A non-boundary-fitted mesh based solid wall boundary numerical simulation method and related device

Abstract

This invention relates to the field of computational fluid dynamics boundary treatment technology, and provides a method and related equipment for numerical simulation of solid-wall boundaries based on non-body meshes. The method includes: acquiring flow field values ​​of multiple mesh nodes near the solid-wall boundary of a non-body mesh, where the mesh nodes include a first layer of mesh nodes near the boundary, and the flow field values ​​include first flow field values ​​of the first layer of mesh nodes; reconstructing a first boundary numerical flux based on the flow field values ​​of the multiple mesh nodes; setting solid-wall boundary conditions and combining these conditions with the flow field values ​​of the multiple mesh nodes to correct the first flow field values ​​of the first layer of mesh nodes, thus obtaining second flow field values ​​for the first layer of mesh nodes; reconstructing a second boundary numerical flux based on the second flow field values; and obtaining a third boundary numerical flux based on the first and second boundary numerical fluxes; and using the third boundary numerical flux to simulate the solid-wall boundary of the non-body mesh. This method can simulate solid-wall boundaries of non-body meshes more effectively and accurately.

Description

Technical Field

[0001] This invention relates to the field of computational fluid dynamics boundary processing technology, and in particular to a method, apparatus, computer device, and computer-readable storage medium for numerical simulation of solid wall boundaries based on non-body meshes. Background Technology

[0002] In numerical simulations of complex flows, two approaches exist: body-fitted meshes and non-body-fitted meshes. Although most commercial software uses body-fitted meshes, non-body-fitted meshes are gaining increasing attention due to their relatively simpler mesh generation. A key issue with non-body-fitted meshes is the handling of solid wall boundary conditions. The most commonly used method is the immersion boundary method based on virtual points. This method sets virtual mesh nodes at or within the solid wall boundary, and the values ​​of these virtual mesh nodes are determined by both the boundary conditions and the governing equations. However, near boundaries with acute angles, thin plates, or similar shapes, the virtual mesh nodes may overlap with the actual mesh nodes. This makes it difficult to accurately simulate the boundary using virtual mesh nodes, or requires setting virtual mesh nodes according to different boundaries, which can lead to processing difficulties. Summary of the Invention

[0003] The purpose of this invention is to provide a numerical simulation method for solid wall boundaries based on non-body meshes, which can better simulate solid wall boundaries of non-body meshes without setting virtual mesh nodes, and avoids the problems of overlapping node settings and program processing difficulties caused by setting virtual mesh nodes to handle solid wall boundaries of non-body meshes in existing methods.

[0004] In a first aspect, embodiments of the present invention provide a numerical simulation method for solid wall boundaries based on non-body meshes, comprising:

[0005] S1. Obtain the flow field values ​​of multiple mesh nodes near the solid wall boundary of the non-body mesh, wherein the mesh nodes include the first layer of mesh nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of mesh nodes;

[0006] S2. The first boundary numerical flux is obtained by reconstructing the flow field values ​​based on the multiple grid nodes;

[0007] S3. Set solid wall boundary conditions, and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid nodes, so as to obtain the second flow field value of the first layer grid nodes;

[0008] S4. Based on the second flow field value, the second boundary numerical flux is reconstructed, and the third boundary numerical flux is obtained according to the first boundary numerical flux and the second boundary numerical flux. The third boundary numerical flux is used to simulate the solid wall boundary of the non-fitted mesh.

[0009] Furthermore, the process of reconstructing the flow field values ​​based on the plurality of grid nodes to obtain the first boundary numerical flux includes:

[0010] The first boundary numerical flux is obtained by eccentrically reconstructing the flow field values ​​of the multiple grid nodes.

