An LU-SGS implicit advance calculation method on an adaptive Cartesian grid

Abstract

The invention discloses an LU-SGS implicit propulsion calculation method under an adaptive Cartesian grid, which relates to the field of numerical simulation, and comprises the following steps: step 1: generating an equidistant and uniform initial Cartesian grid based on a size parameter, a motion parameter and aerodynamic parameter of an aircraft model, and allocating a multidimensional array number to each grid according to a dimension of space; step 2: performing a fork tree adaptive encryption on the grid within a preset range of an object surface boundary based on a geometric shape of the aircraft model, and generating an adaptive Cartesian grid required for calculation; step 3: sorting the generated adaptive Cartesian grid to obtain a sorting result; step 4: performing an LU-SGS implicit propulsion calculation based on the sorting result to obtain a numerical simulation calculation result of the aircraft model; the method can realize the LU-SGS implicit propulsion calculation under an adaptive Cartesian grid, thereby accelerating convergence to improve calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation, and in particular to a LU-SGS implicit advancement calculation method under an adaptive Cartesian grid. Background Art

[0002] In computational fluid dynamics (CFD), accelerated convergence techniques are important means to improve the efficiency of numerical simulation, such as local time stepping, implicit advancement format, multiple grids, etc. However, due to the unique fork tree data structure of adaptive Cartesian grid, it is different from traditional structured grid in terms of grid relationship, neighbor search and data management. Therefore, the original accelerated convergence methods need to be extended in adaptive Cartesian grid.

[0003] Among them, although the LU-SGS method based on structured grids has the advantages of good stability and high efficiency, it is difficult to adapt to the fork tree data structure of the adaptive Cartesian grid and the dynamic changes of the grid, and cannot give full play to its advantages. The main idea of ​​the LU-SGS method is to decompose the Jacobi matrix of the left-hand side of the equation into an upper triangular matrix L, a lower triangular matrix U and a diagonal matrix D, and then use the Gauss-Seidel method to solve it. Through the linear approximation of the Jacobi matrix of the convective flux, large matrix operations are avoided, thereby reducing the demand for storage memory and reducing the calculation time. Each advance scanning process under the structured grid is as follows Figure 1 As shown, each iteration only requires a pair of scanning processes (one upward scan and one downward scan). Figure 1 This is a schematic diagram of the structural grid LU-SGS scanning. Figure 1 i and j represent the position number of the unit in two dimensions, such as x 12 represents the cell at position i=1 and j=2.

[0004] The structured grid is very convenient to implement the LU-SGS algorithm because of its clear and simple data structure. However, when it is extended to the adaptive Cartesian grid, problems such as grid balance numbering, reordering, and parallelization will be encountered. Cartesian grids are usually based on hierarchical storage of fork tree data structures (quadtrees in two dimensions and octrees in three dimensions), such as Figure 2 As shown in the figure, the unique tree-like data storage method of the fork tree structure makes the Cartesian grid naturally suitable for the grid adaptation process. Among them, the encrypted leaf grid is linked to the parent unit through a pointer, and is encrypted in the final calculation domain to form a fork tree forest. It is obvious that the traversal order of its grid cannot be achieved by simply looping through the numbered coordinates in the structured grid.

[0005] The existing LU-SGS method has some problems with the fork tree data structure and dynamic grid changes of the adaptive Cartesian grid:

[0006] 1) First, the grid of the fork tree structure needs to be reordered reasonably to improve the memory access speed;

[0007] 2) Secondly, dynamic mesh changes require real-time reconstruction of the LU-SGS algorithm data structure to adapt to the dynamic changes of the mesh.

[0008] 3) Furthermore, in the adaptive Cartesian grid framework, the neighbor relationship of the hanging grid in the transition area between large and small grids is complex, and the balance problem of the upper and lower triangular matrices is closely related to the grid numbering. If the neighbor grid numbering of the hanging grid is inappropriate, it will lead to a degenerate process from Gauss-Seidel iteration to Jacobi iteration. Summary of the invention

[0009] The present invention proposes a LU-SGS implicit boosting calculation method under an adaptive Cartesian grid, the purpose of which is to realize the LU-SGS implicit boosting calculation under an adaptive Cartesian grid, thereby accelerating convergence to improve the calculation efficiency of numerical simulation of aircraft models.

