A method for generating and solving a moving and static interface sliding grid

Abstract

The application provides a method for generating and solving a moving and static interface sliding grid, which comprises the following steps: dividing a simulation calculation domain into a static domain and a moving domain according to the relative motion of the sub-domain, and making the static domain and the moving domain adhere to each other at a moving and static interface; equally indenting the grid points of the static domain and the moving domain at the moving and static interface along the normal direction of the moving and static interface, and then extending to the first layer of grid surfaces in the boundary of the other domain along the normal direction of the moving and static interface to generate a single grid layer nested grid, a static domain boundary and a moving domain boundary; searching the grid elements on the first layer of grid surfaces in the static domain boundary, searching the grid elements containing the grid points on the moving domain boundary, and obtaining the flow field data of the grid points on the moving domain boundary by using the flow field data interpolation of the grid elements; searching the grid elements on the first layer of grid surfaces in the moving domain boundary, searching the grid elements 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 using the flow field data interpolation of the grid elements.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of fluid dynamics (CFD) numerical simulation, and particularly relates to a sliding mesh generation and solving method capable of realizing mesh nesting and data transmission between subdomains in relative motion within a calculation domain. BACKGROUND

[0002] Sliding mesh is an important part of CFD numerical simulation, and is used for solving flow problems in the calculation domain with subdomains in relative motion. By dividing the calculation domain into multiple subdomains and providing each subdomain with an independent mesh system, the sliding mesh technology realizes the nesting of the mesh of each subdomain and the data transmission of the flow field at the interface between the meshes, and then realizes the numerical simulation of the flow field of a moving object. Compared with other dynamic mesh generation and solving technologies, the sliding mesh can maintain its topological structure unchanged during the movement of the object, avoids a large amount of mesh reconstruction calculation, and greatly improves the calculation efficiency of the unsteady flow field of the moving object.

[0003] However, the implementation of the sliding mesh technology faces two challenges, one is how to quickly generate high-quality nested meshes between subdomains, and the other is how to realize high-fidelity transmission of the flow field data in the nested mesh region. To form the nested mesh between subdomains, the boundary surface of the mesh of each subdomain must be extended to the other subdomain, and the quality of the generated extended mesh must be ensured during the extension of the boundary surface of the subdomain. For a subdomain with a large motion / complex motion trajectory object, severe distortion may occur during the mesh extension, resulting in a significant decrease in numerical simulation accuracy, and even calculation divergence. After the nested mesh is generated, data interpolation between adjacent subdomains must be performed on the boundary surface of the nested mesh to complete the exchange of flow field information between the subdomains, and the interpolation method is crucial. If the interpolation accuracy cannot be guaranteed, a large amount of errors will be generated in the data transmission process of the flow field at the boundary surface of the subdomain, greatly affecting the accuracy of the numerical simulation, and even leading to unstable calculation results.

[0004] Therefore, it is of great significance to develop a stable and efficient sliding mesh generation and interpolation technology for realizing the unsteady CFD simulation of a relative motion object. Developing a high-fidelity and robust dynamic-static interface sliding mesh generation and solving technology is of great significance to improve the accuracy and stability of the simulation of dynamic-static interface problems and expand the application range of CFD software in the industrial simulation field. SUMMARY

[0005] In order to overcome the deficiencies in the prior art, the present application provides a dynamic-static interface sliding mesh generation and solving method, which guarantees the quality of the nested mesh and the transmission of the flow field information.

[0006] The technical scheme provided by the present application is as follows:

[0007] The first aspect is a dynamic-static interface sliding mesh generation and solving method, comprising the following steps:

[0008] The sub-domain with relative motion in the simulation calculation domain is divided into a static domain and a moving domain, and the static domain and the moving domain are attached at the dynamic-static interface;

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

[0010] The grid elements on the first layer of grid surfaces in the static domain boundary are searched, and the grid elements containing the grid points on the moving domain boundary are searched, and the flow field data of the grid elements are used for interpolation to obtain the flow field data of the grid points on the moving domain boundary;

[0011] The grid elements on the first layer of grid surfaces in the moving domain boundary are searched, and the grid elements containing the grid points on the static domain boundary are searched, and the flow field data of the grid elements are used for interpolation to obtain the flow field data of the grid points on the static domain boundary.

