Construction method of remote reconstruction algorithm for TVD format extension

What is AI technical title?
AI technical title is built by Patsnap AI team. It summarizes the technical point description of the patent document.
By considering the distance from the plane center to the auxiliary headwind node in the unstructured grid, and using more reasonable position prediction and interpolation methods, the inaccuracy and inefficiency of the position and value prediction of far headwind nodes in the existing technology is solved. Achieve high-precision and high-efficiency TVD format expansion.

CN118468754BActive Publication Date: 2025-02-25CHONGQING UNIV

View PDF 0 Cites 0 Cited by

Patent Information

Application Number: CN202410634605.X
Authority / Receiving Office: CN · China
Patent Type: Patents(China)
Current Assignee / Owner
Filing Date: 2024-05-20
Publication Date: 2025-02-25
Estimated Expiration: 2044-05-20

AI Technical Summary

Technical Problem

In unstructured mesh, existing remote reconstruction algorithms are difficult to accurately predict the location and values of far-front wind nodes, and are less efficient, introducing a complex vector calculation process.

Method used

By considering the distance from the surface center to the auxiliary headwind node, a more reasonable far headwind node position prediction method is adopted, and by interpolation methods containing more headwind information and a method that considers the physical value difference between the actual point and the auxiliary point, TVD is improved The format accuracy avoids complex vector calculations.

Benefits of technology

A more reasonable prediction of far-front wind node position is achieved, the accuracy and computing efficiency of TVD format is improved, and it is suitable for numerical simulation of convective-dominated problems.

✦ Generated by Eureka AI based on patent content.

Smart Images

Figure CN118468754B_ABST

Patent Text Reader

Abstract

The present invention relates to the technical field of fluid dynamics engineering, and in particular to a construction method of a far-end reconstruction algorithm for TVD format expansion. In an unstructured grid, an upwind point and a downwind point are projected onto a normal line passing through the midpoint of an adjacent interface to obtain an auxiliary node; a point on the extension line of the auxiliary node connection line whose distance to the auxiliary upwind node is the same as the distance from the auxiliary upwind node to the midpoint of the adjacent interface is taken as a far upwind node; all grid cells around the vertex closest to the far upwind node in the upwind grid cell are taken as auxiliary far upwind grid cells, and the far upwind node is interpolated with the inverse distance reciprocal including a gradient by means of all auxiliary far upwind grid cells to obtain an interpolation result; and the value of the far upwind node is obtained by correcting the interpolation result for boundedness. Compared with the existing algorithms, the new method has better comprehensive performance in terms of accuracy and efficiency, and can be used for numerical simulation of convection-dominated problems.

Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of fluid dynamics engineering, and in particular to a construction method of a remote reconstruction algorithm for TVD format expansion and its application. Background Art

[0002] In the prior art, in the reconstruction process of the far-end reconstruction algorithm (r-factor algorithm) used to implement the TVD format expansion, the position and variable value of the upwind node U need to be determined. In a structured grid, the far upwind node U is determined, and the r factor can be directly obtained. However, when extended to an unstructured grid, due to differences in grid shape and distribution, the position and value of the far upwind node U are no longer clear. In order to solve this problem, researchers have proposed a variety of reconstruction techniques for far upwind node values (i.e., r-factor algorithms), mainly including extrapolation reconstruction algorithms and interpolation reconstruction algorithms. However, the existing algorithms have unreasonable prediction problems for the positions of far upwind nodes, and usually introduce complex vector calculation processes, which makes the efficiency and accuracy of the existing algorithms low. Summary of the invention

[0003] In view of this, the present invention provides a construction method of a far-end reconstruction algorithm for TVD format expansion, which takes into account the distance from the center of the surface to the auxiliary upwind node, and realizes a more reasonable prediction of the far upwind node position. In addition, the accuracy of the TVD format is improved by an interpolation method that includes more upwind information and a method that considers the physical value difference between the actual point and the auxiliary point; in addition, the introduction of a complex vector calculation process is avoided, thereby improving efficiency.

