CN112560247A - Similar outline structure grid automatic generation method based on reference grid - Google Patents

Similar outline structure grid automatic generation method based on reference grid Download PDF

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CN112560247A
CN112560247A CN202011429287.1A CN202011429287A CN112560247A CN 112560247 A CN112560247 A CN 112560247A CN 202011429287 A CN202011429287 A CN 202011429287A CN 112560247 A CN112560247 A CN 112560247A
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王军旗
许亮
杨武兵
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China Academy of Aerospace Aerodynamics CAAA
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Abstract

The invention discloses a method for automatically generating a similar outline structure grid based on a reference grid, which comprises the following steps: constructing a corresponding reference structure grid based on the selected reference profile; acquiring a characteristic scale of a reference appearance; acquiring the grid number of the grid of the reference structure, the number of the distribution points of each grid line and the distance between the two ends of each grid line; acquiring a characteristic scale of a target shape, wherein the target shape is a type of shape of a corresponding target structure grid to be constructed which is judged to be similar to a reference shape; the method comprises the steps of giving an expected grid number of a target structure grid and calculating out-of-domain boundary parameters; determining the number of the distribution points and the distance between two ends of each grid line of the target structure grid according to the obtained quantity and the given quantity; and generating the target structure grid based on the distribution point number and the distance between two ends of each grid line of the determined target structure grid. According to the invention, the problem that resources and time are wasted because the fine adjustment of the existing grid structure with the complex appearance can be realized only by a mode of artificially reconstructing the grid structure can be solved.

Description

Similar outline structure grid automatic generation method based on reference grid
Technical Field
The invention belongs to the technical field of computational fluid mechanics grid generation, and particularly relates to a similar appearance structure grid automatic generation method based on a reference grid.
Background
Currently, when a Computational Fluid Dynamics (CFD) method is used to solve an actual engineering problem or perform related research, a corresponding computational mesh needs to be constructed based on the shape of a target object. The time consumed by the computing grid generation link occupies a large proportion in the whole computing period, and is one of important factors influencing the efficiency of the whole computing process.
The existing computational grids are divided into two types, namely structural grids and non-structural grids. The unstructured grids are suitable for processing complex geometric structures, but the number of the grids is large, requirements for computing hardware resources are high, and when viscous fluid is computed, the quality of the grids in a near-wall area is poor, and computing accuracy is difficult to guarantee. The structural grid can well control flow direction distribution and grid orthogonality in the boundary layer direction in the near-wall surface area, and the method has the advantages of high boundary layer simulation accuracy and high calculation efficiency. Therefore, structural meshes are still largely adopted in current computational fluid dynamics research and engineering applications.
However, in the face of mesh construction of complex shapes, the difficulty of generating a structural mesh is greater than that of generating an unstructured mesh. The more serious problem is that when the number of grids needs to be adjusted and the local outline size needs to be changed, the grids need to be reconstructed manually, which consumes a lot of manpower, material resources and time. It follows that the generation of complex-shaped structural meshes has been one of the bottleneck problems that hinder the application of CFD engineering.
Disclosure of Invention
The invention aims to solve the problem that resources and time are wasted because fine adjustment of the existing complex-shape grid structure can be realized only by a mode of artificially reconstructing the grid structure.
In order to achieve the above object, the present invention provides an automatic generation method of similar outline structure mesh based on reference mesh, which comprises the following steps:
constructing a corresponding reference structure grid based on the selected reference profile;
acquiring a characteristic scale of the reference appearance;
acquiring the grid number of the reference structure grid, the number of the distribution points of each grid line and the distance between the two ends of each grid line;
acquiring the characteristic scale of a target shape, wherein the target shape is a type of complex shape of a corresponding target structure grid to be constructed which is judged to be similar to the reference shape;
given a desired number of meshes of the target structural mesh and a calculated out-of-domain boundary parameter;
determining the number of the distribution points and the distance between two ends of each grid line of the target structure grid according to the obtained quantity and the given quantity;
and generating the target structure grid based on the determined distribution point number and the distance between two ends of each grid line of the target structure grid.
Preferably, the reference profile is a human representative profile of a predetermined dimension of choice.
Preferably, the step of constructing the respective reference structural mesh based on the selected reference outline is implemented based on mesh generation software.
