JP3201599B2 - Orthogonal difference grid generation device, generation method thereof, and storage medium storing orthogonal difference grid generation program - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an orthogonal difference grid generating apparatus for generating an orthogonal difference grid used for performing various analyzes on a three-dimensional analysis area by using a finite difference method, and a method for generating the orthogonal difference grid. The present invention relates to a storage medium storing an orthogonal difference grid generation program.

[0002]

2. Description of the Related Art There are a finite difference method and a finite element method as numerical solutions of differential equations used for various analyses. When an analysis is performed on a predetermined analysis region using these methods, the analysis region is divided into small regions, and analysis is performed by solving equations for each small region (element). When calculating the state of the ground wind that changes according to the terrain, set a grid (calculation grid) in the three-dimensional area to be analyzed, divide it into small areas, and perform fluid analysis for each three-dimensional small area Obtains a simulation result.

Therefore, when performing an analysis on a three-dimensional area, it is necessary to first set a desired calculation grid in the area. In the example of the above-described ground wind analysis, three-dimensional data of the terrain in the region is created, and a three-dimensional calculation grid reflecting the terrain is set.

Here, the finite difference method has an advantage that the amount of calculation required to generate a grid forming a small area can be reduced as compared with the finite element method, but the degree of approximation of the shape is low. Therefore, the analysis accuracy was poor.

[0005]

As described above, when a predetermined analysis region is performed, the degree of approximation of the shape is lower when the finite difference method is used than when the finite element method is used, and the analysis accuracy is inferior. There was a disadvantage.

Further, in order to generate an orthogonal difference grid in the analysis area, it is necessary to first create three-dimensional shape data of an object existing in the analysis area.

The present invention solves the above-mentioned drawbacks of the prior art and improves the processing efficiency by automatically generating a finite difference grid used in the finite difference method based on predetermined ground data. Provided is an orthogonal difference grid generation apparatus and a method for generating the same, and a storage medium storing an orthogonal difference grid generation program, in which the degree of shape approximation is improved by introducing a shape approximation method using the space occupancy for each calculation grid. The purpose is to do.

[0008]

In order to achieve the above object, the present invention provides an orthogonal difference grid generation for generating an orthogonal difference grid used in a finite difference method for a three-dimensional analysis area including a predetermined terrain. In the apparatus, initial grid generating means for generating an initial grid in the analysis area using contour data of the terrain included in the analysis area as setting conditions for the orthogonal difference grid, and initial grid generating means for generating an initial grid in the analysis area. The initial grid is divided by grid lines corresponding to the positions of the contour lines shown in the contour data, to form a plurality of layer regions having a thickness equal to the height intervals of the contour lines, and for each of the layer regions Generating a grid that reflects the initial grid and subdividing the grid generated in the layer area according to the contour shape included in the division plane of the layer area to generate a secondary grid Case Generating means, and a grid point newly set in the secondary grid generated for each layer area by the secondary grid generating means is reflected in all of the layer areas, whereby the secondary A grid point adjusting means for matching the grid.

[0009] In another aspect, the secondary grid generating means includes: for all grid points forming the secondary grid,
Furthermore, it is determined whether a grid point located in the space or a point located in the soil, and the determination result is defined as an attribute of the grid point,
The grid point adjusting means, for all grid points newly set when matching the secondary grid of each layer region, further determines whether a grid point located in space or a point located in soil. It is characterized in that a judgment is made and the judgment result is defined as an attribute of the grid point.

Further, in another aspect, the secondary grid generating means specifies an arbitrary point on the division plane of the layer area as a reference point, and for each grid point on the division plane of the layer area,
Based on the relative position with respect to the reference point, it is determined whether the grid point is located in the space or the soil, the grid point adjusting means, when matching the secondary grid of each layer area For all newly set grid points, it is determined whether the grid point is located in space or soil based on the relative position with respect to the reference point.

In still another aspect, the secondary lattice, whose lattice points have been matched by the lattice point adjusting means, is input, and the space occupancy in a small area formed by the secondary lattice is calculated. A space occupancy calculating means is further provided.

[0012]

[0013]

[0014]

[0015]

[0016]

Embodiments of the present invention will be described below in detail with reference to the drawings. In the present embodiment, it is assumed that an orthogonal difference grid for calculating the state of the ground wind using the finite difference method is generated.