[0004] The present invention discloses a method for constructing a remote reconstruction algorithm for TVD format extension, which is used to implement the construction of the remote reconstruction algorithm for TVD format extension in an unstructured grid, and includes the following steps:

[0005] Step s1, in an unstructured grid, draw a normal line through the midpoint of the adjacent interface of the upwind unit and the downwind unit, project the upwind point and the downwind point onto the normal line, and obtain an auxiliary upwind node and an auxiliary downwind node respectively;

[0006] Step s2, taking an extension point on the extension line of the line connecting the auxiliary upwind node and the auxiliary downwind node, so that the distance from the extension point to the auxiliary upwind node is the same as the distance from the auxiliary upwind node to the midpoint of the adjacent interface, and determining the extension point as the far upwind node;

[0007] Step s3, selecting the vertex closest to the determined far upwind node in the upwind unit;

[0008] Step s4, determining all units around the vertex as auxiliary far upwind units;

[0009] Step s5, performing inverse distance reciprocal interpolation considering the gradient on the determined far upwind node with the aid of all the determined auxiliary far upwind units, so as to obtain the value of the far upwind node.

[0010] In the construction method of the remote reconstruction algorithm for TVD format expansion disclosed in the first aspect of the present invention, after step s1 and before step s2, step s1-1 is also included to correct the auxiliary upwind nodes and auxiliary downwind nodes obtained in step s1.

[0011] In the construction method of the remote reconstruction algorithm for TVD format extension disclosed in the first aspect of the present invention, in step s1-1, the obtained auxiliary upwind node is corrected by means of the following formula (1):

[0012]

[0013] in Auxiliary upwind node C r The variable value of The vector from the upwind node to the auxiliary upwind node.

[0014] In the construction method of the far-end reconstruction algorithm for TVD format extension disclosed in the first aspect of the present invention, in step s5, the determined far upwind node is subjected to inverse distance reciprocal interpolation considering the gradient based on the following formula (2):

[0015]

[0016] where φ i is the value of the auxiliary far upwind node, d iU A vector that assists the far upwind node to point to the far upwind node. To assist the gradient of the far upwind unit, It is the mth power of the inverse of the distance from the auxiliary far upwind node to the far upwind node.

[0017] In the construction method of the remote reconstruction algorithm for TVD format expansion disclosed in the first aspect of the present invention, the value of m is 0.5.

[0018] In the construction method of the far-end reconstruction algorithm for TVD format expansion disclosed in the first aspect of the present invention, after step s5, step s6 is also included, which limits the interpolation result obtained in step s5 by means of the local extreme values of the adjacent units of the upwind unit.

[0019] In the construction method of the remote reconstruction algorithm for TVD format extension disclosed in the first aspect of the present invention, in step s6, it is performed based on the following formula (3):

[0020]

[0021] Among them, φ U is the far upwind node value obtained after boundedness correction, are the minimum and maximum values of the variables in all adjacent units of the upwind unit, respectively.

[0022] During the construction process of the far-end reconstruction algorithm (r-factor algorithm) of the present invention, the variable value at the far upwind node is obtained by interpolation, which takes into account more upwind direction information relative to the Bruner or Darwi sh extrapolation algorithm, and is therefore more in line with physical laws. In addition, the auxiliary far upwind units called by this construction process are the surrounding units of the upwind unit vertex, avoiding the influence of irrelevant units that are too far away. More importantly, the determined vertex is the vertex closest to the far upwind node, thereby ensuring the maximization of the upwind influence. It should also be emphasized that the implementation of the new algorithm is relatively simple and convenient, and does not involve complex vector calculations, so higher computing efficiency can be achieved.

[0023] The second aspect of the present invention also discloses the application of the construction method of the above-mentioned remote reconstruction algorithm for TVD format expansion, which is applied in numerical simulation of solving convection-dominated problems.

[0024] The third aspect of the present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the computer program, it can implement the construction method of the remote reconstruction algorithm for TVD format expansion disclosed in the first aspect of the present invention.

[0025] Beneficial effects: In the method of the present invention, the distance from the center of the surface to the auxiliary upwind node is taken into account, and a more reasonable prediction of the far upwind node position is achieved. Moreover, the accuracy of the TVD format is improved by an interpolation method that includes more upwind information and a method that considers the difference in physical values between the actual point and the auxiliary point; in addition, the introduction of a complex vector calculation process is avoided, thereby improving efficiency. Compared with existing algorithms, the new method has better comprehensive performance in terms of accuracy and efficiency, and can be used for numerical simulation of convection-dominated problems.