Preferably, the method for automatically generating the similar appearance structure grid further includes:
recording the obtained quantity as a fixed data source in a script program;
recording the given quantity as a non-fixed data source in the script program.
Preferably, the step of determining the number of the wirings and the distance between both ends of each of the grid lines of the target structural grid based on the obtained amount and the given amount is implemented based on the script program.
Preferably, the step of generating the target structure grid based on the determined number of the layout points and the distance between the two ends of each grid line of the target structure grid is implemented by calling corresponding grid generation software based on the script degree.
Preferably, the number of the acquired feature scales of the reference outline is three, and the three acquired feature scales of the target outline are matched with the three feature scales of the reference outline;
the method for determining the distribution number of the grid lines of the target structure grid comprises the following steps:
determining scaling coefficients of the grid point number of the target structure grid relative to the grid point number of the reference structure grid in three characteristic scale directions according to the following first grid point number scaling coefficient calculation formula:
Figure BDA0002826055700000031
Figure BDA0002826055700000032
Figure BDA0002826055700000033
in the above formula, λξ、ληAnd λζIs a scaling factor, gamma, of the number of lattice points of the target structural grid in the three characteristic scale directions relative to the number of lattice points of the reference structural gridξ、γηAnd gammaζScaling factors for the target profile relative to the reference profile at three feature scales, nξ、nηAnd nζTo make an equation
Figure BDA0002826055700000034
Three characteristic scale direction exponentiation indexes of true, SnIs the number of grids of the reference structure grid, SoA desired number of meshes for the target structural mesh;
dividing grid lines of the target structure grid into first-type grid lines and second-type grid lines, wherein the first-type grid lines are grid lines distributed along three characteristic scale directions of the target structure grid, and the second-type grid lines are grid lines which are not distributed along the three characteristic scale directions of the target structure grid;
and taking the product of the scaling coefficient of the grid points in the characteristic scale direction corresponding to the first type of grid lines and the distribution number of the grid lines corresponding to the first type of grid lines of the reference structure grid as the distribution number of the first type of grid lines.
Preferably, the number of points of the second type of grid lines is determined by:
and acquiring a grid point number scaling coefficient in the non-characteristic scale direction corresponding to the second type of grid lines, and taking the product of the grid point number scaling coefficient and the distribution number of the grid lines of the reference structure grid corresponding to the second type of grid lines as the distribution number of the second type of grid lines.
Preferably, the grid point scaling factor in the non-characteristic scale direction corresponding to the second type of grid line is determined according to the following second grid point scaling factor calculation formula:
Figure BDA0002826055700000041
in the above formula, λpThe scaling coefficient of the number of the lattice points in the non-characteristic scale direction corresponding to the second type of lattice lines,
Figure BDA0002826055700000042
γp＝Lpo/Lpn，Lpois the size of the second type of grid line, LpnThe size of the grid line of the reference structure grid corresponding to the grid line of the second type is set.
Preferably, the distance between both ends of the grid line of the target structural grid is determined according to the following calculation formula of the distance between both ends of the grid line:
Dso＝γ·λ-1·Dsn
in the above formula, DsoDistance between both ends of grid line, Ds, of the grid of the target structurenThe distance between two ends of the grid line of the reference structure grid corresponding to the grid line is gamma, the geometric scale scaling coefficient of the grid line is gamma, and the grid point number scaling coefficient of the grid line is lambda.
The invention has the beneficial effects that:
when the fine tuning problem of the complex-shape grid structure is faced, the invention determines the distribution point number and the two-end distance of each grid line of the target structure grid based on the known characteristic dimension of the reference shape, the grid number of the reference structure grid, the distribution point number and the two-end distance of each grid line, the determined target shape characteristic dimension, the expected grid number of the given target structure grid and the boundary parameter outside the calculation domain, and generates the target structure grid based on the distribution point number and the two-end distance of each grid line of the target structure grid. Wherein the target profile is a reference profile after fine tuning.
