Dynamic and static boundary slip grid generation solving method

Abstract

The invention provides a dynamic and static boundary slip grid generation solving method, which comprises the following steps of: dividing a sub-domain of relative motion in a simulation calculation domain into a static domain and a motion domain, and fitting the static domain and the motion domain at a dynamic and static interface; the grid points, located at the dynamic and static interface, of the static domain and the motion domain are retracted at equal intervals in the normal direction of the dynamic and static interface and then extend to the first-layer grid face in the boundary of the opposite domain in the normal direction of the dynamic and static interface, and a single-grid-layer nested grid, a static domain boundary and a motion domain boundary are generated; searching the grid units on the first layer of grid surface in the stationary domain boundary, searching the grid units containing the grid points on the motion domain boundary, and obtaining the flow field data of the grid points on the motion domain boundary by using the flow field data interpolation of the grid units; and searching the grid units on the first layer of grid surface in the motion domain boundary, searching the grid units containing the grid points on the static domain boundary, and obtaining the flow field data of the grid points on the static domain boundary by utilizing the flow field data interpolation of the grid units.

Description

Technical Field

[0001] The invention belongs to the technical field of CFD numerical simulation, and in particular relates to a sliding grid generation and solution method capable of realizing grid nesting and data transmission between subdomains that move relatively within a computational domain. Background Art

[0002] Sliding mesh is an important part of CFD numerical simulation, which is used to solve the flow problem when there are relatively moving subdomains in the computational domain. By dividing the computational domain into multiple subdomains and equipping each subdomain with an independent grid system, the sliding mesh technology realizes the nesting of grids in each subdomain and the data transmission of the flow field at the interface between grids, and then realizes the numerical simulation of the flow field of the moving object. Compared with other dynamic grid generation and solution technologies, the sliding mesh can keep its topological structure unchanged during the movement of the object, avoiding a large number of grid reconstruction calculations and greatly improving the efficiency of the calculation of the unsteady flow field of the moving object.

[0003] However, the implementation of sliding mesh technology faces two challenges. On the one hand, how to quickly generate high-quality nested meshes between subdomains, and on the other hand, how to achieve high-fidelity transmission of flow field data in the nested mesh area. To form nested meshes between subdomains, the boundary surfaces of the two subdomain meshes must be extended to the other subdomain, and the quality of the generated extended mesh must be guaranteed during the extension of the subdomain boundary surface. For subdomains with objects with large motion / complex motion trajectories, serious distortion may occur during the mesh extension process, resulting in a significant decrease in numerical simulation accuracy or even calculation divergence. After the nested mesh generation is completed, data interpolation between adjacent subdomains must be performed on the boundary surfaces of the nested meshes to complete the exchange of flow field information between subdomains. The construction of the interpolation calculation method is crucial. If the interpolation accuracy cannot be guaranteed, a large number of errors will be generated in the process of transferring flow field data on the subdomain boundary surface, which will greatly affect the accuracy of the numerical simulation and even lead to unstable calculation results.

[0004] Therefore, the development of stable and efficient sliding mesh generation and interpolation technology is crucial to realize unsteady CFD simulation with relative motion objects. The development of high-fidelity and robust sliding mesh generation and solution technology for dynamic-static interface is of great significance to improve the accuracy and stability of dynamic-static interface problem simulation and expand the application scope of CFD software in the field of industrial simulation. Summary of the invention

[0005] In order to overcome the deficiencies in the prior art, the inventors have conducted intensive research and provided a method for generating and solving a dynamic-static interface sliding grid, which ensures the quality of the nested grid and the transmission of flow field information.

[0006] The technical solution provided by the present invention is as follows:

[0007] In a first aspect, a method for generating and solving a sliding mesh at a dynamic-static interface includes:

[0008] The subdomain of relative motion in the simulation calculation domain is divided into a static domain and a motion domain, and the static domain and the motion domain are fitted at the static-dynamic interface;

[0009] The grid points of the static domain and the moving domain at the static-dynamic interface are indented equidistantly along the normal direction of the static-dynamic interface, and then extended along the normal direction of the static-dynamic interface to the first layer of grid surface in the boundary of the other domain, generating a single-grid layer nested grid, a static domain boundary and a moving domain boundary;

[0010] Searching for grid cells on the first layer of grid surface within the static domain boundary, searching for grid cells containing grid points on the motion domain boundary, and using flow field data of the grid cells to interpolate to obtain flow field data of the grid points on the motion domain boundary;

[0011] The grid cells on the first layer of grid surface within the motion domain boundary are searched to find the grid cells containing the grid points on the static domain boundary, and the flow field data of the grid cells are interpolated to obtain the flow field data of the grid points on the static domain boundary.