FIG. 1 is a block diagram showing a configuration of an orthogonal difference grid generating apparatus according to an embodiment of the present invention. Referring to FIG. 1, an orthogonal difference grid generation device according to the present embodiment includes an initial grid generation unit 10 that generates an initial three-dimensional grid (hereinafter, referred to as an initial grid) for an analysis range, and an generated initial grid. A secondary grid creating unit 20 that divides the grid into a plurality of layer areas having an appropriate thickness and creates independent three-dimensional coordinate data for each layer area; and a different grid for each layer area based on the grid data of each layer area. Grid point adjustment unit 30 for adjusting the number of points
And a shape approximating unit 40 for approximating the terrain shape based on the proportion of the space occupied by each grid, and a grid for outputting the calculated coordinate values, attributes, and space occupancy of each grid surrounded by the grid points. A data output unit 50. Further, the storage device 100 that stores the terrain data 110 to be analyzed is connected to the orthogonal difference grid generation device of the present embodiment. The storage device 100 can temporarily store grid data generated during the processing according to the present embodiment as necessary, or can be used as an output destination of the finally generated grid data.

The orthogonal difference grid generating apparatus of the present embodiment configured as described above comprises, for example, a program-controlled CPU mounted on a personal computer, workstation, or other computer system, and a RAM or other internal memory. Is achieved. A computer program for controlling the CPU is provided by being stored in a magnetic disk, an optical disk, a semiconductor memory, or another general storage medium, and loaded into an internal memory of the computer system to realize the functions of the above-described function execution units. In FIG. 1,
Only the characteristic configuration in the present embodiment is described, and the description of other general configurations is omitted.

In the above configuration, the initial grid generator 10
Generates an initial grid in the analysis target area. Referring to FIG. 2 showing the operation of the initial grid generating unit 10, the initial grid generating unit 10 first sets a rectangular parallelepiped analysis target area including a space below the ground surface and a space above the ground surface in a three-dimensional orthogonal coordinate system. (Step 201). Then, the number of divisions is input to the coordinate axes in each direction (step 202). Here, the number of divisions is a number that specifies how many divisions of the analysis target area are performed in the direction of the coordinate axis. Therefore, by dividing each coordinate axis of the analysis target area by the input number of divisions, the length of one side of the initial lattice can be calculated, whereby the division position in each coordinate axis direction is determined. In the present embodiment, the contour data 11 in the terrain data 110 is used in the Z-axis direction.
By using 1, the input of the number of divisions can be omitted. That is, the coordinate value of each contour line shown in the contour line data 111 can be set as a division position in the Z-axis direction (height direction) of the analysis target area. The setting of the analysis target area and the input of the number of divisions are performed by the user using a keyboard, a mouse, and other appropriate input devices. next,
An initial grid is generated by actually dividing the analysis target area according to the number of divisions of each coordinate axis (step 203).

The secondary grid generator 20 includes an initial grid generator 1
The analysis target area in which the initial lattice is generated by 0 is divided at the division position in the Z-axis direction (coordinate values of each contour line) to obtain a plurality of layer areas having a thickness equal to the length of the initial lattice in the Z-axis direction. . Then, a lattice (secondary lattice) is generated for each layer region by generating a three-dimensional lattice for distinguishing the soil and the space for each obtained layer region. The three-dimensional grid is generated based on the contour shape of the surface of each layer region.
The dimensional grid is projected in the Z-axis direction by the width of the contour line.

Referring to the flowchart of FIG. 3 showing the operation of the secondary grid generation unit 20, the secondary grid generation unit 20 first divides the analysis area in which the initial grid is generated into layer areas corresponding to contour lines ( Step 301), the grid points are reconstructed for each layer region (step 302). Thus, in each layer region, (the number of divisions + 1) lattice points exist in the X and Y axis directions, and two lattice points exist in the Z axis direction. In addition, lattice points are arranged at the same position on the top surface and the bottom surface of each layer region.

Next, focusing on one of the contour shapes appearing on the division surface (upper surface or bottom surface) of each layer region, the two-dimensional lattice of the surface is appropriately subdivided by the following procedure.
First, an arbitrary point in the closed space formed by the contour lines is designated and set as a reference point for distinguishing the soil from the space (step 303). The reference point is specified by the user using an appropriate input device. Next, it is determined whether or not a contour partial curve can be approximated by a quadratic polynomial in a unit area surrounded by four grid points (hereinafter, referred to as a calculation cell) according to the property of the quadratic curve. (Step 304). If approximation can be made by a second-order polynomial, the four lattice points are determined, and the coefficients of the approximated terms are stored in a predetermined file (step 306).