Therefore, when the number of grids and the local outline dimension of the complex-outline grid structure need to be fine-tuned, the method for automatically generating the similar-outline structure grid based on the reference grid can obtain key parameters for generating the target structure grid, namely the number of the distribution points and the distance between two ends of each grid line of the target structure grid, and automatically generate the target structure grid based on the key parameters, so that the problem that resources and time are wasted due to the fact that fine tuning of the existing complex-outline grid structure can be achieved only in a mode of manually reconstructing the grid structure is effectively solved.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
Fig. 1 shows a flow chart of an implementation of a method for automatically generating a grid of similar appearance structure based on a reference grid according to an embodiment of the invention.
FIG. 2 illustrates a reference structure grid diagram according to an embodiment of the present invention.
Fig. 3 shows a topology diagram of a reference structure mesh according to an embodiment of the invention.
FIG. 4 shows a three feature scale and corresponding grid point number diagram for a reference profile, according to an embodiment of the invention.
FIG. 5 shows a schematic diagram of three feature scales and corresponding grid point numbers for a target shape, according to an embodiment of the invention.
FIG. 6 shows a schematic diagram of target shape computation out-of-domain boundary scale parameters, according to an embodiment of the invention.
FIG. 7 is a schematic diagram illustrating the layout and spacing of grid lines of a target structural grid according to an embodiment of the invention.
FIG. 8 illustrates a target structure grid map in accordance with an embodiment of the present invention.
FIG. 9 illustrates a flow diagram for automatic generation of a target structural grid according to an embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below. While the following describes preferred embodiments of the present invention, it should be understood that the present invention may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Example (b): fig. 1 shows a flowchart of an implementation of the method for automatically generating a grid with similar outline structure based on a reference grid according to the present embodiment. Referring to fig. 1, the method for automatically generating a grid with a similar outline structure based on a reference grid in this embodiment includes the following steps:
s100, constructing a corresponding reference structure grid based on the selected reference appearance;
s200, acquiring a characteristic scale of the reference appearance;
step S300, acquiring the grid number of the reference structure grid, the distribution point number of each grid line and the distance between two ends of each grid line;
step S400, obtaining a characteristic scale of a target shape, wherein the target shape is a complex shape of a corresponding target structure grid to be constructed, which is judged to be similar to the reference shape;
step S500, setting the expected grid number of the target structure grid and calculating out-of-domain boundary parameters;
step S600, determining the number of the distribution points and the distance between the two ends of each grid line of the target structure grid according to the obtained quantity and the given quantity;
step S700, generating the target structure grid based on the determined distribution point number and the distance between two ends of each grid line of the target structure grid.
In step S100 of this embodiment, the reference outline is a typical outline of a selected predetermined scale.
Step S100 of this embodiment is implemented based on poitwise software.
The method for automatically generating the similar outline structure grid based on the reference grid further comprises the following steps:
recording the obtained quantity as a fixed data source in a TCL/TK script program;
the given amount is recorded as a non-fixed data source in the TCL/TK script program.
Step S600 of the present embodiment is implemented based on a TCL/TK script program.
Step S700 of this embodiment is implemented by a poitwise software call based on the TCL/TK script program.
Most mesh making is realized by some commercial software, wherein poitwise is the current general mesh generation software for calculating fluid. The pointwise software not only has stronger manual interactive manufacturing capability of a structural grid and an unstructured grid, but also provides a mode for calling a pointwise command to manufacture the grid by compiling a TCL/TK script language, and provides a possible technical approach for realizing automatic generation of the grid.
In this embodiment, the number of the acquired feature scales of the reference outline is three, and the three acquired feature scales of the target outline are matched with the three feature scales of the reference outline;
the method for determining the distribution number of the grid lines of the target structure grid comprises the following steps:
determining scaling coefficients of the grid point number of the target structure grid relative to the grid point number of the reference structure grid in three characteristic scale directions according to the following first grid point number scaling coefficient calculation formula:
Figure BDA0002826055700000071
Figure BDA0002826055700000072
Figure BDA0002826055700000073
in the above formula, λξ、ληAnd λζIs a scaling factor, gamma, of the number of lattice points of the target structural grid in the three characteristic scale directions relative to the number of lattice points of the reference structural gridξ、γηAnd gammaζScaling factors for the target profile relative to the reference profile at three feature scales, nξ、nηAnd nζTo make an equation
Figure BDA0002826055700000074
Three characteristic scale direction exponentiation indexes of true, SnIs the number of grids of the reference structure grid, SoA desired number of meshes for the target structural mesh;
dividing grid lines of the target structure grid into first-type grid lines and second-type grid lines, wherein the first-type grid lines are grid lines distributed along three characteristic scale directions of the target structure grid, and the second-type grid lines are grid lines which are not distributed along the three characteristic scale directions of the target structure grid;
and taking the product of the scaling coefficient of the grid points in the characteristic scale direction corresponding to the first type of grid lines and the distribution number of the grid lines corresponding to the first type of grid lines of the reference structure grid as the distribution number of the first type of grid lines.