[0012] In a second aspect, a dynamic-static interface sliding grid generation and solving device comprises:

[0013] one or more processors;

[0014] a storage device for storing one or more programs,

[0015] When the one or more programs are executed by the one or more processors, the one or more processors implement the dynamic-static interface sliding grid generation and solution method described in the first aspect.

[0016] In a third aspect, a readable storage medium stores a computer program, which, when executed by a processor, implements the method for generating and solving the dynamic-static interface sliding mesh described in the first aspect.

[0017] In a fourth aspect, a computer program product is provided, the computer program product comprising: a computer program (also referred to as code, or instruction), which, when executed, executes the dynamic-static interface slip mesh generation and solution method described in the first aspect.

[0018] A method for generating and solving a dynamic-static interface sliding grid provided by the present invention has the following beneficial effects:

[0019] (1) The present invention provides a sliding grid generation method, which can obtain a high-quality single-grid layer nested grid by giving grid indentation and extension rules to ensure that the boundary grid is indented and extended at equal distances;

[0020] (2) The present invention provides a sliding grid interpolation method, which searches for grid cells on the first layer of grid surfaces within the boundary of a stationary domain, searches for grid cells containing grid points on the boundary of a moving domain, and uses flow field data of the grid cells to interpolate to obtain flow field data of the grid points on the boundary of the moving domain; searches for grid cells on the first layer of grid surfaces within the boundary of a moving domain, searches for grid cells containing grid points on the boundary of a stationary domain, and uses flow field data of the grid cells to interpolate to obtain flow field data of the grid points on the boundary of the stationary domain, thereby effectively realizing the transmission of flow field information. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the sliding mesh generation process;

[0022] Figure 2 It is a schematic diagram of the sliding grid domain;

[0023] Figure 3 This is a schematic diagram of slip surface identification;

[0024] Figure 4 It is a schematic diagram of slip surface interpolation;

[0025] Figure 5 Identify schematic diagrams for grid cell topology;

[0026] Figure 6 This is an example of high-speed railway passing through a tunnel;

[0027] Figure 7 This is a simulation of the sliding mesh effect of a high-speed railway passing through a tunnel, where the black part is the original dynamic and static interface;

[0028] Figure 8 For the transmission of pressure waves of high-speed railways passing through tunnels;

[0029] Fig. 9 Generate renderings for TCD computational grid and sliding grid;

[0030] Fig.10 This is the transient result cloud diagram of TCD non-stationary flow field;

[0031] Fig.11 This is the TCD simulation performance curve. DETAILED DESCRIPTION

[0032] The following detailed description of the present invention will make the features and advantages of the present invention more clear and explicit.

[0033] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0034] The invention provides a method for solving sliding grid generation at a dynamic-static interface, which comprises two parts: sliding grid generation and sliding grid interpolation, so as to realize flow field information transmission between dynamic and static subdomains of a computational domain.

[0035] Step 1: Sliding mesh generation

[0036] The sliding mesh generation process is shown in Figure 1 .like Figure 1 As shown, the original grid subdomain A and subdomain B are fitted at the dynamic and static interface, subdomain A is the static domain (or motion domain), and subdomain B is the motion domain (or static domain). First, at the dynamic and static interface, the subdomain A and B grids are indented inward along the normal direction of the dynamic and static interface. After the indentation is completed, a layer of grid is extended outward along the normal direction of the dynamic and static interface to form a single-grid layer nested grid.

[0037] In order to ensure the quality of nested meshes, it is necessary to ensure that the mesh is indented and extended at equal distances. During the indentation process, the mesh extension direction is the inner normal direction, and the indentation distance of each subdomain along the normal direction of the dynamic and static interface must be determined. The indentation distance d of each subdomain is 缩进 It is determined in the following way: obtain all grid points of the subdomain on the dynamic and static interface and the grid edges in the subdomain connected to them, select the shortest edge among the grid edges connected to all grid points, multiply the length of the shortest edge by the retraction coefficient, and obtain the retraction distance of the subdomain.

[0038] d 缩进A =k A min(l A )

[0039] d 缩进B =k B min(l B )

[0040] Where, d 缩进A and d 缩进B are the indentation distances of subdomains A and B respectively; k A and k B are the indentation coefficients of subdomains A and B, respectively, usually ranging from 1 / 3 to 1 / 2; l A and l B They are the grid edges within the subdomains that connect all the grid points on the dynamic and static interfaces of subdomains A and B.