On the other hand, when the calculation cell cannot be approximated by the second-order polynomial, the calculation cell is divided into four by bisectors of each side (step 3).
05). At this time, a new grid point is set at the midpoint of each side. Then, for a new calculation cell after the division, that is, a calculation cell of a quarter of the calculation cell before the division surrounded by four grid points including the new grid point,
It is determined again whether or not approximation can be made with a second-order polynomial (step 304). The above-described division of the calculation cell and the determination of whether or not approximation is possible are repeated until the partial curve of the contour line in the calculation cell can be approximated by a quadratic polynomial. Then, when a new grid point for dividing the calculation cell is set, when the grid point is determined, its coordinate value is reflected on the X and Y axes.

As described above, when the contour lines can be approximated to the second-order polynomials in all the calculation cells, each of the four grid points constituting the calculation cells is converted to a point or space located on the soil. Whether the point is located is determined based on the relative position with respect to the reference point, and the determination result is defined as an attribute of the grid point (step 307).

The grid point adjusting unit 30 includes a secondary grid generating unit 20
By reflecting the newly set lattice points and their attributes for each layer region in all layer regions, the lattice matching of each layer region is achieved. Referring to the flowchart of FIG. 4 showing the operation of the grid point adjustment unit 30, the grid point adjustment unit 30 firstly sets the coordinate values of the grid points on the X and Y axes newly set and determined in each layer region. This is reflected in the layer area (step 401). Then, in all the layer regions, the attributes of the grid points added in step 401 are defined by the same method as that performed in step 307 of FIG. 3 (step 402).

The shape approximating unit 40 approximates the topographic shape based on the ratio of the space occupied by each grid (space occupancy). Referring to the flowchart of FIG. 5 showing the operation of the shape approximating unit 40, the shape approximating unit 40 first calculates the area of the soil portion in the calculation cell (step 501). next,
The space occupancy in the calculation cell is calculated by the following formula for calculating the area ratio between the space portion and the soil portion in the cross section of the calculation cell (step 502). Space occupancy = (area of calculation cell)-(area of soil part)
/ (Area of calculation cell) The value that the space occupancy actually has is a real number from “0” to “1”. When the value is “0”, it means that the calculation cell is filled with soil, and when the value is “1”, it means that the space is completely free of soil. If all the four grid points included in the calculation cell have the same attribute, it is not necessary to calculate the space occupancy, so the occupancy is set to “0” or “1”.

The space occupancy calculated as described above does not indicate the contour of the terrain (contour shape) in the calculation cell, but the behavior of the fluid largely depends on the space occupancy in a certain area. Therefore, in the fluid analysis, it may be considered that the topography is approximated by the space occupancy of each calculation cell.

The grid data output unit 50 outputs the grid point coordinate values on each coordinate axis, the attribute information of all grid points, and the space occupancy in all calculation cells, obtained by the operation of each function execution unit. Output in a format that can be read by a fluid calculation program that uses grid data.

[0029]

Next, embodiments of the present invention will be described in detail with reference to the drawings. 6 to 14 show a process of setting an orthogonal difference grid in the analysis target area and generating data relating to the grid.

First, the initial grid generator 10 generates the topographic data 1
Input 10 to generate an initial grid. That is, as shown in FIG. 6, a reference point of an area to be analyzed in the terrain data 110 is determined. Then, the relative position is determined by inputting the length in the X-axis direction and the length in the Y-axis direction with respect to the reference point, and the entire analysis target area is defined as one rectangular parallelepiped. Next, the defined number of divisions in the X-axis direction and the Y-axis direction of the analysis target area are input, and according to the input division number and the number of contour lines of the terrain data in the area, as shown in FIG. X-axis, Y-axis and Z
A three-dimensional initial lattice is formed by equally dividing each in the axial direction.

Next, the secondary grid generating unit 20 inputs the initial grid generated by the initial grid generating unit 10 and divides the analysis target area where the initial grid is generated into the divided positions in the Z-axis direction, that is, the heights of the contour lines. Then, division is performed for each layer region at a position corresponding to the above, and the lattice of each layer region is rearranged. Thereby, a three-dimensional lattice (secondary lattice) of each layer region as shown in FIG. 8 is generated.