[0011] Furthermore, the flow field values ​​of the grid nodes include the original flow field values. The step of setting solid wall boundary conditions and combining the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field values ​​of the first layer of grid nodes and obtain the second flow field values ​​of the first layer of grid nodes includes:

[0012] Determine the corresponding first layer mesh nodes on the solid wall boundary. Boundary nodes This makes the first layer of mesh nodes and the boundary node The direction of the line connecting the solid wall boundary is the outward normal direction;

[0013] Get the node closest to the boundary The original flow field values ​​of multiple grid nodes, including the first layer grid nodes. First flow field value ;

[0014] The boundary nodes are calculated using extrapolation based on the original flow field values ​​of the multiple grid nodes. The original flow field value and its first-order and second-order boundary normal derivatives , ;

[0015] The boundary node The original flow field value and first and second derivatives , Rotate to the outer normal of the solid wall boundary to obtain the boundary node. rotating flow field value and its first and second normal derivatives , ;

[0016] For the boundary node rotating flow field value and its first and second normal derivatives , Perform feature projection to obtain boundary nodes. Projected value of rotating flow field and its first and second normal derivatives , ;

[0017] The boundary nodes on the solid wall boundary The normal velocity is set to zero, in conjunction with the boundary node. Projected value of rotating flow field Adjust its rotating flow field value and the boundary nodes on the solid wall boundary. The pressure normal derivative is set according to the centripetal force formula, combined with the boundary nodes. The first normal derivative of the projection value of the rotating flow field Adjust the boundary nodes The first normal derivative of the rotating flow field value ;

[0018] Adjusted boundary nodes rotating flow field value Taylor series expansion along the outward normal of the solid wall boundary yields the first layer of mesh nodes. rotating flow field value ;

[0019] Through the first layer of grid nodes rotating flow field value The second flow field value of the first layer grid node is obtained.

[0020] Furthermore, the adjusted boundary nodes rotating flow field value Taylor series expansion along the outward normal of the solid wall boundary yields the first layer of mesh nodes. P rotating flow field value The steps include:

[0021] Calculate the first layer of mesh nodes and the boundary node Length between h ;

[0022] Based on the boundary nodes rotating flow field value The first-order normal derivative The second-order normal derivative and the length h Calculate the first layer of mesh nodes P rotating flow field value .

[0023] Furthermore, the first layer of mesh nodes P rotating flow field value Obtain the first layer of mesh nodes Second flow field value include:

[0024] The first layer of grid nodes P rotating flow field value Rotate the first layer of mesh nodes from the outer normal of the solid wall boundary to the original direction to obtain the corrected mesh nodes. Second flow field value .

[0025] Furthermore, the step of reconstructing the second boundary numerical flux based on the second flow field value and obtaining the third boundary numerical flux based on the first boundary numerical flux and the second boundary numerical flux includes:

[0026] Based on the first layer of grid nodes Corrected second flow field value The numerical flux of the second boundary is obtained by performing eccentric reconstruction.

[0027] Obtain the first layer of mesh nodes First flow field value before correction The feature matrix;

[0028] The third boundary numerical flux is calculated based on the first boundary numerical flux, the second boundary numerical flux, and the feature matrix.

[0029] Furthermore, the step of simulating the solid boundary of the non-fitted mesh using the third boundary numerical flux includes:

[0030] The flow field values ​​of the grid nodes are updated based on the third boundary numerical flux, and the solid boundary of the non-body mesh is simulated based on the updated grid node flow field values.

[0031] Secondly, embodiments of the present invention provide a numerical simulation device for solid-wall boundaries based on a non-body mesh, comprising:

[0032] The acquisition module is used to acquire the flow field values ​​of multiple mesh nodes near the solid wall boundary of the non-body mesh, wherein the mesh nodes include the first layer of mesh nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of mesh nodes.

[0033] The reconstruction module is used to reconstruct the first boundary numerical flux based on the flow field values ​​of the multiple grid nodes;

[0034] The correction module is used to set solid wall boundary conditions and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid nodes and obtain the second flow field value of the first layer grid nodes.

[0035] The simulation module is used to reconstruct the second boundary numerical flux based on the second flow field value, and to obtain the third boundary numerical flux based on the first boundary numerical flux and the second boundary numerical flux, and to simulate the solid wall boundary of the non-body mesh using the third boundary numerical flux.

[0036] Thirdly, embodiments of the present invention provide a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in the numerical simulation method for solid wall boundaries based on non-body meshes.

[0037] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the numerical simulation method for solid-wall boundaries based on non-body meshes.