[0041] During the extension process, the mesh extension direction is the outward normal direction, and the extension distance is d 延伸 It is obtained by adding the indentation distances of the two subdomain grids. The calculation formula is as follows:

[0042] d 延伸A =d 延伸B =d 缩进A +d 缩进B

[0043] The extension lengths of the two subdomains are kept consistent, thus forming a single-layer mesh nesting of the two subdomains, ensuring the quality of the nested mesh.

[0044] The generated sliding mesh is a single-mesh layer nested mesh, that is, the two subdomains extend toward each other to the first mesh surface within the boundary of the other domain, the first mesh layer within the boundary of the moving domain overlaps with the first mesh layer within the boundary of the stationary domain, and the first mesh layer within the boundary of the stationary domain overlaps with the first mesh layer within the boundary of the moving domain. The overlapping surface of the two subdomains is defined as the sliding surface. Figure 1 and Figure 2 As shown, two slip surfaces are formed after the mesh extension is completed, and each slip surface includes two parts, namely, the superimposed motion domain boundary surface & the first layer mesh surface in the static domain boundary, and the superimposed static domain boundary surface & the first layer mesh surface in the motion domain boundary.

[0045] This sliding mesh generation method is applicable to structured and unstructured meshes in 2D and 3D. In 2D, the extended mesh is a quadrilateral mesh; in 3D, the extended mesh is a hexahedral mesh. The sliding mesh generation method supports axial sliding mesh generation (such as axial compressor / turbine) and radial sliding mesh generation (such as radial compressor / turbine, pump, high-speed rail tunnel, etc.).

[0046] Step 2: Sliding grid interpolation

[0047] The core of sliding grid interpolation is to identify the sliding surface and complete the interpolation of the sliding surface flow field data, so as to provide corresponding boundary conditions for each subdomain and realize the iterative calculation of the subdomain flow field.

[0048] Slip surface recognition means that for each grid point on the boundary of the motion domain (static domain), the grid cells on the first layer of the grid surface within the boundary of the paired static domain (motion domain) are searched, and the grid cell containing the grid point is searched. Figure 3 As shown in the figure, triangular / quadrilateral mesh cells are two common geometric topologies on the mesh surface. For each mesh point on the boundary of the motion / stationary domain, a mesh cell containing the mesh point must be searched on the first layer of mesh close to the boundary surface in the paired domain. There are two successful recognition criteria: 1) the mesh point is inside the mesh cell; 2) the mesh point is on the edge of the mesh cell.

[0049] Slip surface identification includes: identifying slip surfaces with constant axial coordinate values, and searching for mesh cells on the slip surface defined by (radial r, circumferential θ) coordinates; identifying slip surfaces with constant radial coordinate values, and searching for mesh cells on the slip surface defined by (axial x, circumferential θ) coordinates. The vertex coordinates of each mesh cell are looped, and when the coordinates of the fourth mesh vertex are the same as the coordinates of the first mesh vertex, they are identified as triangular cells, and then interpolation calculations are performed; if the coordinates of the fifth mesh vertex are the same as the coordinates of the first mesh vertex, they are identified as quadrilateral cells, and then interpolation calculations are performed.

[0050] After the slip surface identification is completed, the slip surface data interpolation refers to the interpolation of the first layer of grid surfaces within the stationary domain boundary to the grid points on the moving domain boundary, and the interpolation of the first layer of grid surfaces within the moving domain boundary to the grid points on the stationary domain boundary, thereby completing the flow field data update of the grid points on the extended boundary and providing updated boundary conditions for the corresponding subdomains until the flow field converges.

[0051] The interpolation weight coefficient of the grid point is constructed as a function of the distance from the vertex of the grid cell where the grid point is located to the grid point:

[0052]

[0053] q=f2f3q1+f3f4q2+f1f4q3+f1f2q4

[0054] Among them, d1, d2, d3, and d4 are the distances from the grid point to the four vertices of the grid unit, q1, q2, q3, and q4 are the corresponding variable values ​​of the four vertices, f2f3, f3f4, f1f4, and f1f2 are the corresponding weight coefficients of the four vertices, and q is the interpolated grid point variable value.

[0055] To ensure the interpolation accuracy is second-order accuracy, the number of vertices of the grid unit where the grid point is located corresponds to the number of interpolation weight coefficients of the grid point, and the sum of all interpolation weight coefficients of the grid point is 1. The flow field variable value of each vertex of the grid unit where the grid point is located is multiplied by the interpolation weight coefficient corresponding to the vertex, and then summed to obtain the interpolation data of the grid point on the boundary.

