, the coarse grid is a uniformly distributed grid in the streamwise direction and the spanwise direction, and a non-uniformly distributed grid in the normal direction, and the fine grid is a uniformly distributed grid or a non-uniformly distributed grid in the streamwise direction, the normal direction and the spanwise direction.

[0026] In some embodiments, the method further comprises:

[0027] After all the target grid points in a two-dimensional plane are configured with physical information, the above-mentioned coarse and fine grid interpolation method for wall turbulence calculation is repeatedly performed on other two-dimensional planes perpendicular to the normal direction until all the fine grid points are configured with physical information.

[0028] In a second aspect, the embodiments of the present application provide a coarse and fine grid interpolation system for wall turbulence calculation, which is used to realize interpolation of grid point physical information between a coarse grid and a fine grid in the process of wall turbulence calculation, and the system comprises:

[0029] an obtaining module, which obtains a target grid point of a fine grid, determines a plurality of adjacent grid points of the target grid point in a coarse grid, and calculates the relative distance between the target grid point and each of the adjacent grid points;

[0030] a judging module, configured to obtain a minimum distance from the plurality of relative distances, and compare the minimum distance with half of a minimum scale of the fine grid, wherein the minimum scale is a minimum scale among all streamwise and spanwise pitches of the fine grid;

[0031] a difference processing module, configured to, according to the comparison result, configure physical information for the target grid point by using a preset hybrid interpolation strategy.

[0032] In a third aspect, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method in the first aspect when executing the computer program.

[0033] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, which stores a computer program, and the program is executable on a processor to implement the method in the first aspect.

[0034] Compared with the related art, the coarse-fine grid fast interpolation technology for wall turbulence calculation provided in the embodiment of the present application aims to solve the problems of large calculation amount and complex implementation process of the existing interpolation method. Half of the minimum grid pitch of the fine grid is used as a judgment standard to intelligently switch the interpolation mode. For each fine grid point, when the distance between the fine grid point and the nearest coarse grid point is less than the standard, 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 standard, the inverse distance weighted average method is used for interpolation. The method simplifies the complex calculation problem on the premise of ensuring the distortionlessness of the physical information by explicitly taking half of the minimum fine grid scale as the standard for judging whether the fine grid point is directly assigned the physical quantity on the nearest coarse grid value point. The method avoids the cumbersome calculation process in the traditional method, effectively reduces the algorithm complexity, and significantly improves the speed and efficiency of the interpolation calculation. BRIEF DESCRIPTION OF DRAWINGS

[0035] The accompanying drawings, which are included to provide a further understanding of the present application and constitute a part of this application, illustrate certain illustrative embodiments of the present application and together with the description serve to explain the present application. In the drawings:

[0036] Figure 1 FIG. 1 is a flowchart of a coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of the present application;

[0037] Figure 2 FIG. 2 is a schematic diagram of grid interpolation according to an embodiment of the present application;

[0038] Figure 3 FIG. 3 is a schematic diagram of coarse grid grid point distribution according to an embodiment of the present application;

[0039] Figure 4 is a fine grid node distribution diagram according to an embodiment of the present application;

[0040] Figure 5 is a local flow field diagram before interpolation according to an embodiment of the present application;

[0041] Figure 6 is a local flow field diagram after interpolation according to an embodiment of the present application;

[0042] Figure 7 is a structure block diagram of a coarse-fine grid interpolation system for wall turbulence calculation according to an embodiment of the present application;

[0043] Figure 8 is a flow chart of another coarse-fine grid interpolation method for wall turbulence calculation according to an embodiment of the present application;

[0044] Figure 9 is an internal structure diagram of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is described and explained below in connection with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application.

[0046] Obviously, the drawings in the following description are only some examples or embodiments of the present application, and for those of ordinary skill in the art, the present application can be applied to other similar scenarios without creative labor based on these drawings. In addition, it can be understood that although the efforts made in this development process can be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacture or production changes based on the technical content disclosed in the present application are only routine technical means and should not be understood as insufficient disclosure of the present application.

[0047] In the present application, "embodiment" means that the specific features, structures or characteristics described in connection with the embodiment can be included in at least one embodiment of the present application. The phrase appears at various places in the specification does not necessarily refer to the same embodiment, nor is it mutually exclusive or alternative to other embodiments. Those of ordinary skill in the art explicitly and implicitly understand that the embodiments described in the present application can be combined with other embodiments without conflict.