[0038] Compared with the prior art, the embodiments of the present invention have the following advantages: The embodiments of the present invention reconstruct the first boundary numerical flux based on the flow field values ​​of multiple grid nodes on the solid wall boundary of a non-body mesh, and then combine the solid wall boundary conditions and the flow field values ​​of the grid nodes to correct the first flow field values ​​of the first layer of grid nodes near the boundary, thereby obtaining the corrected second flow field value; the second boundary numerical flux is reconstructed based on the corrected second flow field value, and the third boundary numerical flux is obtained according to the first boundary numerical flux and the second boundary numerical flux; finally, the third boundary numerical flux is used to simulate the solid wall boundary of the non-body mesh, thereby introducing boundary information into the flow field numerical simulation of the non-body mesh. This allows the present invention to simulate the solid wall boundary of the non-body mesh better and more accurately without setting virtual grid nodes, avoiding the problems of overlapping node settings and program processing difficulties caused by the need to set virtual grid nodes according to different boundaries in the prior art. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart of an embodiment of a numerical simulation method for solid wall boundaries based on a non-fitted mesh according to the present invention;

[0041] Figure 2 This is a schematic diagram of the structure of a one-dimensional mesh node near the solid wall boundary of a non-fitted mesh according to the present invention;

[0042] Figure 3 This is a schematic diagram of the structure of a two-dimensional mesh node near the non-fitted mesh solid wall boundary of the present invention;

[0043] Figure 4 This is a schematic diagram of an embodiment of a numerical simulation device for solid-wall boundaries based on a non-fitted mesh, according to the present invention.

[0044] Figure 5 This is a schematic diagram of the basic structure of a computer device according to the present invention.

[0045] exist Figure 4 In Chinese: 401. Acquisition module, 402. Reconstruction module, 403. Correction module, 404. Simulation module;

[0046] exist Figure 5 In Chinese: 500, computer equipment; 501, memory; 502, processor; 503, network interface. Detailed Implementation

[0047] The following description provides many different embodiments or examples for implementing various features of the invention. The elements and arrangements described in the specific examples below are only for concise expression of the invention and are merely examples, not intended to limit the invention.

[0048] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0049] like Figure 1 As shown, Figure 1 This is a flowchart of an embodiment of a numerical simulation method for solid wall boundaries based on non-body meshes according to the present invention. The above-mentioned numerical simulation method for solid wall boundaries based on non-body meshes includes the following steps:

[0050] S1. Obtain the flow field values ​​of multiple mesh nodes near the solid wall boundary of the non-body mesh, wherein the mesh nodes include the first layer of mesh nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of mesh nodes;

[0051] S2. The first boundary numerical flux is obtained by reconstructing the flow field values ​​based on the multiple grid nodes.

[0052] In this embodiment of the invention, complex fluid flow is simulated using a non-volume-fitted mesh, and the fluid flow governing equations (or flow field governing equations) can be used. In other words, the flow field values ​​at the grid nodes in a non-fitted mesh can be obtained by solving the flow field governing equations; where W Represents flow field variables, represent The derivative with respect to time, represent The derivative with respect to space.

[0053] If the fluid flows in a one-dimensional inviscid manner, then the flow field variables are... ,Right now W It is a vector composed of density, velocity, and pressure. Its characteristic matrix and If the fluid flows in a two-dimensional inviscid manner, then the flow field variables are... ,Right now W It is determined by density, Towards speed, A vector consisting of velocity and pressure.

[0054] The aforementioned mesh nodes consist of nodes located near the solid wall boundary of the non-body mesh. Specifically, in the case of one-dimensional inviscid flow, the mesh nodes near the solid wall boundary of the non-body mesh are as follows: Figure 2 As shown, where For grid nodes close to the boundary, For the first layer of grid nodes near the boundary, These are boundary nodes, not nodes within a non-fitted mesh. Therefore, the flow field value corresponding to the above mesh node is... , The first flow field value is given by the first layer of grid nodes. Then, the first boundary numerical flux is reconstructed from these flow field values. Specifically, the first boundary numerical flux can be obtained by eccentrically reconstructing the flow field values ​​of multiple grid nodes. In computational fluid dynamics, numerical flux usually refers to the flow field variable. W The inflow (outflow) at the unit interface (i.e., the spatial changes in density, velocity, and pressure in the flow field); furthermore, the numerical derivative can be calculated by dividing the difference in numerical flux at both ends of the unit interface by the grid spacing.