In this embodiment, the determination manner of the number of points arranged on the second type of grid lines is as follows:
and acquiring a grid point number scaling coefficient in the non-characteristic scale direction corresponding to the second type of grid lines, and taking the product of the grid point number scaling coefficient and the distribution number of the grid lines of the reference structure grid corresponding to the second type of grid lines as the distribution number of the second type of grid lines.
Determining the grid point scaling coefficient in the non-characteristic scale direction corresponding to the second type of grid line according to the following second grid point scaling coefficient calculation formula:
Figure BDA0002826055700000081
in the above formula, λpThe scaling coefficient of the number of the lattice points in the non-characteristic scale direction corresponding to the second type of lattice lines,
Figure BDA0002826055700000082
γp＝Lpo/Lpn，Lpois the size of the second type of grid line, LpnThe size of the grid line of the reference structure grid corresponding to the grid line of the second type is set.
Determining the distance between the two ends of the grid lines of the target structure grid according to the following calculation formula of the distance between the two ends of the grid lines:
Dso＝γ·λ-1·Dsn
in the above formula, DsoDistance between both ends of grid line, Ds, of the grid of the target structurenThe distance between two ends of the grid line of the reference structure grid corresponding to the grid line is gamma, the geometric scale scaling coefficient of the grid line is gamma, and the grid point number scaling coefficient of the grid line is lambda.
Fig. 9 shows a flowchart of automatic generation of the target structural grid of the present embodiment. The method for automatically generating a grid with similar outline structure based on a reference grid according to this embodiment will be described in more detail with reference to fig. 9:
1. aiming at a certain similar shape, selecting a shape with a specific scale as a reference shape to construct a reference structure networkThe grid, the reference structure grid and the grid topology are shown in fig. 2 and 3, respectively. The number of the grid of the reference structure grid is Sn。
2. The dot arrangement number and the distance between the two ends of each grid line (connector) of the reference structure grid are recorded in a TCL/TK script program.
3. On the reference profile, three feature scales (corresponding to three grid directions) are chosen, respectively noted as: l isξn，Lηn，Lζn(ii) a The grid points corresponding to the three characteristic scales are respectively recorded as: n is a radical ofξn，Nηn，Nζn. The three characteristic dimensions of the reference profile and the number of corresponding grid points are shown in fig. 4.
4. For the target shape, after setting the outer boundary of the calculation region, acquiring three characteristic scales corresponding to the reference shape, and respectively recording the three characteristic scales as Lξo，Lηo，Lζo(ii) a The grid points corresponding to the three characteristic scales are respectively recorded as: n is a radical ofξo，Nηo，Nζo. The three characteristic dimensions of the reference profile and the number of corresponding grid points are shown in fig. 5.
5. The desired number of meshes of the target structure mesh is So. The calculated regional outer boundary dimensions Eu, Eb, Eh, Es, and Ed are given. Automatically generating an upper quarter ellipsoid as an upper calculation domain outer boundary surface according to Eu, Eb, Eh and Es; and automatically generating a lower quarter ellipsoid as a lower calculation domain outer boundary surface according to Eu, Eb, Ed and Es. The target outline calculation out-of-domain boundary scale parameters are shown in fig. 6.
6. According to the parameters, the distribution number of each conductor on the target structure grid and the interval Ds between two ends are automatically calculated by a TCL/TK script program1、Ds2. The layout and the end-to-end spacing of the grid lines of the target structural grid are shown in fig. 7.
7. And calling a TCL/TK script program in the Pointwise software to automatically generate a target structure grid, as shown in FIG. 8.