[0010] To achieve the above object, the present invention provides a LU-SGS implicit boosting calculation method under an adaptive Cartesian grid, the method comprising:

[0011] Step 1: Generate an equidistant and uniform initial Cartesian grid based on the aircraft model size parameters, aircraft model motion parameters and aerodynamic parameters, and assign a multidimensional array number to each grid according to the dimension of the space;

[0012] Step 2: Based on the geometric shape of the aircraft model, the grid within the preset range of the object surface boundary is adaptively encrypted using a fork tree to generate the adaptive Cartesian grid required for calculation;

[0013] Step 3: Sort the generated adaptive Cartesian grid to obtain a sorting result;

[0014] Step 4: Perform LU-SGS implicit propulsion calculation based on the sorting results to obtain the numerical simulation calculation results of the aircraft model;

[0015] Wherein, the step 3 specifically includes:

[0016] Step 3.1: Determine the computational domain in the generated adaptive Cartesian grid;

[0017] Step 3.2: In the computational domain, the initial Cartesian grids are numbered and sorted according to the multidimensional array number of the grid. If the grid is an encrypted grid, the subgrid number of the encrypted grid is used to replace the number position of the encrypted grid, and the numbering of the internal grid of the object surface is skipped. The sorting result is obtained based on the numbering results of all leaf grids, where the leaf grid is a grid unit without subgrids.

[0018] Among them, reasonable reordering of the grid structure can ensure that the grid order after reordering satisfies the balanced numbering, thereby ensuring the efficiency of the implicit advancement calculation.

[0019] Among them, this method can manage the data of the Cartesian grid under the fork tree structure and improve the flow field propulsion efficiency of the adaptive Cartesian grid CFD simulation, thereby improving the convergence speed of the numerical simulation calculation of the aircraft model to save the calculation time of the engineering simulation.

[0020] Among them, a multidimensional array number is allocated to the initial Cartesian grid according to the dimension of the space, specifically including: a multidimensional array number (i, j) is allocated to each grid according to the dimension of the space, the grid (i, j) indicates that the grid is located in the i-th column and the j-th row, and the value range of i and j is a natural number greater than or equal to 1.

[0021] The initial Cartesian grids are numbered and sorted in the computational domain according to the multidimensional array number of the grids, specifically including:

[0022] Step a: Use the smallest multidimensional array number (1, 1) in the computational domain as the starting grid for sorting, and the array number of the starting grid satisfies i+j=2;

[0023] Step b: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=3: starting from the grid with the largest i value, sort the grids in the previous step in a way that i decreases and j increases; that is, (2, 1) to (1, 2), which is a 45° oblique line from the lower right to the upper left in the computational domain in terms of spatial position;

[0024] Step c: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=4: starting from the grid with the largest i value, sort the grids in the previous step in a way that i decreases and j increases; that is, (3, 1) to (2, 2) to (1, 3);

[0025] Repeat steps a to c in the manner of increasing the value of i+j by 1, until the multidimensional array with the largest number in the computational domain (imax, jmax) is sorted as the end grid of the sorting, imax is the maximum value of i, and jmax is the maximum value of j. At this point, it can be proved that the sorting satisfies the balanced numbering.

[0026] The adaptively encrypted subgrid shares the same multidimensional array number with the parent grid, the adaptively encrypted subgrid is sorted, inserted into the sort position of the parent grid of the adaptively encrypted subgrid, and the sort position of the parent grid is replaced by the sort of the subgrid, specifically including:

[0027] Assuming that there are adaptively encrypted subgrids in the grid (i, j), all subgrids of the grid (i, j) are sorted to obtain a sorting result, and the sorting result replaces the sorting position of the grid (i, j);

[0028] The ordering of subgrids is as follows: after one encryption, grid (i, j) obtains 4 subgrids, and the order of the 4 subgrids is as follows: the lower left subgrid is ranked first, the lower right subgrid is ranked second, the upper left subgrid is ranked third, and the upper right subgrid is ranked fourth. It can be understood that the ordering of subgrids follows the mirrored Z rule, specifically: after one encryption, the initial grid obtains 4 subgrids, and the order of the subgrids is lower left (subgrid 1) ~ lower right (subgrid 2) ~ upper left (subgrid 3) ~ upper right (subgrid 4). The center points of the 4 grids are connected in sequence to form a horizontally mirrored letter Z.