[0026] The following is a description of the embodiments and reference numerals shown in the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the calculation template for three adjacent grid points.

[0028] Figure 2 A flow chart of the method steps of the present invention is shown.

[0029] Figure 3A schematic diagram of the far-end reconstruction algorithm (r-factor algorithm) SNEW1D of the present invention is shown. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other without conflict.

[0031] Numerical simulation of convection-dominated problems is one of the important tasks in aerodynamics. The numerical simulation method for solving convection-dominated problems based on the TVD format includes the following steps:

[0032] Construct the one-dimensional convection equation:

[0033] φ t +(aφ) x =0 (4);

[0034] Where φ=φ(x,t) represents the transport variable, a represents the transport speed, and it is assumed that a is a positive constant.

[0035] Specifically, three adjacent cells can be used as calculation templates, where U, C, and D are the far upwind point, the upwind point, and the downwind point, respectively. Figure 1 shown.

[0036] Then, the space is discretized into units of uniform length I i =[x i-1 / 2 ,x i+1 / 2 ], i is the coordinate number, unit length

[0037] Then, the semi-discrete form of equation (10) can be written as:

[0038]

[0039] in, is the flux at two adjacent interfaces. Δx=x f -x e ,Right now Represents the difference between the x coordinates of two adjacent faces. f It is expressed by Hou as:

[0040]

[0041]

[0042] in d Cf and d fD are the distances from the center of the adjacent interface to C and D, respectively. UC Indicates the distance from point U to point C, d CD Represents the distance from point C to point D.

[0043] The flux limiter ψ(r) in equation (6) is a function of the r factor, and different function forms represent different numerical formats. The r factor in equation (7) represents the ratio between the headwind and tailwind gradients.

[0044] As shown in the r factor of formula (7), when the TVD format is applied in numerical simulation, the position and variable value of the far upwind node U need to be determined. In structured grids, the far upwind node U is determined, and the r factor can be directly obtained. However, when extended to unstructured grids, due to differences in grid shape and distribution, the position and value of the far upwind node U are no longer clear. In order to solve this problem, researchers have proposed a variety of reconstruction techniques for far upwind node values (i.e., r-factor algorithms), mainly including interpolation reconstruction algorithms and interpolation reconstruction algorithms. This paper proposes a new r-factor algorithm based on interpolation reconstruction to improve the accuracy and efficiency of the TVD format when applied in unstructured grids. The specific steps are as follows:

[0045] Step s1: In the unstructured grid, a normal line is drawn through the midpoint of the adjacent interface f between the upwind unit and the downwind unit, and the upwind point C and the downwind point D are projected onto the normal line to obtain the auxiliary upwind nodes C and D, respectively. r and auxiliary downwind node D r ;

[0046] Step s2, at the auxiliary upwind node C r and auxiliary downwind node D r Take the extension point U on the extension line of the connecting line, and make the extension point U reach the auxiliary upwind node C r Distance With auxiliary upwind node C r The distance to the midpoint of the adjacent interface f The same, that is The extension point is determined as the far upwind node U(new);

[0047] Step s3, selecting the vertex a closest to the determined far upwind node U(new) in the upwind unit;

[0048] Step s4, all units around the vertex a are determined as auxiliary far upwind units i, and the auxiliary far upwind nodes therein are determined respectively, such as Figure 3A, B, E, I, G points;

[0049] Step s5, using all the determined auxiliary far upwind units i, the determined far upwind node U(new) is interpolated with an inverse distance reciprocal taking into account the gradient, so as to obtain the value φ of the far upwind node U .

[0050] After step s1 and before step s2, step s1-1 is further included, in which the auxiliary upwind node C obtained in step s1 is r The correction is performed by using the following formula (1) to correct the auxiliary upwind node C r To make corrections:

[0051]

[0052] in Auxiliary upwind node C r value, Point upwind point C to auxiliary upwind node C r Vector.

[0053] In step s5, the determined far upwind node is interpolated with inverse distance considering the gradient based on the following formula (2):

[0054]

[0055] where φ i is the value of the auxiliary far upwind node, d iU A vector that assists the far upwind node to point to the far upwind node. To assist the gradient of the far upwind unit, It is the mth power of the inverse of the distance from the auxiliary far upwind node to the far upwind node.

[0056] In a preferred embodiment, the value of m is 0.5.