[0056] If after searching, the grid point on the slip surface has no corresponding grid cell on the first layer of the grid surface within the boundary of the pairing domain, then the grid cell closest to the grid point (that is, the grid point with the shortest distance from the center of the grid cell) is used as the interpolation grid cell, and the interpolation weight coefficient is constructed as a function of the inverse of the distance from each vertex of the grid cell to the grid point:

[0057]

[0058] k=k1+k2+k3+k4,

[0059]

[0060] q=f1q1+f2q2+f3q3+f4q4

[0061] Where d1, d2, d3, and d4 are the distances from the grid point to the four vertices of the grid unit closest to the grid point, q1, q2, q3, and q4 are the corresponding variable values ​​of the four vertices, f1, f2, f3, and f4 are the corresponding weight coefficients of the four vertices, and q is the interpolated grid point variable value.

[0062] To ensure that the interpolation accuracy is still second-order accuracy, the number of vertices of the interpolation grid unit corresponds to the number of interpolation weight coefficients of the grid point, and the sum of all interpolation weight coefficients of the grid point is 1. At this time, the flow field variable value of each vertex of the interpolation grid unit is * the interpolation weight coefficient corresponding to the vertex, and then summed to obtain the interpolation data of the grid point on the boundary. Slip surface data interpolation is as follows Figure 4 shown.

[0063] Figure 6 The figure is a schematic diagram of the mesh used for high-speed rail tunnel simulation. The black mesh area is the static mesh area, which includes the area near the tunnel wall and the air area outside the tunnel. The red mesh is the calculation area near the high-speed rail. During the calculation process, the red area moves along the axis with the high-speed rail, and there is a dynamic and static interface composed of arcs and planes between the red area and the black mesh area.

[0064] Figure 7 The effect diagram of sliding mesh generation for high-speed railway tunnel simulation. As can be seen from the figure, after the sliding mesh extension preprocessing, the two subdomains (red parts) have achieved outward ( Figure 7 a) and inward ( Figure 7 b) is extended and nested to form two sliding surfaces, which proves the effectiveness of the sliding mesh generation method in the present invention.

[0065] Figure 8 The pressure wave transmission effect at a certain instant in the process of high-speed rail passing through the tunnel is demonstrated. Through the sliding grid interpolation calculation, the dynamic transmission of pressure waves when the high-speed rail is running in the tunnel can be observed. The head of the high-speed rail is impacted by the airflow, resulting in a significant increase in pressure. According to the principle of action and reaction of forces, this increase in pressure will generate pressure waves in the airflow near the head. And propagate to both sides of the tunnel. This phenomenon verifies the effectiveness of the sliding grid generation and interpolation method in the present invention and the correctness of the physical model.

[0066] Fig. 9This is the aerodynamic simulation grid diagram of the first-stage semi-transonic axial compressor (Transonic Compressor Darmstadt, hereinafter referred to as TCD) of the Darmstadt University of Technology. The compressor consists of three rows of blades, which are the rotor, stator and outlet guide vane in the order of the inlet direction. There is a dynamic and static interface between the first row of rotors and the second row of stators (see Fig. 9 a). Fig. 9 b is the effect diagram of the sliding mesh generation for TCD simulation, where the red line represents the original dynamic and static interface. After the sliding mesh extension, the two subdomains realize mesh extension and nesting respectively, forming two sliding surfaces, which proves the effectiveness of the sliding mesh generation method in the present invention.

[0067] Fig.10 The transient results of the TCD unsteady flow field predicted by the sliding mesh method are shown, including pressure, stream velocity and entropy distribution. It can be observed that the sliding mesh method realizes the high-fidelity mutual transfer of data on both sides of the slip surface, ensures the continuity of the flow field near the slip surface, and proves the physical correctness of the developed sliding mesh generation and interpolation method.

[0068] Fig.11 The performance curves obtained by simulating TCD using the sliding grid method and the steady mixing surface method are shown, and the simulation results are compared with the experimental data. From the performance curves, it can be seen that compared with the steady mixing surface method, the sliding grid method significantly improves the prediction accuracy of the stall margin, and the prediction of the stall point is also closer to the experimental results.

[0069] The present invention also provides a dynamic-static interface sliding grid generation and solving device, comprising:

[0070] one or more processors;

[0071] a storage device for storing one or more programs,

[0072] When the one or more programs are executed by the one or more processors, the one or more processors implement the dynamic-static interface sliding grid generation and solution method described in the first aspect.

[0073] The present invention also provides a readable storage medium having a computer program stored thereon, and when the program is executed by a processor, the method for generating and solving the dynamic-static interface sliding grid described in the first aspect is implemented.

[0074] The readable storage medium includes, but is not limited to, various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0075] The present invention also provides a computer program product, which includes: a computer program (also referred to as code, or instruction), which, when executed, executes the dynamic-static interface slip grid generation and solution method described in the first aspect.