[0055] The process of obtaining numerical flux from the flow field values ​​at grid nodes is called reconstruction, such as in the second-order method:

[0056]

[0057] in, f The flow field value representing the grid node is... W , The numerical flux between grid nodes is represented as... In this invention, due to the nodes on the boundary... There is no flow field value, therefore the boundary nodes Nearby boundary numerical flux This formula cannot be used, but it can be done through grid nodes. , The flow field values ​​were obtained using an eccentric reconstruction method, as shown in the following calculation formula:

[0058]

[0059] If it is a two-dimensional inviscid flow, the mesh nodes near the solid wall boundary of the non-body mesh are as follows: Figure 3 As shown, the arc lines represent boundaries, solid nodes represent mesh nodes, and thickened mesh nodes represent other mesh nodes. For the first layer of mesh nodes closest to the boundary, the first flow field value of the first layer of mesh nodes is... ; For nodes on the boundary, in this invention, boundary nodes are... For nodes that do not belong to the non-fitted mesh, only boundary nodes are obtained. The normal velocity is 0. Near the boundary, first layer mesh node. exist Axial direction ( Figure 3 First boundary numerical flux in the horizontal direction use This indicates that, similarly, the eccentric reconstruction method described above is used to obtain the result, by selecting multiple grid nodes near the same grid line, such as... P , N Flow field values ​​of etc. , The numerical flux near the boundary nodes can be calculated by using the flow field values ​​of multiple grid nodes near the same grid line of the first-layer grid nodes near the boundary and reconstructing them eccentrically. This method yields a relatively accurate numerical flux of the first boundary.

[0060] S3. Set solid wall boundary conditions, and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid node, so as to obtain the second flow field value of the first layer grid node.

[0061] Furthermore, the flow field values ​​of the aforementioned multiple grid nodes include the original flow field values, and step S3 specifically includes:

[0062] Determine the corresponding first layer mesh nodes on the solid wall boundary. Boundary nodes This makes the first layer of mesh nodes and the boundary node The direction of the line connecting the solid wall boundary is the outward normal direction;

[0063] Get the node closest to the boundary The original flow field values ​​of multiple grid nodes, including the first layer grid nodes. First flow field value ;

[0064] The boundary nodes are calculated using extrapolation based on the original flow field values ​​of the multiple grid nodes. The original flow field value and its first-order and second-order boundary normal derivatives , ;

[0065] The boundary node The original flow field value and first and second derivatives Rotate to the outer normal of the solid wall boundary to obtain the boundary node. rotating flow field value and its normal first and second derivatives , .

[0066] For the boundary node rotating flow field value and its first normal derivative Perform feature projection to obtain boundary nodes. Projected value of rotating flow field and its first normal derivative ;

[0067] The boundary nodes on the solid wall boundary The normal velocity is set to zero, in conjunction with the boundary node. Projected value of rotating flow field Adjust its rotating flow field value and the boundary nodes on the solid wall boundary. The pressure normal derivative is set according to the centripetal force formula, combined with the boundary nodes. The first normal derivative of the projection value of the rotating flow field Adjust the boundary nodes The first normal derivative of the rotating flow field value ;

[0068] Adjusted boundary nodes rotating flow field value Taylor series expansion along the outward normal of the solid wall boundary yields the first layer of mesh nodes. rotating flow field value ;

[0069] Through the first layer of grid nodes rotating flow field value Obtain the first layer of mesh nodes P Second flow field value .

[0070] In this embodiment of the invention, for a two-dimensional inviscid flow field, the first layer of grid nodes near the aforementioned boundary... P corresponding boundary nodes From boundary geometric information and P The point positions are determined, so that the above first layer of grid nodes P With the above boundary nodes The direction of the line (in) See also Figure 3 () represents the outward normal of the aforementioned solid wall boundary, i.e., the boundary node. This is the intersection of the external normal and the solid wall boundary. Then, the mesh nodes are adjusted in conjunction with the solid wall boundary conditions. P The value is corrected. Specifically, the node closest to the boundary can be obtained. Multiple nearby grid nodes (including nodes) P and P The original flow field values ​​of the surrounding grid nodes. (including the first layer of grid nodes) First flow field value ),based on Boundary nodes are obtained using extrapolation. Flow field value The first and second normal derivatives are obtained, and the boundary nodes are obtained by rotating them to the outward normal direction of the solid wall boundary. Rotating flow field value and its first and second normal derivatives , And then , Perform feature projection to obtain the projected value. and its first and second normal derivatives , ;wherein the projection matrix L For grid nodes The original flow field value Rotate to the outer normal of the boundary And perform feature projection on the left feature matrix, for example, the rotation variable for any point in the above two-dimensional flow field. ,in , These are the normal and tangential velocities, respectively. Let be the speed of sound, then its corresponding left and right eigenma matrices are respectively , ,and Let be the identity matrix; denote the boundary nodes. rotating flow field value Its rotational projection value Then, combining the boundary conditions and the projection value Can be Adjustments and corrections are made, specifically calculated using the following system of equations:

[0071]

[0072] For convenience, the equations in the system and All omitted (The same applies below), the first line of the equation system is based on the above solid wall boundary conditions, namely the normal velocity of the boundary wall. Get 0 It is the left characteristic matrix L The i Line number j The elements of the column, then the adjusted... A Taylor series expansion along the outward normal of the aforementioned solid wall boundary yields the first layer of mesh nodes. rotating flow field value .

[0073] Furthermore, in the adjusted Before performing a Taylor series expansion along the outward normal of the solid wall boundary, calculate the aforementioned boundary nodes. Rotating flow field value First-order normal derivative Then, based on the above rotating flow field values... First-order and second-order normal derivatives , Further refine the first-layer mesh nodes rotating flow field value Specifically, the aforementioned boundary nodes First normal derivative of rotating flow field This can be obtained by solving the following system of equations.

[0074]

[0075] The first line of the equations consists of the formula for centripetal force in rotational motion. (The pressure gradient equals the centripetal force) is obtained, where For boundary wall The radius of curvature of the point. The right-hand term in the last three lines is... Point rotation projection value The last three elements.

[0076] The first layer of mesh nodes can then be obtained by correcting the process using Taylor series expansion. rotating flow field value :

[0077]

[0078] in, h For grid nodes and boundary nodes The length between them. This is determined by the boundary nodes. The extrapolated flow field values ​​and their first and second derivatives are rotated to better integrate with boundary conditions. After adjustment via eigenprojection, the first flow field values ​​of the first-layer mesh nodes are more accurately corrected, resulting in more precise corrections to the first-layer mesh node values. The second flow field value, specifically the first layer of mesh nodes. P rotating flow field value Rotate the first layer of mesh nodes from the outer normal of the solid wall boundary to the original direction to obtain the modified mesh nodes described above. Second flow field value .

[0079] S4. Based on the second flow field value, the second boundary numerical flux is reconstructed, and the third boundary numerical flux is obtained according to the first boundary numerical flux and the second boundary numerical flux. The third boundary numerical flux is used to simulate the solid wall boundary of the non-fitted mesh.

[0080] Furthermore, step S4 specifically includes:

[0081] Based on the first layer of grid nodes Corrected second flow field value The numerical flux of the second boundary is obtained by performing eccentric reconstruction.

[0082] Obtain the first layer of mesh nodes First flow field value before correction The feature matrix;

[0083] The third boundary numerical flux is calculated based on the first boundary numerical flux, the second boundary numerical flux, and the feature matrix.

[0084] In this embodiment of the invention, the first layer of mesh nodes is first... P rotating flow field value The mesh nodes are obtained by rotating the outer normal of the solid wall boundary back to the original direction. Corrected second flow field value Then based on the first layer of mesh nodes Corrected second flow field value and the flow field values ​​of other grid nodes on the same nearby grid line, such as Figure 3 Grid nodes in N, M The numerical flux of the second boundary is obtained by performing eccentric reconstruction. Specifically, it can be reconstructed using the following second-order method:

[0085] Alternatively, the following third-order reconstruction can be used:

[0086]

[0087] Further obtain the above-mentioned first-layer mesh nodes Flow field values ​​before correction The left characteristic matrix L The first line Right characteristic matrix R The first column It should be noted that the grid nodes The original flow field value before correction (i.e., the original flow field value). The eigenma matrix of the feature projection is the same as the eigenma matrix of the feature projection after rotation to the out-of-bounds normal; that is, rotation does not affect the eigenma matrix. 、 From the above feature matrix L and R The value is taken from the middle; then the numerical flux of the third boundary mentioned above. The first boundary numerical flux can be obtained through the above. Second boundary numerical flux and characteristic matrix 、 The calculation yielded:

[0088]

[0089] Furthermore, the aforementioned third boundary numerical flux can be utilized. Simulate a solid-wall boundary with a non-fitted mesh, specifically based on the numerical flux of the third boundary. The flow field values ​​of the mesh nodes are updated, and the solid-wall boundary of the non-body mesh is simulated based on the updated flow field values ​​of the mesh nodes. Through these steps, boundary information can be incorporated into the numerical simulation of the flow field of the non-body mesh. The flow field values ​​at the boundary points and their first and second normal derivatives are used to correct the mesh nodes simulating the solid-wall boundary of the non-body mesh, improving the accuracy of the mesh nodes. This allows the present invention to better simulate the solid-wall boundary of the non-body mesh without setting virtual mesh nodes.

[0090] In summary, this invention reconstructs the first boundary numerical flux based on the flow field values ​​of multiple grid nodes at the solid wall boundary of a non-body mesh. Then, it combines the solid wall boundary conditions and the flow field values ​​of the grid nodes to correct the first flow field values ​​of the first layer of grid nodes near the boundary, resulting in a corrected second flow field value. Based on the corrected second flow field value, a second boundary numerical flux is reconstructed, and a third boundary numerical flux is obtained based on the first and second boundary numerical fluxes. Finally, the third boundary numerical flux is used to simulate the solid wall boundary of the non-body mesh, thereby introducing boundary information into the numerical simulation of the non-body mesh. This allows the invention to better and more accurately simulate the solid wall boundary of the non-body mesh without setting virtual grid nodes, avoiding the problems of overlapping node settings and program processing difficulties caused by setting virtual grid nodes according to different boundaries in the prior art.

[0091] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, nor are they necessarily executed on the same device or machine. Instead, they can be executed at different times and in different places, and their execution order is not necessarily sequential. Instead, they can be executed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0092] Secondly, such as Figure 4 As shown, Figure 4 This is a schematic diagram of an embodiment of a numerical simulation device for solid-wall boundaries based on a non-body mesh, according to the present invention. The embodiment of the present invention provides a numerical simulation device for solid-wall boundaries based on a non-body mesh, comprising:

[0093] The acquisition module 401 is used to acquire the flow field values ​​of multiple grid nodes near the solid wall boundary of the non-body mesh, wherein the grid nodes include a first layer of grid nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of grid nodes.

[0094] The reconstruction module 402 is used to reconstruct the first boundary numerical flux based on the flow field values ​​of the multiple grid nodes;

[0095] The correction module 403 is used to set solid wall boundary conditions and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid node and obtain the second flow field value of the first layer grid node.

[0096] The simulation module 404 is used to reconstruct the second boundary numerical flux based on the second flow field value, and to obtain the third boundary numerical flux based on the first boundary numerical flux and the second boundary numerical flux, and to simulate the solid wall boundary of the non-body mesh using the third boundary numerical flux.

[0097] The numerical simulation device for solid wall boundaries based on non-body meshes provided in this invention can achieve... Figure 1 To avoid repetition, the various implementation methods and corresponding beneficial effects in the method embodiments will not be described again here.

[0098] Thirdly, embodiments of the present invention provide a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in the numerical simulation method for solid wall boundaries based on non-body meshes.

[0099] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the numerical simulation method for solid-wall boundaries based on non-body meshes.

[0100] For details, please see Figure 5 , Figure 5 This is a schematic diagram of the basic structure of a computer device according to an embodiment of the present invention. The computer device 500 includes a memory 501, a processor 502, and a network interface 503 that are interconnected via a system bus. It should be noted that only the computer device 500 with components 501-503 is shown in the figure; however, it should be understood that it is not required to implement all the components shown, and more or fewer components can be implemented instead. Those skilled in the art will understand that the computer device described here is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0101] The computer device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device can interact with the user via a keyboard, mouse, remote control, touchpad, or voice control.