The algorithm for the connector distribution point number and the distance between two ends of the target structure grid specifically comprises the following steps:
the main idea is as follows:
conclusion 1: the total number of grids is approximately proportional to the product of the number of grid points on the three characteristic scales;
conclusion 2: the scaling coefficient of the grid point number in three characteristic directions is in direct proportion to the nth power of the scaling coefficient of the scale, and the method is obtained through practice: the value range of n can be (0.5, 1);
conclusion 3: the connector dot spacing is inversely proportional to the number of grid dots.
(1) Let lambdaξ＝Nξo/Nξn，λη＝Nηo/Nηn，λζ＝Nζo/NζnDefine λξ、λη、λζScaling coefficients of the target grid points relative to the grid points of the reference grid in the three characteristic scale directions;
(2) let gamma beξ＝Lξo/Lξn，γη＝Lηo/Lηn，γζ＝Lζo/LζnDefine γξ、γη、γζScaling coefficients of three characteristic scales of the target shape relative to the reference shape;
(3) from conclusion 2:
Figure BDA0002826055700000101
wherein n isξ、nη、nζIs the power exponent in three characteristic directions;
(4) the calculation formula of the scaling coefficients of the lattice points in the three characteristic scale directions is as follows:
Figure BDA0002826055700000102
Figure BDA0002826055700000103
Figure BDA0002826055700000104
(5) for all the connectors on the target grid, the number of distribution points can be set in two types of connectors. One is the connector along three characteristic dimension directions, is the key connector of the grid, is obtained by the point number scaling factor of the grid in each direction multiplying the grid point number of the corresponding reference grid; another is a connector in the non-dominant eigen-scale direction, and the distribution point can be calculated by the dominant-direction average scaling factor as follows:
order:
Figure BDA0002826055700000105
let a connector have a dimension L in the reference profilepnDimension in target profile is LpoOrder: gamma rayp＝Lpo/Lpn，λp＝Npo/Npn，λpFor the secondary connector grid point scaling factor, then:
Figure BDA0002826055700000106
therefore, the point distribution number of all the connectors on the target grid can be obtained by multiplying the grid point number of the corresponding reference grid by the corresponding number scaling coefficient;
(6) the method for calculating the distance between two ends of the connector comprises the following steps: let the target grid end spacing to be calculated be DsoIt sets the interval of the corresponding reference grid end as Dsn. From conclusion 3:
Dso＝γ·λ-1·Dsn
wherein, γ is a scaling factor of the geometric scale of the connected conductor, and λ is a scaling factor of the number of mesh points of the connected conductor.
According to the method for automatically generating the similar-appearance structural grid based on the reference grid, the TCL/TK language script is called by using pointwise software aiming at one type of similar appearance, the structural grid of one type of appearance can be automatically generated only by changing a small number of control numbers, meanwhile, the total amount of the grid is randomly changed, the capability of better adapting to appearance scale change is achieved, the grid manufacturing efficiency is improved, and the labor cost is reduced.
The method for automatically generating the similar appearance structure grid based on the reference grid further has the following beneficial effects:
firstly, only a reference grid is constructed once according to a reference appearance, and after grid characteristic parameters of the reference grid are compiled and written into a TCL/TK language script, a target structure grid can be automatically generated for any similar appearance with the same grid topological structure, so that the time for manually manufacturing the grid is greatly saved, and the computational fluid mechanics scientific research or engineering application efficiency is effectively improved.
And secondly, the total number of the target grids can be set arbitrarily in advance, and the deviation between the total number of the target grids obtained by automatic generation and the total number of the preset grids can be controlled within 10%.
And thirdly, automatically calculating the grid points of all the connectors of the target grid according to the main characteristic scale of the target shape, the characteristic scale of the reference shape and the total number of the grids.
And fourthly, automatically calculating the distance between two ends of all the connectors of the target grid according to the main characteristic dimension of the target shape and the characteristic dimension of the reference shape.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (10)

1. The method for automatically generating the similar outline structure grid based on the reference grid is characterized by comprising the following steps of:
constructing a corresponding reference structure grid based on the selected reference profile;
acquiring a characteristic scale of the reference appearance;
acquiring the grid number of the reference structure grid, the number of the distribution points of each grid line and the distance between the two ends of each grid line;
acquiring the characteristic scale of a target shape, wherein the target shape is a type of shape of a corresponding target structure grid to be constructed which is judged to be similar to the reference shape;
given a desired number of meshes of the target structural mesh and a calculated out-of-domain boundary parameter;
determining the number of the distribution points and the distance between two ends of each grid line of the target structure grid according to the obtained quantity and the given quantity;
and generating the target structure grid based on the determined distribution point number and the distance between two ends of each grid line of the target structure grid.