[0029] Insert the sorting results of the four sub-grids and replace the sorting of the corresponding parent grid positions;

[0030] If there is a sub-grid at a higher level in the sub-grid (that is, if the initial grid is encrypted multiple times, that is, a grid of the sub-grid still has sub-grids), recursive processing is performed, and the sub-grids at a higher level are sorted using the above sub-grid sorting method and then replace the sorting of the corresponding parent grid position until all leaf grids in the computational domain are traversed.

[0031] If the center of a leaf grid is located inside the object surface during the sorting process, the leaf grid is skipped and does not participate in the sorting. The sorting results are stored in a linked list pointer manner. The linked list pointer can be stored in a smaller memory space, saving storage space.

[0032] Among them, in step 4, during the LU-SGS implicit advancement calculation based on the sorting results, for the hanging grid in the calculation domain, a target point for constructing the hanging grid into a uniform grid is obtained; and the flow field information of the target point is calculated based on the flow field information of the grid around the target point.

[0033] The hanging grids are divided into the first type of hanging grids and the second type of hanging grids. The first type of hanging grids are: the neighboring grids of the first grid have a subgrid with a higher level than the first grid; the second type of hanging grids are: the neighboring grids of the first grid have a parent grid with a lower level than the first grid;

[0034] For the first type of hanging grid, a first target point corresponding to the uniform grid constructed by constructing the first type of hanging grid is obtained, a first target grid is obtained based on the first target point, four subgrids corresponding to the first target grid are obtained, and flow field information of the first target point is obtained by interpolation calculation based on flow field information of the four subgrids;

[0035] For the second type of suspended grid, obtain the second target point corresponding to the second type of suspended grid constructed as a uniform grid, obtain the distance from the center point of the grid surrounding the second target point to the second target point and sort them from small to large according to the distance, obtain the first 4 corresponding grids in the sorting, and obtain the flow field information of the second target point by interpolation calculation based on the flow field information of the first 4 corresponding grids in the sorting.

[0036] Among them, this method realizes LU-SGS calculation under adaptive Cartesian grid through approximate interpolation calculation of hanging grid neighbors, thereby accelerating convergence to improve calculation efficiency.

[0037] For the first type of hanging grid, the flow field information of the first target point is obtained by averaging the flow field information of the four subgrids.

[0038] Among them, for the second type of hanging grids, based on the flow field information of the first 4 corresponding grids, the flow field information of the second target point is obtained by inverse distance weight or weighted least squares interpolation calculation.

[0039] The present invention realizes implicit advancement calculation under adaptive Cartesian grid, and proposes a fork tree structure reordering rule and LU-SGS implicit advancement calculation method under adaptive Cartesian grid. The technical solution has the following beneficial effects and advantages:

[0040] Reordering rules: By using a specially designed sorting path to traverse all leaf cells and reordering them according to a specially designed sorting method, a balanced numbered grid distribution is achieved. This can improve memory access speed and accelerate the calculation speed of numerical simulation of aircraft models using the LU-SGS method.

[0041] Simplified data management: By using linked list pointers to store relevant information, the reordering process can be flexibly called during parallel partitioning and dynamic grid adaptation, and no additional memory space is required after the grid distribution reaches a stable state.

[0042] Efficient grid neighbor interpolation algorithm: For hanging grid neighbors in the transition area between large and small grids, simple interpolation is used to obtain the required information, avoiding complex matrix operations and coordinate transformations, thereby reducing storage memory requirements and calculation time.