[0048] Unless otherwise defined, technical terms and scientific terms used in the present application shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "a", "an", "one", "this", and the like, as used in the present application, do not denote a limitation of quantity, and can mean one or more. The terms "comprising", "containing", "having", and the like, as used in the present application, are intended to cover the process, method, system, product, or apparatus that comprises, contains, or has the specified steps or units, without limiting the number of steps or units. The terms "connected", "coupled", and the like, as used in the present application, are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The term "plurality" means two or more. The term "and / or" describes the associated relationship of associated objects, and means that there can be three relationships, for example, "A and / or B" can mean that A exists alone, A and B exist together, and B exists alone. The character " / " generally means that the associated objects before and after are in an "or" relationship. The terms "first", "second", "third", and the like, as used in the present application, are merely to distinguish similar objects, and do not represent a specific order of the objects.

[0049] The method provided by the embodiments of the present application can be applied to many fields of computational fluid dynamics (CFD), such as turbulent flow research, aircraft aerodynamic design, aerodynamic analysis, etc. In these fields, structured grids are widely used due to their regularity of topological structure, especially in direct numerical simulation (DNS) and large eddy simulation (LES) of wall turbulence. The interpolation method proposed in the embodiments aims to provide a fast and effective way to generate fine grid initial fields from coarse grid calculation results for such computing scenarios.

[0050] Figure 1 is a flow chart of a coarse-fine grid interpolation method for wall turbulence calculation according to the embodiments of the present application, as shown in Figure 1 The flow chart includes the following steps:

[0051] In step S101, the target grid point of the fine grid is obtained, the plurality of adjacent grid points of the target grid point in the coarse grid are determined, and the relative distances between the target grid point and each adjacent grid point are calculated. Specifically, the step includes:

[0052] 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.

[0053] 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).

[0054] 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.

[0055] 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, , .

[0056] 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.

[0057] 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.

[0058] 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.

[0059] 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).

[0060] 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.

[0061] S3, determine the multiple neighboring grid points of the target grid point in the coarse grid;

[0062] 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:

[0063] P1 ,

[0064] P2 ,

[0065] P3 and

[0066] P4 .

[0067] wherein, , Here, "mod" means integer division, which returns the largest integer less than or equal to the quotient. For example, , , If it is a boundary point, i.e., x = 0 or x = 1, then let (or , , (or , ).

[0068] This step S3 is a positioning step of interpolation calculation. By using the uniformity of the coarse grid on a specific plane, positioning can be efficiently completed through simple integer division, and the precise coordinates of the four adjacent points are determined. This operation provides a basis for subsequent distance calculation and weighted interpolation.

[0069] S4, after determining the four adjacent grid points, the relative distances between the target grid point and each adjacent grid point are further calculated.

[0070] In a specific embodiment, the distances of the fine grid points P0 to P1, P2, P3 and P4 are calculated. Let the distances of the fine grid points P0 to P1, P2, P3 and P4 be , , and . Taking P1 as an example, the distance is calculated using the Pythagorean theorem , .

[0071] It can be understood that , and are calculated in a similar manner to , which will not be described in this embodiment.

[0072] Through the above step S101, the target grid point of the fine grid is obtained, the multiple adjacent grid points of the target grid point in the coarse grid are determined, and the relative distances between the target grid point and each adjacent grid point are calculated. By calculating the Euclidean distance, the proximity of the geometric position is converted into a specific numerical value, providing a data basis for subsequent interpolation algorithms. These distance values are key parameters for determining which interpolation strategy to use and calculating the weight coefficient.

[0073] S102, obtain the minimum distance among the plurality of relative distances, and compare the minimum distance with half of the minimum scale of the fine grid, wherein the minimum scale is the minimum scale among all streamwise and spanwise pitches of the fine grid; specifically comprising:

[0074] S1, find the minimum value among the four distances calculated in the above steps, and obtain the minimum scale of the fine grid in the streamwise and spanwise directions. The minimum scale is defined as the minimum value among all streamwise and spanwise pitches of the fine grid. It should be noted that since the fine grid can be non-uniform, it is necessary to traverse all fine grid cells to determine this value.