[0012] The second aspect is a dynamic-static interface sliding mesh generation and solving device, comprising:

[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 mesh generation and solving method of the first aspect.

[0016] The third aspect is a readable storage medium, which stores a computer program, and the program is executed by a processor to implement the dynamic-static interface sliding mesh generation and solving method of the first aspect.

[0017] The fourth aspect is a computer program product, which comprises a computer program (also referred to as code or instructions), and when the computer program is executed, the dynamic-static interface sliding mesh generation and solving method of the first aspect is executed.

[0018] The dynamic-static interface sliding mesh generation and solving method provided by the application has the following beneficial effects:

[0019] (1) The application provides a sliding mesh generation method, which guarantees equidistant inlaid and extension of the boundary grid by giving the grid inlaid and extension rules, and can obtain high-quality single grid layer nested mesh;

[0020] (2) The application provides a sliding grid interpolation method, which searches the grid cells on the first layer of grid surfaces in the static domain boundary, searches the grid cells containing the grid points on the moving domain boundary, and obtains the flow field data of the grid points on the moving domain boundary by using the flow field data of the grid cells for interpolation; searches the grid cells on the first layer of grid surfaces in the moving domain boundary, searches the grid cells containing the grid points on the static domain boundary, and obtains the flow field data of the grid points on the static domain boundary by using the flow field data of the grid cells for interpolation, thereby effectively realizing the flow field information transmission. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A schematic diagram for generating a sliding grid is shown in the figure.

[0022] Figure 2 A schematic diagram for a sliding grid domain is shown in the figure.

[0023] Figure 3 A schematic diagram for sliding surface identification is shown in the figure.

[0024] Figure 4 A schematic diagram for sliding surface interpolation is shown in the figure.

[0025] Figure 5 A schematic diagram for grid cell topology identification is shown in the figure.

[0026] Figure 6 A high-speed rail tunneling example is shown in the figure.

[0027] Figure 7 A simulation sliding grid effect diagram for high-speed rail tunneling is shown in the figure, in which the black color represents the original dynamic-static interface.

[0028] Figure 8 A pressure wave transmission for high-speed rail tunneling is shown in the figure.

[0029] Figure 9 A TCD calculation grid and sliding grid generation effect diagram is shown in the figure.

[0030] Figure 10 A TCD non-steady flow field transient result cloud diagram is shown in the figure.

[0031] Figure 11 A TCD simulation performance curve is shown in the figure. DETAILED DESCRIPTION

[0032] The features and advantages of the present application will become more apparent from the following detailed description in conjunction with the accompanying drawings.

[0033] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations.

[0034] The application provides a moving and static interface sliding grid generation and solving method, which comprises a sliding grid generation and a sliding grid interpolation, so as to realize the transmission of flow field information between moving and static subdomains of a calculation domain.

[0035] Step one, sliding grid generation

[0036] The sliding grid generation process is shown in Figure 1 As shown in Figure 1 , the original grid subdomains A and B are attached at the moving and static interface, the subdomain A is a static domain (or a moving domain), and the subdomain B is a moving domain (or a static domain). First, the subdomain A and B grids are inwards retracted along the normal direction of the moving and static interface, and then a layer of grids is extended outwards along the normal direction of the moving and static interface, so as to form a single grid layer nested grid.

[0037] In order to ensure the quality of the nested grid, it is necessary to ensure the equal retraction and extension of the grid. In the retraction process, the grid extension direction is the inner normal direction, and the retraction distance of each subdomain along the normal direction of the moving and static interface needs to be determined. The retraction distance d 缩进 of each subdomain is determined in the following way: all the grid points of the subdomain on the moving and static interface and the grid edges in the subdomain connected with the grid points are obtained, the shortest edge is selected from the grid edges connected with all the grid points, and the retraction distance of the subdomain is obtained by multiplying the edge length of the shortest edge by a retraction coefficient.