[0043] Flexible application in complex flow fields: This method is suitable for numerical simulation of complex flow fields, such as numerical simulation of aircraft models, and has broad application prospects in CFD engineering. It can improve computational efficiency and achieve fast CFD numerical simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation on the embodiments of the present invention;

[0045] Figure 1 Schematic diagram of LU-SGS scanning of structural grid;

[0046] Figure 2 It is a schematic diagram of a two-dimensional adaptive Cartesian grid fork tree structure;

[0047] Figure 3 It is a flowchart of the LU-SGS implicit advancement calculation method under an adaptive Cartesian grid;

[0048] Figure 4 It is a schematic diagram of the adaptive Cartesian grid distribution;

[0049] Figure 5 Schematic diagram of adaptive Cartesian grid number reordering;

[0050] Figure 6 It is a schematic diagram of the adaptive Cartesian grid recursive Z curve;

[0051] Figure 7 It is a schematic diagram of Gauss-Seidel iteration;

[0052] Figure 8 Schematic diagram of the interpolation template of the two-dimensional grid transition area corresponding to the first type of hanging grid;

[0053] Fig. 9 Schematic diagram of the interpolation template of the two-dimensional grid transition area corresponding to the second type of hanging grid;

[0054] Fig.10 This is a schematic diagram of the adaptive Cartesian grid for the airfoil example;

[0055] Fig.11 Schematic diagram of the convergence curve of residual with the number of iteration steps in different formats. DETAILED DESCRIPTION

[0056] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0057] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those within the scope of this description. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0058] Embodiment 1;

[0059] Please refer to Figure 3 , Figure 3 The figure is a flow chart of an LU-SGS implicit advancement calculation method under an adaptive Cartesian grid. The present invention provides an LU-SGS implicit advancement calculation method under an adaptive Cartesian grid, and the method comprises:

[0060] Step 1: Based on the aircraft model size parameters, aircraft model motion parameters and aerodynamic parameters, generate an equidistant and uniform initial Cartesian grid, and assign a multidimensional array number to each grid according to the dimension of the space; wherein the aircraft model size parameters are parameters related to the aircraft model size, the aerodynamic parameters include: incoming flow velocity, density, pressure, angle of attack, etc., and the motion parameters include: initial angle of attack, amplitude, reduction frequency, center of mass position, etc.;

[0061] Step 2: Based on the geometric shape of the aircraft model, the grid within the preset range of the object surface boundary is adaptively encrypted by a fork tree to generate an adaptive Cartesian grid required for calculation; the preset range may be a distance or range near the object surface boundary or a corresponding setting, and the specific size may be adjusted according to actual needs, and the embodiment of the present invention does not make corresponding limitations;

[0062] Step 3: Sort the generated adaptive Cartesian grid to obtain a sorting result;

[0063] Step 4: Perform LU-SGS implicit propulsion calculation based on the sorting results to obtain the numerical simulation calculation results of the aircraft model;

[0064] Wherein, the step 3 specifically includes:

[0065] Step 3.1: Determine the computational domain in the generated adaptive Cartesian grid;

[0066] Step 3.2: In the computational domain, the initial Cartesian grids are numbered and sorted according to the multidimensional array number of the grid. If the grid is an encrypted grid, the subgrid number of the encrypted grid is used to replace the number position of the encrypted grid, and the numbering of the internal grid of the object surface is skipped. The sorting result is obtained based on the numbering results of all leaf grids, where the leaf grid is a grid unit without subgrids.

[0067] Among them, in the embodiment of the present invention, the key points and improvements in the present invention are described in detail below. Regarding the LU-SGS and the corresponding aircraft model numerical simulation part, the existing method can be adopted, and reference can be made to CN116738891A and CN117332511A. The embodiment of the present invention will not be repeated accordingly.