[0057] In the case of excessively large gradients, the inverse distance weighted interpolation method of the gradient will lead to the destruction of the boundedness of the format, resulting in non-physical overshoot and other problems. To solve this problem, after step s5, step s6 is further included, which limits the interpolation result obtained in step s5 by means of the local extreme values of the neighboring units of the upwind unit, which is specifically based on the following formula (3):

[0058]

[0059] Among them, φ U is the interpolated far upwind node value, are the minimum and maximum values of the variables in all adjacent units of the upwind unit, respectively.

[0060] During the construction process of the far-end reconstruction algorithm (r-factor algorithm) of the present invention, the variable value at the far upwind node is obtained by interpolation, which takes into account more upwind direction information relative to the Bruner or Darwi sh extrapolation algorithm, and is therefore more in line with physical laws. In addition, the auxiliary far upwind units called by this construction process are the surrounding units of the upwind unit vertex, avoiding the influence of irrelevant units that are too far away. More importantly, the determined vertex is the vertex closest to the far upwind node, thereby ensuring the maximization of the upwind influence. It should also be emphasized that the implementation of the new algorithm is relatively simple and convenient, and does not involve complex vector calculations, so higher computing efficiency can be achieved.

[0061] The second aspect of the present invention also discloses the application of the construction method of the above-mentioned remote reconstruction algorithm for TVD format expansion, which is applied in numerical simulation of solving convection-dominated problems.

[0062] The third aspect of the present invention also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the computer program, it can implement the construction method of the remote reconstruction algorithm for TVD format expansion disclosed in the first aspect of the present invention.

[0063] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0064] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0065] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein, for example. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for constructing a remote reconstruction algorithm for TVD format extension, which is used to implement the construction of a remote reconstruction algorithm for TVD format extension in an unstructured grid, characterized in that: The following steps are involved: Step s1, in an unstructured grid, draw a normal line through the midpoint of the adjacent interface of the upwind unit and the downwind unit, project the upwind point and the downwind point onto the normal line, and obtain corresponding auxiliary upwind nodes and auxiliary downwind nodes respectively; Step s2, taking an extension point on the extension line of the line connecting the auxiliary upwind node and the auxiliary downwind node, so that the distance from the extension point to the auxiliary upwind node is the same as the distance from the auxiliary upwind node to the midpoint of the adjacent interface, and determining the extension point as the far upwind node; Step s3, selecting the vertex closest to the determined far upwind node in the upwind unit; Step s4, determining all units around the vertex as auxiliary far upwind units; Step s5, performing inverse distance reciprocal interpolation considering the gradient on the determined far upwind node with the aid of all the determined auxiliary far upwind units, so as to obtain the value of the far upwind node; In step s5, the determined far upwind node is interpolated with inverse distance considering the gradient based on the following formula (2): where φ U* is the interpolated far upwind node value, φ i is the value of the auxiliary far upwind node, d iU A vector that assists the far upwind node to point to the far upwind node. To assist the gradient of the far upwind unit, The mth power of the reciprocal of the distance from the auxiliary far upwind node to the far upwind node, where m is 0.5; After step s5, the method further includes step s6, in which the interpolation result obtained in step s5 is limited by using the local extreme values of the neighboring units of the upwind unit; in step s6, the following formula (3) is used: where φ U is the far upwind node value obtained after boundedness correction, are the minimum and maximum values of the variables in all adjacent units of the upwind unit, respectively.

2. The method for constructing a remote reconstruction algorithm for TVD format extension according to claim 1, characterized in that: After step s1 and before step s2, step s1-1 is further included to correct the auxiliary upwind node and the auxiliary downwind node obtained in step s1.

3. The method for constructing a remote reconstruction algorithm for TVD format extension according to claim 2, characterized in that: In step s1-1, the obtained auxiliary upwind node is corrected by means of the following formula (1): in Auxiliary upwind node C r value, The vector from the upwind point to the auxiliary upwind node.

4. An application of the method for constructing a remote reconstruction algorithm for TVD format expansion according to any one of claims 1 to 3, characterized in that: The construction method of the remote reconstruction algorithm for TVD format expansion is applied in numerical simulations for solving convection-dominated problems.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, it is able to implement the method for constructing a remote reconstruction algorithm for TVD format expansion according to any one of claims 1-3.