[0075] In one specific embodiment, the minimum value among , , and and the minimum scale of the fine grid are found. The minimum value among , , and can be found using the bubble algorithm or the function provided by the program, and is denoted as , . The minimum scale of the fine grid is read in and is denoted as . Here, the minimum scale means the minimum value among all streamwise and spanwise pitches of the fine grid, which can be represented as

[0076] S2, determine which interpolation strategy to use by comparing the minimum distance with the size of the fine grid. This step is the key to ensuring the accuracy and feasibility of the interpolation algorithm.

[0077] Step S102 prepares for the subsequent strategy selection. By finding the distance (dmin) between the target point and the nearest point with the minimum distance, and determining a characteristic length (δ) that can represent the resolution of the fine grid, two core parameters for judging the relative distance between the two are established. dmin reflects the specific location characteristics of the current point, while δ provides a global scale reference, and the comparison of the two is the basis for selecting the interpolation strategy subsequently.

[0078] S103, according to the comparison result, configure the physical information of the target grid point by using the preset hybrid interpolation strategy.

[0079] This step is the core of the technical solution. A hybrid interpolation strategy is used to select different interpolation methods according to the relative distance between the target grid point and the nearest coarse grid point, in order to balance the accuracy, robustness and efficiency of the calculation. The basis for comparison is to compare the minimum distance dmin with half of the minimum scale of the fine grid (δ / 2).

[0080] When dmin<δ / 2, the direct assignment strategy is adopted. If the distance between the target grid point P0 and some coarse grid point is too small, the inverse distance weighted interpolation may cause problems. Because in the inverse distance weighted algorithm, the weight is inversely proportional to the square of the distance, a very small distance will cause the corresponding weight to become very large, thereby introducing instability in numerical calculation or even causing floating point overflow error. In addition, if multiple adjacent fine grid points are all interpolated from the same coarse grid points by weighting, when they are all very close to a coarse grid point, their interpolation results will be very close, which may lose the physical details.

[0081] To avoid these problems, the present application proposes that when the minimum distance dmin is less than half of the minimum size δ of the fine grid, the physical information fold of the adjacent grid point with the smallest relative distance to the target grid point P0 is directly assigned to the target grid point P0.

[0082] In this embodiment, using the threshold δ / 2 can ensure that the physical quantity of any coarse grid point will be directly assigned to at most one fine grid point. When dmin<δ / 2, the fine grid point directly assigned by the physical quantity on a coarse grid point is at most one. This is because the distance between any two different fine grid points is at least δ. If there are two different fine grid points P0 and P0' that are 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.

[0083] When dmin≥δ / 2, the inverse distance weighted interpolation strategy is adopted. When the distance between the target grid point P0 and all four adjacent coarse grid points is relatively far, it indicates that P0 is located inside the coarse grid cell, and the inverse distance weighted (IDW) interpolation algorithm is adopted at this time. This algorithm believes that the closer the adjacent point to the target point, the greater the influence of its physical information on the target point.

[0084] First, the interpolation weight of each adjacent grid point is calculated. Specifically, the square inverse of the relative distance between each adjacent grid point and the target grid point is obtained as the distance influence value of each adjacent grid point;

[0085] Then, the distance influence values of all the adjacent grid points are summed to obtain a total influence value, and a normalized interpolation weight of any adjacent grid point is obtained by dividing the distance influence value corresponding to the adjacent grid point by the total influence value; finally, the physical information of the four adjacent grid points is weighted and summed based on the normalized interpolation weights to obtain the physical information of the target grid point.

[0086] In a specific embodiment, when dmin> δ / 2, it is indicated that no coarse grid point is too close to the fine grid point P0, and inverse distance weighted average is used for interpolation of P0. The calculation method is: . Wherein represents the interpolation weight, and the expression is: .

[0087] After all the target grid points on a two-dimensional plane (for example, the wall surface of j=1) are configured with physical information, the process moves to the two-dimensional plane of the next normal height (for example, j=2), and the above steps are repeated to perform interpolation for all fine grid points on the plane. This process will continue until all fine grid points on all normal planes (j=1 to Ny) are configured with physical information, thereby completing the interpolation of the entire three-dimensional fine grid.

[0088] In step S103, a hybrid interpolation strategy is proposed to switch between the "direct assignment" and "inverse distance weighted" methods by comparing the distance between the target point and the nearest coarse grid point and the size of the fine grid. This design can not only avoid numerical instability and physical distortion caused by too close distance through direct assignment, but also ensure the smoothness and accuracy of interpolation when the point is located in the grid through inverse distance weighting, achieving the balance between robustness and accuracy.