[0102] The memory 501 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 501 may be an internal storage unit of the computer device 500, such as the hard disk or memory of the computer device 500. In other embodiments, the memory 501 may also be an external storage device of the computer device 500, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. Of course, the memory 501 may also include both internal storage units and external storage devices of the computer device 500. In this embodiment, the memory 501 is typically used to store the operating system and various application software installed on the computer device 500, such as program code for a numerical simulation method of solid-wall boundaries based on non-volume meshes. Furthermore, the memory 501 can also be used to temporarily store various types of data that have been output or will be output.

[0103] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A numerical simulation method for solid wall boundaries based on non-fitted meshes, characterized in that, include: S1. Obtain the flow field values ​​of multiple mesh nodes near the solid wall boundary of the non-body mesh, wherein the mesh nodes include the first layer of mesh nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of mesh nodes. S2. The first boundary numerical flux is obtained by reconstructing the flow field values ​​based on the multiple grid nodes; S3. Set solid wall boundary conditions, and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid nodes, thereby obtaining the second flow field value of the first layer grid nodes; S4. Based on the second flow field value, the second boundary numerical flux is reconstructed, and the third boundary numerical flux is obtained according to the first boundary numerical flux and the second boundary numerical flux. The third boundary numerical flux is used to simulate the solid wall boundary of the non-fitted mesh. The first boundary numerical flux obtained by reconstructing the flow field values ​​based on the multiple grid nodes includes: The first boundary numerical flux is obtained by eccentrically reconstructing the flow field values ​​of the multiple grid nodes; The flow field values ​​of the grid nodes include the original flow field values. The step of setting solid wall boundary conditions and combining the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field values ​​of the first layer of grid nodes and obtain the second flow field values ​​of the first layer of grid nodes includes: Determine the corresponding first layer mesh nodes on the solid wall boundary. Boundary nodes This makes the first layer of mesh nodes and the boundary node The direction of the line connecting the solid wall boundary is the outward normal direction; Get the node closest to the boundary The original flow field values ​​of multiple grid nodes, including the first layer grid nodes. First flow field value ; The boundary nodes are calculated using extrapolation based on the original flow field values ​​of the multiple grid nodes. The original flow field value and its first-order and second-order boundary normal derivatives ; The boundary node The original flow field value and first and second derivatives Rotate to the outer normal of the solid wall boundary to obtain the boundary node. rotating flow field value and its first and second normal derivatives ; For the boundary node rotating flow field value and its first and second normal derivatives Perform feature projection to obtain boundary nodes. Projected value of rotating flow field and its first and second normal derivatives , ; The boundary nodes on the solid wall boundary The normal velocity is set to zero, in conjunction with the boundary node. Projected value of rotating flow field Adjust its rotating flow field value and the boundary nodes on the solid wall boundary. The pressure normal derivative is set according to the centripetal force formula, combined with the boundary nodes. The first normal derivative of the projection value of the rotating flow field Adjust the boundary nodes The first normal derivative of the rotating flow field value ; Adjusted boundary nodes rotating flow field value Taylor series expansion along the outward normal of the solid wall boundary yields the first layer of mesh nodes. rotating flow field value ; Through the first layer of grid nodes rotating flow field value Obtain the first layer of mesh nodes Second flow field value ; The adjusted boundary nodes rotating flow field value A Taylor series expansion along the outward normal of the solid wall boundary yields the rotating flow field values ​​at the first layer mesh node P. The steps include: Calculate the first layer of mesh nodes and the boundary node The length h between them; Based on the boundary nodes rotating flow field value The first-order normal derivative The second-order normal derivative The rotational flow field value of the first layer grid node P is calculated using the length h. ; The rotating flow field value passing through the first layer of grid nodes P Obtain the first layer of mesh nodes Second flow field value include: The rotating flow field value of the first layer grid node P Rotate the first layer of mesh nodes from the outer normal of the solid wall boundary to the original direction to obtain the corrected mesh nodes. Second flow field value .

2. The method as described in claim 1, characterized in that, The process of reconstructing the second boundary numerical flux based on the second flow field value and obtaining the third boundary numerical flux based on the first boundary numerical flux and the second boundary numerical flux includes: Based on the first layer of grid nodes Corrected second flow field value The numerical flux of the second boundary is obtained by performing eccentric reconstruction. Obtain the first layer of mesh nodes First flow field value before correction The feature matrix; The third boundary numerical flux is calculated based on the first boundary numerical flux, the second boundary numerical flux, and the feature matrix.