[0068] Wherein, in the embodiment of the present invention, allocating a multidimensional array number to the initial Cartesian grid according to the dimension of the space specifically includes: allocating a multidimensional array number (i, j) to each grid according to the dimension of the space, the grid (i, j) indicates that the grid is located in the i-th column and the j-th row, and the value range of i and j is a natural number greater than or equal to 1. Wherein, in the embodiment of the present invention, numbering and sorting the initial Cartesian grids according to the multidimensional array numbers of the grids in the computational domain specifically includes:

[0069] Step a: Use the smallest multidimensional array number (1, 1) in the computational domain as the starting grid for sorting, and the array number of the starting grid satisfies i+j=2;

[0070] Step b: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=3: starting from the grid with the largest i value, sort the grids in the previous step in a way that i decreases and j increases;

[0071] Step c: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=4: starting from the grid with the largest i value, sort the grids in the previous step in a manner that i decreases and j increases;

[0072] Repeat the above sorting method in such a way that the value of i+j increases by 1 until the multidimensional array with the largest number in the calculation domain (imax, jmax) is used as the sorting end grid, imax is the maximum value of i, and jmax is the maximum value of j.

[0073] In the embodiment of the present invention, the adaptively encrypted sub-grid and the parent grid share the same multi-dimensional array number, the adaptively encrypted sub-grid is sorted, inserted into the sort position of the parent grid of the adaptively encrypted sub-grid, and the sort position of the parent grid is replaced by the sort of the sub-grid, specifically including:

[0074] Assuming that there are adaptively encrypted subgrids in the grid (i, j), all subgrids of the grid (i, j) are sorted to obtain a sorting result, and the sorting result replaces the sorting position of the grid (i, j);

[0075] The subgrids are sorted as follows: after one encryption, the grid (i, j) obtains 4 subgrids, and the sorting order of the 4 subgrids is: the lower left subgrid is ranked first, the lower right subgrid is ranked second, the upper left subgrid is ranked third, and the upper right subgrid is ranked fourth;

[0076] Insert the sorting results of the four sub-grids and replace the sorting of the corresponding parent grid positions;

[0077] If there is a sub-grid at a higher level in the sub-grid, recursive processing is performed, and the sub-grid at a higher level is sorted using the above sub-grid sorting method and then replaces the sorting of the corresponding parent grid position until all leaf grids in the computational domain are traversed.

[0078] In this embodiment of the present invention, if a leaf grid is encountered in the sorting process and the grid center is located inside the object plane, the leaf grid is skipped and does not participate in the sorting.

[0079] The following example describes this method in detail:

[0080] Taking the two-dimensional adaptive Cartesian grid as an example, the typical immersed boundary adaptive refined Cartesian grid distribution in the computational domain is as follows: Figure 4 That is, there may be hanging grids with large grids and small grids (a large grid may be on the same line / plane with multiple small grid neighbors. In order to ensure the quality of the grid and solution, the level difference between adjacent grids cannot be greater than 1). At the same time, there are also situations where neighbors are located inside the object surface near the object surface. These characteristics are obviously different from structured / unstructured grids.

[0081] Among them, hanging mesh refers to a mesh topology feature in which the nodes (or boundaries) of the hanging mesh cells are not aligned with the standard mesh in other directions in the local structure of the mesh.

[0082] After the layout of the grid distribution is determined, the next step is to reorder the adaptive Cartesian grid. Because when using the LU-SGS method, there is a certain dependency on upstream and downstream grid data, that is, the neighbor number of a grid unit is required to be larger or smaller than it. If the difference between the number of neighbors with large numbers and the number of neighbors with small numbers is within a preset range (the number of neighbors of a grid may be an odd number or an even number. If it is an even number, it is considered that the number of neighbors with large numbers is equal to the number of neighbors with small numbers. If it is an odd number, it is considered that the difference between the number of neighbors with large numbers and the number of neighbors with small numbers is within the preset range), it is called balanced numbering; otherwise, it is called unbalanced numbering. Unbalanced numbering will reduce the maximum allowed CFL number, thereby seriously affecting the efficiency of implicit advancement. Taking the local adaptive Cartesian grid distribution as an example, the reordering method of the present invention is as follows Figure 5 shown.