[0089] Through the above steps S101 to S103, the embodiment of the present application provides a coarse-fine grid fast interpolation technology for wall turbulence calculation, which aims to solve the problem of large calculation amount and complex implementation process of existing grid interpolation technology in ensuring high accuracy. By introducing a judgment step, that is, comparing the relationship between the distance of the fine grid point and the nearest coarse grid point and the minimum size of the fine grid, the interpolation method is switched between "direct assignment" and "inverse distance weighting". Finally, under the premise of ensuring that the interpolation result can well 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.

[0090] To more specifically illustrate the technical effect of the method of the present application, an example of a flat plate turbulence is shown below.

[0091] The incoming flow Mach number , the incoming flow Reynolds number The flat plate turbulence is taken as an example to show the effect of the interpolation method. The size of the calculation domain is .Figure 3 is a schematic diagram of a coarse grid node distribution according to an embodiment of the present application, as shown, the coarse grid is uniformly distributed in the flow direction and the spanwise direction, and the number of grid points in three directions is . Figure 4 is a schematic diagram of a fine grid node distribution according to an embodiment of the present application, as shown, the fine grid is encrypted in the region of , and the number of grid points in three directions is . Both the coarse and fine grids adopt hyperbolic tangent function to encrypt the wall surface in the normal direction, and the distribution of the two grids in the normal direction is the same.

[0092] Figure 5 is a local schematic diagram of a flow field before interpolation according to an embodiment of the present application, Figure 6 is a local schematic diagram of a flow field after interpolation according to an embodiment of the present application, Figure 5 and give the local flow field before interpolation and after interpolation of the flow velocity u cloud diagram with the normal height of y = 0.01750821 inch. It can be found by comparing and that the interpolation method can well maintain the physical information of the coarse grid flow field and provide a flow field close to the real physical condition for the fine grid.

[0093] This embodiment directly shows the practical application effect of the scheme and method of the present application through a specific flat plate turbulent flow calculation case. By comparing the flow field cloud diagrams before and after interpolation, it is proved that the method can successfully retain the key physical flow structure when transmitting information from the coarse grid to the locally encrypted fine grid, and the result is smooth and reasonable. It strongly proves the effectiveness and practical value of the present application in providing high-quality initial field.

[0094] In the second aspect, the embodiments of the present application also provide a coarse and fine grid interpolation system for wall turbulent flow calculation. The system is used for realizing the grid point information interpolation operation between the coarse grid and the fine grid in the wall turbulent flow calculation process. Figure 7 is a structural block diagram of a coarse and fine grid interpolation system for wall turbulent flow calculation according to an embodiment of the present application, as shown in Figure 7 , the system comprises:

[0095] The acquisition module 70 is used for acquiring a target grid point of the fine grid, determining a plurality of adjacent grid points of the target grid point in the coarse grid, and calculating the relative distance between the target grid point and each adjacent grid point;

[0096] The judgment module 71 is used for acquiring the minimum distance in the plurality of relative distances, and comparing the minimum distance with half of the minimum scale of the fine grid, wherein the minimum scale is the minimum scale in all flow direction and spanwise direction distances of the fine grid; ​​

[0097] 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.

[0098] 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.

[0099] 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.

[0100] 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.

[0101] 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.

[0102] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by computer program instructions related to hardware, and the computer program can be stored in a non-volatile computer readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments of each method. Any reference to memory, storage, database, or other medium used in each embodiment provided by the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0103] The above embodiments only express several embodiments of the present application, and the description is specific and detailed, but it cannot be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of the present application. Therefore, the scope of protection of the patent of the present application should be subject to the appended claims.

Claims

1. A coarse-fine grid interpolation method for wall turbulence calculation, characterized in that, Used in the process of calculating in-wall turbulence The method for interpolating the physical information of grid points between coarse and fine grids 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, specifically including: 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.

2. The method according to claim 1, characterized in that, Based on the relative 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.

3. 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.

4. The method according to claim 3, 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.

5. The method according to claim 3, 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.

6. 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 5 is repeated on other two-dimensional planes perpendicular to the normal until all fine mesh points have been configured with physical information.

7. 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 point according to the comparison result and through a preset hybrid interpolation strategy. Specifically, when the minimum distance is less than half of 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.

8. 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 6.

9. 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 6.

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