[0038] d 缩进A =k A min(l A )

[0039] d 缩进B =k B min(l B )

[0040] In the formula, d 缩进A and d 缩进B are the retraction distances of the subdomains A and B respectively; k A and k B are the retraction coefficients of the subdomains A and B respectively, and are generally 1 / 3-1 / 2; l A and l B are the grid edges in the subdomains A and B connected with all the grid points on the moving and static interface respectively.

[0041] In the extension process, the grid extension direction is the outer normal direction, and the extension distance d 延伸 is obtained by adding the retraction distances of the grids of the two subdomains, and 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 length of the two sub-domains is consistent, thereby forming a single-layer grid nested of the two sub-domains, and ensuring the nested grid quality.

[0044] The generated sliding grid is a single-layer nested grid, that is, each of the two sub-domains extends to the first layer grid surface in the boundary of the other sub-domain, the first layer grid in the moving domain boundary and the first layer grid in the static domain boundary overlap, the first layer grid in the static domain boundary and the first layer grid in the moving domain boundary overlap, and the overlapping surface of the two sub-domains is defined as the sliding surface. Figure 1 and Figure 2 As shown in the figure, after the grid extension, two sliding surfaces are formed, each of which includes two parts, that is, the first layer grid surface in the overlapping moving domain boundary and the static domain boundary, and the first layer grid surface in the overlapping static domain boundary and the moving domain boundary.

[0045] The sliding grid generation method is applicable to two-dimensional and three-dimensional structured and unstructured grids. In the two-dimensional case, the extended grid is a quadrilateral grid; in the three-dimensional case, the extended grid is a hexahedral grid. The sliding grid generation method supports axial sliding grid generation (such as axial flow compressor / turbine), radial sliding grid generation (such as radial flow compressor / turbine, pump, high-speed train tunnel, etc.).

[0046] Step two, sliding grid interpolation

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

[0048] Sliding surface identification refers to: for each grid point on the boundary of the moving domain (static domain), search for the grid element on the first layer grid surface in the paired static domain (moving domain) boundary, and search for the grid element containing the grid point. The sliding surface identification result is shown in Figure 3 As shown in the figure, the triangular / quadrilateral grid element is the two common geometric topologies on the grid surface, and for each grid point on the moving / static domain boundary, the grid element containing the grid point must be searched on the first layer grid near the boundary surface in the paired domain. The identification success criteria include two kinds: 1) the grid point is in the grid element; 2) the grid point is on the edge of the grid element.

[0049] The slip surface recognition includes: recognizing the slip surface with constant axial coordinate value, and searching the grid unit defined by (radial r, circumferential θ) coordinates on the slip surface; recognizing the slip surface with constant radial coordinate value, and searching the grid unit defined by (axial x, circumferential θ) coordinates on the slip surface. The vertex coordinates of each grid unit are cycled, when the 4th grid vertex coordinate is the same as the 1st grid vertex coordinate, it is recognized as a triangular unit, and then interpolation calculation is performed; if the 5th grid vertex coordinate is the same as the 1st grid vertex coordinate, it is recognized as a quadrilateral unit, and then interpolation calculation is performed.

[0050] After the slip surface recognition is completed, the slip surface data interpolation refers to the interpolation of the first layer grid surface in the static domain boundary to the grid point on the moving domain boundary, and the interpolation of the first layer grid surface in the moving domain boundary to the grid point on the static domain boundary, so as to complete the flow field data update of the grid point on the extended boundary, and provide updated boundary conditions for the corresponding sub-domain, 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 unit where the grid point is located to the grid point:

[0052]

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

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

[0055] To ensure that 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 values of each vertex of the grid unit where the grid point is located are multiplied by the corresponding interpolation weight coefficient of 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 unit containing it on the first layer grid surface in the paired domain boundary, the searched grid unit closest to the grid point (i.e. the grid point has the shortest distance to the center of the grid unit) is taken as the interpolation grid unit, and the interpolation weight coefficient is constructed as a function of the reciprocal of the distance from each vertex of the grid unit to the grid point:

[0057]

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

[0059]

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

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

[0062] To ensure that the interpolation accuracy is still second-order accuracy, the number of interpolation weight coefficients of the grid point corresponds to the number of vertices of the interpolation grid cell, and the sum of all interpolation weight coefficients of the grid point is 1. At this time, the flow field variable values of the vertices of the interpolation grid cell are multiplied by the interpolation weight coefficients corresponding to the vertices, and then summed to obtain the interpolation data of the grid point on the boundary. The interpolation of the slip surface data is as shown in Figure 4 .