[0083] The overall sorting method is the same as the previous numbering method. A multidimensional array number is assigned to each grid according to the spatial dimension. For example, the (i, j) grid in two dimensions means that it is located in the i-th column and the j-th row. Therefore, the value range of i and j is a natural number starting from 1:

[0084] a) Initial position: the grid with the smallest multidimensional array number (1, 1) in the computational domain is used as the starting grid for sorting. The array number of this grid satisfies i+j=2;

[0085] b) Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=3, and sort them according to the rule that i decreases and j increases, that is: (2, 1)~(1, 2), which is the 45° oblique line from the lower right to the upper left in the computational domain from the spatial position; sequentially, sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=4, and sort them according to the rule that i decreases and j increases, that is: (3, 1)~(2, 2)~(1, 3); sequentially, until the grid with the largest multidimensional array number (imax, jmax) in the computational domain is sorted as the end point. At this point, it can be proved that the sorting satisfies the balanced numbering;

[0086] c) Processing of encrypted grids. When encountering an encrypted Cartesian grid, recursively search all its sub-units from the fork tree structure. The traversal order of the sub-units follows the mirror Z rule. Specifically, the initial grid is encrypted once to obtain 4 sub-grids. The order of the sub-grids is lower left (sub-1) ~ lower right (sub-2) ~ upper left (sub-3) ~ upper right (sub-4). The center points of the 4 grids are connected in sequence to form a horizontal mirror letter "Z", corresponding to Figure 5 The right side enlarges 1'~2'…~7' and uses this sequence to replace the original grid 5.

[0087] d) skip the inner grid, Figure 4 After reordering, the grid Figure 6 As shown, when an internal grid is encountered (judged based on the relationship between the object surface and the grid, if the center of the grid is inside the object surface, it is an internal grid), the current grid sorting is skipped.

[0088] In the actual calculation process, after parallel partitioning and dynamic grid adaptation, the reordering process of the present invention needs to be called. If the grid distribution reaches stability, the reordering curve remains unchanged, and the relevant information can be stored in a smaller memory space through the linked list pointer.

[0089] (2) After the reordered grid, the implicit LU-SGS sweep can be started. Since this method involves the Gauss-Seidel iteration process of the equation system, Figure 7 As shown, Figure 7 Here n is the value at time n, n+1 is the value at time n+1, and solving the current grid requires one layer of neighbor information of the adjacent grid.

[0090] In the adaptive Cartesian grid solver, neighbor information should be stored. For Cartesian grids in uniform areas, the adjacent grids are the same size, so the neighbor information can be used directly without additional spatial coordinate transformation; however, in the transition area between large and small grids, additional processing is required to obtain neighbor information. Since LU-SGS is actually a combination of approximate LU decomposition and symmetric Gauss-Seidel iteration, each iteration does not require an exact solution, and convergence will naturally be achieved over time. Therefore, the present invention adopts Figure 8-Figure 9 The template in , obtains the required information of the corresponding neighbors through simple interpolation:

[0091] In the process of LU-SGS implicit advancement calculation based on the sorting results, for the hanging grid in the calculation domain, a target point for constructing the hanging grid into a uniform grid is obtained; the flow field information of the target point is calculated based on the flow field information of the grid around the target point.

[0092] The hanging grids are divided into the first type of hanging grids and the second type of hanging grids; the first type of hanging grids are: the neighboring grids of the first grid have a subgrid with a higher level than the first grid; the second type of hanging grids are: the neighboring grids of the first grid have a parent grid with a lower level than the first grid;

[0093] For the first type of hanging grid, a first target point corresponding to the uniform grid constructed by constructing the first type of hanging grid is obtained, a first target grid is obtained based on the first target point, four subgrids corresponding to the first target grid are obtained, and flow field information of the first target point is obtained by interpolation calculation based on flow field information of the four subgrids;

[0094] For the second type of suspended grid, obtain the second target point corresponding to the second type of suspended grid constructed as a uniform grid, obtain the distance from the center point of the grid surrounding the second target point to the second target point and sort them from small to large according to the distance, obtain the first 4 corresponding grids in the sorting, and obtain the flow field information of the second target point by interpolation calculation based on the flow field information of the first 4 corresponding grids in the sorting.

[0095] For the first type of hanging grid, the flow field information of the first target point is obtained by averaging the flow field information of the four subgrids. For the second type of hanging grid, the flow field information of the second target point is obtained by inverse distance weighting or weighted least squares interpolation based on the flow field information of the first four corresponding grids.