[0076] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, microwave, etc.) mode to another website site, computer, server or data center.

[0077] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0078] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0079] The present invention has been described in detail above in conjunction with specific implementations and exemplary examples, but these descriptions cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, a variety of equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its implementation methods, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be subject to the attached claims.

[0080] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for generating and solving a sliding grid at a dynamic and static interface, characterized in that: include: The subdomain of relative motion in the simulation calculation domain is divided into a static domain and a motion domain, and the static domain and the motion domain are fitted at the static-dynamic interface; The grid points of the static domain and the moving domain at the static-dynamic interface are indented equidistantly along the normal direction of the static-dynamic interface, and then extended along the normal direction of the static-dynamic interface to the first layer of grid surface in the boundary of the other domain, generating a single-grid layer nested grid, a static domain boundary and a moving domain boundary; Searching for grid cells on the first layer of grid surface within the static domain boundary, searching for grid cells containing grid points on the motion domain boundary, and using flow field data of the grid cells to interpolate to obtain flow field data of the grid points on the motion domain boundary; The grid cells on the first layer of grid surface within the motion domain boundary are searched to find the grid cells containing the grid points on the static domain boundary, and the flow field data of the grid cells are interpolated to obtain the flow field data of the grid points on the static domain boundary.

2. The method for generating and solving the dynamic-static interface sliding grid according to claim 1 is characterized in that: In the step of retracting the grid points of the static domain and the moving domain at the static-dynamic interface at equal intervals along the normal direction of the static-dynamic interface, the retraction distance is determined by: obtaining all grid points of the static domain or the moving domain on the static-dynamic interface and the grid edges in the domain connected to them, selecting the shortest edge among the grid edges connected to all the grid points, and multiplying the length of the shortest edge by the retraction coefficient to obtain the retraction distance of the static domain or the moving domain.

3. The method for generating and solving the dynamic-static interface sliding grid according to claim 2 is characterized in that: The indentation coefficient is 1 / 3 to 1 / 2.

4. The method for generating and solving the dynamic-static interface sliding grid according to claim 1 is characterized in that: In the step of extending along the normal direction of the static and dynamic interface to the first layer of mesh surface within the boundary of the other domain, the extension distances of the static domain and the dynamic domain are equal, and the extension distance = the retracted distance of the static domain + the retracted distance of the dynamic domain.

5. The method for generating and solving the dynamic-static interface sliding grid according to claim 1 is characterized in that: The step of interpolating the flow field data of the grid cells to obtain the flow field data of the grid points on the boundary of the motion domain, or the step of interpolating the flow field data of the grid cells to obtain the flow field data of the grid points on the boundary of the static domain, is implemented in the following manner: The interpolation weight coefficient of the grid point is constructed as a function of the distance from the vertex of the grid unit where the grid point is located to the grid point. The number of vertices of the grid unit where the grid point is located corresponds to the number of interpolation weight coefficients of the grid point, and the sum of all interpolation weight coefficients of the grid point is 1; The flow field variable value of each vertex of the grid unit where the grid point is located is multiplied by the interpolation weight coefficient corresponding to the vertex, and then summed up to obtain the flow field data of the grid point on the boundary.

6. The method for generating and solving the dynamic-static interface sliding grid according to any one of claims 1 to 5, characterized in that: The method also includes: searching for grid cells on the first layer grid surface within the static domain boundary or the motion domain boundary. If, after searching, a grid point on the static domain boundary or the motion domain boundary has no corresponding grid cell on the first layer grid surface within the pairing domain boundary, the searched grid cell closest to the grid point is used as an interpolation grid cell.

7. The method for generating and solving the dynamic-static interface sliding grid according to claim 6 is characterized in that: Also includes: When a grid point on the boundary of a stationary domain or a moving domain has no corresponding grid cell on the first layer of grid surface within the boundary of the paired domain, the flow field data of the grid point on the boundary is determined as follows: The interpolation weight coefficient is constructed as a function of the inverse of the distance from each vertex of the interpolation grid unit to the corresponding grid point, the number of vertices of the interpolation grid unit is the number of the interpolation weight coefficients of the grid point, and the sum of all the interpolation weight coefficients of the grid point is 1; The flow field variable value of each vertex of the interpolation grid unit is multiplied by the interpolation weight coefficient corresponding to the vertex, and then the sum is obtained to obtain the flow field data of the grid point on the boundary.

8. A computer program product, characterized in that The computer program product comprises: a computer program, which, when executed, executes the method for generating and solving the dynamic-static interface slip mesh described in the first aspect.

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