2. The method of claim 1, wherein the reference outline is a human outline of a predetermined size selected.
3. The method of claim 1, wherein the step of constructing a corresponding reference structural mesh based on the selected reference outline is implemented based on mesh generation software.
4. The method of automatically generating a grid of similar appearance structures according to claim 1, further comprising:
recording the obtained quantity as a fixed data source in a script program;
recording the given quantity as a non-fixed data source in the script program.
5. The method according to claim 4, wherein the step of determining the number of the wirings and the distance between both ends of each of the grid lines of the target structural grid based on the obtained quantity and the given quantity is implemented based on the script program.
6. The method according to claim 5, wherein the step of generating the target structural mesh based on the determined number of the mesh points and the distance between both ends of each mesh line of the target structural mesh is implemented by a corresponding mesh generation software call based on the script degree.
7. The method according to claim 1, wherein the number of the obtained feature scales of the reference outline is three, and the obtained three feature scales of the target outline are matched with the three feature scales of the reference outline;
the method for determining the distribution number of the grid lines of the target structure grid comprises the following steps:
determining scaling coefficients of the grid point number of the target structure grid relative to the grid point number of the reference structure grid in three characteristic scale directions according to the following first grid point number scaling coefficient calculation formula:
Figure FDA0002826055690000021
Figure FDA0002826055690000022
Figure FDA0002826055690000023
in the above formula, λξ、ληAnd λζIs a scaling factor, gamma, of the number of lattice points of the target structural grid in the three characteristic scale directions relative to the number of lattice points of the reference structural gridξ、γηAnd gammaζScaling factors for the target profile relative to the reference profile at three feature scales, nξ、nηAnd nζTo make an equation
Figure FDA0002826055690000024
Three characteristic scale direction exponentiation indexes of true, SnIs the number of grids of the reference structure grid, SoA desired number of meshes for the target structural mesh;
dividing grid lines of the target structure grid into first-type grid lines and second-type grid lines, wherein the first-type grid lines are grid lines distributed along three characteristic scale directions of the target structure grid, and the second-type grid lines are grid lines which are not distributed along the three characteristic scale directions of the target structure grid;
and taking the product of the scaling coefficient of the grid points in the characteristic scale direction corresponding to the first type of grid lines and the distribution number of the grid lines corresponding to the first type of grid lines of the reference structure grid as the distribution number of the first type of grid lines.
8. The method according to claim 7, wherein the second type of grid lines are determined by the following way:
and acquiring a grid point number scaling coefficient in the non-characteristic scale direction corresponding to the second type of grid lines, and taking the product of the grid point number scaling coefficient and the distribution number of the grid lines of the reference structure grid corresponding to the second type of grid lines as the distribution number of the second type of grid lines.
9. The method according to claim 8, wherein the scaling factor of the number of lattice points in the non-characteristic scale direction corresponding to the second type of lattice line is determined according to the following second scaling factor calculation formula of the number of lattice points:
Figure FDA0002826055690000031
in the above formula, λpThe scaling coefficient of the number of the lattice points in the non-characteristic scale direction corresponding to the second type of lattice lines,
Figure FDA0002826055690000032
γp＝Lpo/Lpn，Lpois the size of the second type of grid line, LpnBeing the reference structure grid and the second type gridThe size of the grid lines to which the lines correspond.
10. The method according to claim 9, wherein the distance between both ends of the grid line of the target structural grid is determined according to the following calculation formula:
Dso＝γ·λ-1·Dsn
in the above formula, DsoDistance between both ends of grid line, Ds, of the grid of the target structurenThe distance between two ends of the grid line of the reference structure grid corresponding to the grid line is gamma, the geometric scale scaling coefficient of the grid line is gamma, and the grid point number scaling coefficient of the grid line is lambda.
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