[0096] For the grid-centered solver, the flow field variables are all located at the center of the grid, so the interpolation template can be divided into two cases: Figure 8As shown, the left neighbor of grid i is an encrypted grid. In this case, since the distances from the grid center points c1~c4 to the node i-1 are equal, that is, the weights are equal, the 4-point average can be used to obtain the required variable, that is, , q i-1 is the variable information corresponding to node i-1, and the simplification of bilinear interpolation. q represents a variable, and the subscript represents the corresponding node. This formula can reach second-order accuracy. If c1~c4 still has subunits, it will be processed recursively.

[0097] The second type Fig. 9 , that is, the right neighbor of grid i is a coarsened grid. In this case, the four grids closer to the virtual i+1 point are considered as templates, and then the variable information at point i+1 is obtained by inverse distance weighting or weighted least squares interpolation. Take inverse distance interpolation as an example: ,same q represents a variable, and the subscript represents the corresponding node. d is the distance from the corresponding node to the i+1 point, and e is the natural logarithm.

[0098] The three-dimensional case is similar. For the first case, the sub-unit average is performed, and for the second case, the closer grid is selected for inverse distance weighting or weighted least squares interpolation.

[0099] This method reorders the leaf Cartesian grids in the computational domain to achieve balanced numbering by reasonably applying the fork tree data structure of the adaptive Cartesian grid; and realizes LU-SGS implicit advancement through the hanging grid neighbor interpolation algorithm in the grid transition area. This method is flexible and simple, and can be widely used in CFD engineering numerical simulation to improve computational efficiency and achieve fast CFD numerical simulation.

[0100] Verification example: This example is tested in the adaptive Cartesian grid program. A two-dimensional NA0012 airfoil inviscid flow example is selected. The incoming flow Ma=0.15, the incoming flow angle of attack is 5 degrees, and the Roe approximate Riemann solution is selected with the third-order MUSCL format to discretize the convection term. For comparison, the time advancement considers the LU-SGS method of the present invention and explicit advancement. The initial geometric adaptive grid is shown in Fig.10 .

[0101] Fig.11Comparison of residual convergence curves under different methods, including explicit format and implicit format and different CFL numbers, shows that the explicit method is sensitive to the CFL Courant number. When it is 0.4, the residual has no downward trend and cannot meet the stability requirements; while the adaptive Cartesian grid method proposed in the present invention can better implement the LUSGS implicit advancement algorithm. In this example, the CFL Courant number can be relaxed to about 100, and deep convergence is achieved, thereby achieving the effect of accelerating calculation, proving the effectiveness and feasibility of the method proposed in the present invention. At the same time, this method also provides a technical means for the implementation of other implicit algorithms on an adaptive Cartesian grid.