[0063] Figure 6 It is a grid diagram for simulating high-speed train passing through a tunnel. The black grid area is a static grid area, including the near-tunnel wall part area inside the tunnel and the air part area outside the tunnel, and the red grid is the calculation area near the high-speed train. During the calculation, the red area moves along the axis direction following the high-speed train, and there is an interface between the red area and the black grid area, which is composed of a circular arc and a plane.

[0064] Figure 7 It is a generated effect diagram of the sliding grid for simulating high-speed train passing through a tunnel. As can be seen from the diagram, after the sliding grid extension preprocessing, the two subdomains (red part) realize the extension and nesting outward ( Figure 7 a) and inward ( Figure 7 b) respectively, forming two slip surfaces, which proves the effectiveness of the sliding grid generation method in the present application.

[0065] Figure 8 It shows the pressure wave transmission effect at a certain moment during the process of high-speed train passing through a tunnel. Through the sliding grid interpolation calculation, it can be observed that the dynamic transmission of pressure wave when the high-speed train runs in the tunnel. The head of the high-speed train is impacted by the airflow, resulting in a significant increase in pressure. According to the principle of action and reaction, this increase in pressure will generate a pressure wave in the airflow near the head, which will propagate to both sides of the tunnel. This phenomenon verifies the effectiveness of the sliding grid generation and interpolation method in the present application and the correctness of the physical model.

[0066] Figure 9Figure 1 is a diagram of a grid for aerodynamic simulation of a transonic compressor Darmstadt (hereinafter referred to as TCD). The compressor is composed of three rows of blades, in the order of rotor, stator and outlet guide vane in the direction of inlet. There is a rotor-stator interface between the first row of rotor and the second row of stator (see Figure 1). Figure 9 a). Figure 9 Figure 2 is a diagram of the effect of the slip grid generation for TCD simulation, in which the red line represents the original rotor-stator interface. After the extension of the slip grid, the two sub-domains achieve grid extension and nesting respectively, forming two slip surfaces, which proves the effectiveness of the slip grid generation method in the present application.

[0067] Figure 10 Figure 3 shows the transient results of the unsteady flow field of TCD predicted by the slip grid method, including pressure, streamwise velocity and entropy distribution. It can be observed that the slip grid method realizes high-fidelity mutual transmission of data on both sides of the slip surface, ensuring the continuity of the flow field near the slip surface, and proving the physical correctness of the developed slip grid generation and interpolation method.

[0068] Figure 11 Figure 4 shows the performance curves of TCD simulation obtained by the slip grid method and the steady mixing plane method, and compares the simulation results with the experimental data. From the performance curves, it can be seen that compared with the steady mixing plane method, the slip grid method significantly improves the prediction accuracy of the stall margin, and is closer to the experimental results at the stall point.

[0069] The present application also provides a rotor-stator interface slip 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, so that the one or more processors implement the rotor-stator interface slip grid generation and solving method of the first aspect.

[0073] The present application also provides a readable storage medium having a computer program stored thereon, which is executed by a processor to implement the rotor-stator interface slip grid generation and solving method of the first aspect.

[0074] The readable storage medium includes but is not limited to: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and various program code storage media.

[0075] The application further provides a computer program product, which comprises a computer program (also referred to as code or instructions) that, when executed, performs the dynamic boundary sliding mesh generation and solving method of the first aspect.

[0076] In the above embodiments, the implementation can be wholly or partially realized by software, hardware, firmware or any combination thereof. When realized by software, the implementation can be wholly or partially realized in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed by a computer, the computer instructions wholly or partially produce the processes or functions described in the embodiments of the present application. The computer can be a general purpose computer, a special purpose computer, a computer network or other programmable apparatus. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through a wired (for example, coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (for example, infrared, microwave, etc.) manner.