3. The method as described in claim 1, characterized in that, The step of simulating the solid boundary of the non-fitted mesh using the third boundary numerical flux includes: The flow field values ​​of the grid nodes are updated based on the third boundary numerical flux, and the solid boundary of the non-body mesh is simulated based on the updated grid node flow field values.

4. A numerical simulation device for solid-wall boundaries based on non-body meshes, characterized in that, include: The acquisition module is used to acquire the flow field values ​​of multiple mesh nodes near the solid wall boundary of the non-body mesh, wherein the mesh nodes include a first layer of mesh nodes near the boundary, and the flow field values ​​include the first flow field values ​​of the first layer of mesh nodes. The reconstruction module is used to reconstruct the first boundary numerical flux based on the flow field values ​​of the multiple grid nodes; The correction module is used to set solid wall boundary conditions and combine the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field value of the first layer grid nodes and obtain the second flow field value of the first layer grid nodes. The simulation module is used to reconstruct the second boundary numerical flux based on the second flow field value, and to obtain the third boundary numerical flux based on the first boundary numerical flux and the second boundary numerical flux, and to simulate the solid wall boundary of the non-fitted mesh using the third boundary numerical flux. The first boundary numerical flux obtained by reconstructing the flow field values ​​based on the multiple grid nodes includes: The first boundary numerical flux is obtained by eccentrically reconstructing the flow field values ​​of the multiple grid nodes; The flow field values ​​of the grid nodes include the original flow field values. The step of setting solid wall boundary conditions and combining the solid wall boundary conditions with the flow field values ​​of the multiple grid nodes to correct the first flow field values ​​of the first layer of grid nodes and obtain the second flow field values ​​of the first layer of grid nodes includes: Determine the corresponding first layer mesh nodes on the solid wall boundary. Boundary nodes This makes the first layer of mesh nodes and the boundary node The direction of the line connecting the solid wall boundary is the outward normal direction; Get the node closest to the boundary The original flow field values ​​of multiple grid nodes, including the first layer grid nodes. First flow field value ; The boundary nodes are calculated using extrapolation based on the original flow field values ​​of the multiple grid nodes. The original flow field value and its first-order and second-order boundary normal derivatives ; The boundary node The original flow field value and first and second derivatives Rotate to the outer normal of the solid wall boundary to obtain the boundary node. rotating flow field value and its first and second normal derivatives ; For the boundary node rotating flow field value and its first and second normal derivatives Perform feature projection to obtain boundary nodes. Projected value of rotating flow field and its first and second normal derivatives , ; The boundary nodes on the solid wall boundary The normal velocity is set to zero, in conjunction with the boundary node. Projected value of rotating flow field Adjust its rotating flow field value and the boundary nodes on the solid wall boundary. The pressure normal derivative is set according to the centripetal force formula, combined with the boundary nodes. The first normal derivative of the projection value of the rotating flow field Adjust the boundary nodes The first normal derivative of the rotating flow field value ; Adjusted boundary nodes rotating flow field value Taylor series expansion along the outward normal of the solid wall boundary yields the first layer of mesh nodes. rotating flow field value ; Through the first layer of grid nodes rotating flow field value Obtain the first layer of mesh nodes Second flow field value ; The adjusted boundary nodes rotating flow field value A Taylor series expansion along the outward normal of the solid wall boundary yields the rotating flow field values ​​at the first layer mesh node P. The steps include: Calculate the first layer of mesh nodes and the boundary node The length h between them; Based on the boundary nodes rotating flow field value The first-order normal derivative The second-order normal derivative The rotational flow field value of the first layer grid node P is calculated using the length h. ; The rotating flow field value passing through the first layer of grid nodes P Obtain the first layer of mesh nodes Second flow field value include: The rotating flow field value of the first layer grid node P Rotate the first layer of mesh nodes from the outer normal of the solid wall boundary to the original direction to obtain the corrected mesh nodes. Second flow field value .

5. A computer device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in the numerical simulation method for solid wall boundaries based on non-body meshes as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps in the numerical simulation method for solid wall boundaries based on non-body meshes as described in any one of claims 1-3.

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