[0102] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0103] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A LU-SGS implicit boosting calculation method under an adaptive Cartesian grid, characterized in that: The method comprises: Step 1: Generate an equidistant and uniform initial Cartesian grid based on the aircraft model size parameters, aircraft model motion parameters and aerodynamic parameters, and assign a multidimensional array number to each grid according to the dimension of the space; Step 2: Based on the geometric shape of the aircraft model, the grid within the preset range of the object surface boundary is adaptively encrypted using a fork tree to generate the adaptive Cartesian grid required for calculation; Step 3: Sort the generated adaptive Cartesian grid to obtain a sorting result; Step 4: Perform LU-SGS implicit propulsion calculation based on the sorting results to obtain the numerical simulation calculation results of the aircraft model; Wherein, the step 3 specifically includes: Step 3.1: Determine the computational domain in the generated adaptive Cartesian grid; Step 3.2: In the computational domain, the initial Cartesian grids are numbered and sorted according to the multidimensional array number of the grids. If the grid is an encrypted grid, the subgrid number of the encrypted grid is used to replace the number position of the encrypted grid, and the numbering of the internal grids of the object surface is skipped. The sorting result is obtained based on the numbering results of all leaf grids, where the leaf grid is a grid unit without subgrids. Allocating a multidimensional array number to the initial Cartesian grid according to the dimension of the space, specifically including: allocating a multidimensional array number (i, j) to each grid according to the dimension of the space, the grid (i, j) indicates that the grid is located in the i-th column and the j-th row, and the value range of i and j is a natural number greater than or equal to 1; The initial Cartesian grids are numbered and sorted in the computational domain according to the multidimensional array number of the grids, including: Step a: Use the smallest multidimensional array number (1, 1) in the computational domain as the starting grid for sorting, and the array number of the starting grid satisfies i+j=2; Step b: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=3: starting from the grid with the largest i value, sort the grids in the previous step in a way that i decreases and j increases; Step c: Sort all grids in the computational domain whose multidimensional array number (i, j) satisfies i+j=4: starting from the grid with the largest i value, sort the grids in the previous step in a manner that i decreases and j increases; Repeat steps a to c in the manner of increasing the value of i+j by 1, until the multidimensional array with the largest number in the computational domain (imax, jmax) is used as the sorting end grid, imax is the maximum value of i, and jmax is the maximum value of j; The adaptively encrypted sub-grid shares the same multi-dimensional array number with the parent grid. The adaptively encrypted sub-grid is sorted and inserted into the sort position of the parent grid of the adaptively encrypted sub-grid, and the sort position of the parent grid is replaced by the sort of the sub-grid, including: Assuming that there are adaptively encrypted subgrids in the grid (i, j), all subgrids of the grid (i, j) are sorted to obtain a sorting result, and the sorting result replaces the sorting position of the grid (i, j); The subgrids are sorted as follows: after one encryption, the grid (i, j) obtains 4 subgrids, and the sorting order of the 4 subgrids is: the lower left subgrid is ranked first, the lower right subgrid is ranked second, the upper left subgrid is ranked third, and the upper right subgrid is ranked fourth; Insert the sorting results of the four sub-grids and replace the sorting of the corresponding parent grid positions; If there is a sub-grid at a higher level in the sub-grid, recursive processing is performed, and the sub-grid at a higher level is sorted using the above sub-grid sorting method and then replaces the sorting of the corresponding parent grid position until all leaf grids in the computational domain are traversed.

2. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 1, characterized in that: During the sorting process, if the center of a leaf grid is located inside the object surface, the leaf grid is skipped and does not participate in the sorting.

3. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 1, characterized in that: The sorting results are stored using linked list pointers.

4. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 1, characterized in that: In step 4, during the LU-SGS implicit advancement calculation based on the sorting result, for the hanging grid in the calculation domain, a target point for constructing the hanging grid into a uniform grid is obtained; The flow field information of the target point is calculated based on the flow field information of the grid around the target point.

5. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 4, characterized in that: The hanging grids are divided into the first type of hanging grids and the second type of hanging grids; the first type of hanging grids are: the neighboring grids of the first grid have a subgrid with a higher level than the first grid; the second type of hanging grids are: the neighboring grids of the first grid have a parent grid with a lower level than the first grid; For the first type of hanging grid, a first target point corresponding to the uniform grid constructed by constructing the first type of hanging grid is obtained, a first target grid is obtained based on the first target point, four subgrids corresponding to the first target grid are obtained, and flow field information of the first target point is obtained by interpolation calculation based on flow field information of the four subgrids; For the second type of suspended grid, obtain the second target point corresponding to the second type of suspended grid constructed as a uniform grid, obtain the distance from the center point of the grid surrounding the second target point to the second target point and sort them from small to large according to the distance, obtain the first 4 corresponding grids in the sorting, and obtain the flow field information of the second target point by interpolation calculation based on the flow field information of the first 4 corresponding grids in the sorting.

6. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 5, characterized in that: For the first type of hanging grid, the flow field information of the first target point is obtained by averaging the flow field information of the four subgrids.

7. The LU-SGS implicit boosting calculation method under an adaptive Cartesian grid according to claim 5, characterized in that: For the second type of hanging grids, based on the flow field information of the first 4 corresponding grids, the flow field information of the second target point is obtained by inverse distance weighting or weighted least squares interpolation calculation.

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