[0077] Those skilled in the art can understand that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

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

[0079] The application has been described in detail above with reference to specific embodiments and exemplary examples, but these descriptions cannot be understood as limiting the application. Those skilled in the art understand that various equivalent replacements, modifications or improvements can be made to the technical solutions and embodiments of the application without departing from the spirit and scope of the application, and these all fall within the scope of the application. The protection scope of the application is subject to the appended claims.

[0080] The contents not described in detail in the specification of the present application are the known technology of those skilled in the art.

Claims

1. A method for generating and solving a moving boundary interfacial slip grid, characterized in that, include: The simulation computation domain is divided into a static domain and a dynamic domain, which are attached at the interface between the static and dynamic domains. The grid points located at the interface between the static and dynamic domains are indented at equal intervals along the normal of the interface, and then extended along the normal of the interface to the first grid surface within the boundary of the other domain, generating a single-grid nested grid, the boundary of the static domain, and the boundary of the dynamic domain. The grid cells on the first layer of the grid surface within the static domain boundary are searched. The grid cells containing grid points on the moving domain boundary are found. The flow field data of the grid points on the moving domain boundary are obtained by interpolation using the flow field data of the grid cells. The grid cells on the first layer of the grid surface within the boundary of the moving domain are searched. Grid cells containing grid points on the boundary of the stationary domain are found. The flow field data of the grid points on the boundary of the stationary domain is obtained by interpolation using the flow field data of the grid cells.

2. The method of claim 1, wherein, In the step of equidistantly indenting the grid points of the static and dynamic domains located at the interface along the normal of the interface, the indentation distance is determined as follows: obtain all grid points of the static or dynamic domain at the interface and the grid edges connected to them within the domain; select the shortest edge among all the grid edges connected to the grid points; multiply the length of the shortest edge by the indentation coefficient to obtain the indentation distance of the static or dynamic domain.

3. The method of claim 2, wherein, The indentation coefficient is 1 / 3 to 1 / 2.

4. The method of claim 1, wherein, In the step of extending along the normal of the static-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 shrinkage distance of the static domain + the shrinkage distance of the dynamic domain.

5. The method of claim 1, wherein, The steps of obtaining flow field data of grid points on the boundary of the moving domain by interpolating the flow field data of grid cells, or obtaining flow field data of grid points on the boundary of the stationary domain by interpolating the flow field data of grid cells, are implemented in the following manner: The interpolation weight coefficients of the grid points are constructed as a function of the distance from the vertex of the grid cell to the grid point. The number of vertices in the grid cell 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. Multiply the flow field variable values ​​of each vertex of the grid cell containing the grid point by the interpolation weight coefficient corresponding to that vertex, and then sum them to obtain the flow field data of the grid point on the boundary.

6. The method of claim 1 to 5, wherein, It also includes: searching for grid cells on the first layer of grid surface within the boundary of the static domain or the boundary of the moving domain. If, after searching, there is no corresponding grid cell containing a grid point on the boundary of the static domain or the boundary of the moving domain within the first layer of grid surface within the paired domain boundary, then the grid cell closest to that grid point is used as the interpolation grid cell.

7. The method for generating and solving the sliding mesh at the dynamic-static interface according to claim 6, characterized in that, Also includes: When a grid point on the boundary of a stationary or moving domain has no corresponding grid cell on the first layer of the grid within the paired domain boundary, the flow field data of the grid point on the boundary is determined as follows: The interpolation weight coefficients are constructed as a function of the reciprocal of the distance from each vertex of the interpolation grid cell to the corresponding grid point. The number of vertices in the interpolation grid cell is equal to the number of interpolation weight coefficients for that grid point, and the sum of all interpolation weight coefficients for a grid point is 1. The flow field data of the grid points on the boundary are obtained by multiplying the flow field variable values ​​of each vertex of the interpolation grid cell by the interpolation weight coefficient corresponding to that vertex and then summing them.

8. A computer program product, characterized in that, The computer program product includes: a computer program that, when the computer program is run, executes the dynamic-static boundary sliding mesh generation and solution method as described in any one of claims 1 to 7.

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