Next, with respect to the three-dimensional lattice of each layer region, for example, focusing on the contour shape appearing on the upper surface, the two-dimensional lattice of the surface is subdivided. First, an arbitrary point in a closed space formed by contour lines is defined as a reference point. Here, as shown in FIG. 9, one of the grid points in the initial grid inside the contour line is set as a reference point.

Next, for all calculation cells belonging to the two-dimensional grid and through which the contour partial curve passes, the partial curve is
Whether it can be approximated by a degree polynomial is determined by the presence or absence of an inflection point of the partial curve and the number of extreme values. Specifically, when there is no inflection point and the number of extrema is one or less, it is determined that approximation is possible. FIG. 10 shows examples of the case where approximation is possible (A) and the case where approximation is not possible (B). If it is determined that approximation is possible, four points (vertexes of the four corners of the calculation cell) belonging to the calculation cell are determined as grid points. When it is determined that the approximation is impossible, the grid is subdivided into quarters to set a new calculation cell, and a partial curve of a contour passing through the new calculation cell, as shown in FIG. It is determined again whether or not approximation can be made with a second-order polynomial.

After determining whether approximation is possible or not for all calculation cells, the secondary grid generation unit 20 defines attributes for grid points belonging to each calculation cell. That is, since the reference point is one grid point in a closed area surrounded by contour lines, as shown in FIG. 12, the contour line crosses a straight line connecting the grid point whose attribute is to be defined and the reference point. If
The grid point is defined as an attribute (space attribute) indicating that it is a space. In addition, as shown in FIG. 13, if the contour line does not cross a straight line connecting the grid point whose attribute is to be defined and the reference point, the grid point is defined as an attribute (soil attribute) indicating that it is soil. .

After reconstructing the grid points and defining the attributes for each layer area, the grid point adjusting unit 30 calculates the X coordinate values and Y coordinate values of the newly generated grid points in each layer area.
This is reflected on the X and Y coordinates of all layer areas. As a result of this processing, new grid points are generated in some layer areas, and the attributes of the added grid points are defined.

Next, the shape approximating unit 40 calculates the area of the soil area surrounded by the contour lines approximated by the second-order polynomial, calculates the area ratio between the space part and the soil part, and calculates the space occupancy of each calculation cell. Is defined as In FIG. 14, the space occupancy is “0”.
, The space occupancy is “1”, and the space occupancy is between “0” and “1”.

Lastly, the grid data output unit 50 stores the coordinate values of the grid points on each coordinate axis, the attribute information of all grid points, and the space occupancy in all calculation cells, using a fluid calculation program that uses grid data. Output in a format that can be read by.

Although the present invention has been described with reference to the preferred embodiments, the present invention is not necessarily limited to the above embodiments. For example, in the above-described embodiment, the application to the system for analyzing the state of the ground wind based on the terrain data is described. If similar data is created, it is possible to analyze the state of the airflow around the object based on the data.

Specifically, the shape of the object is traced for each of several cross sections by using an existing scanning device, and the shape data for each cross section, that is, the contour of the object is treated in the same manner as the contour line, whereby the orthogonality is obtained. This can be data for generating a difference grid.

Further, among the grid data created according to the present invention, coordinate data and attribute data of grid points are used to calculate
Three-dimensional shape data can be created. That is, according to the present invention, a three-dimensional orthogonal difference grid reflecting the data can be created from two-dimensional data such as terrain data, so that it can be used as a kind of solid modeler. .

[0041]

As described above, according to the orthogonal difference grid generation apparatus and the generation method thereof and the storage medium storing the orthogonal difference grid generation program of the present invention, the calculation grid is automatically formed from the existing terrain data. Since it can be generated, there is no need to create three-dimensional data of the region to be analyzed in advance, and there is an effect that the efficiency of the analysis process can be improved.

When the present invention is applied to fluid analysis in a three-dimensional space such as ground wind analysis, the object shape in the small area is approximated by the space occupancy of each small area divided by the calculation grid. This has the effect that a sufficient degree of shape approximation can be obtained for analysis.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of an orthogonal difference grid generation device according to an embodiment of the present invention.

FIG. 2 is a flowchart illustrating an operation of an initial grid generation unit according to the present embodiment.

FIG. 3 is a flowchart illustrating an operation of a secondary grid generation unit according to the embodiment.

FIG. 4 is a flowchart illustrating an operation of a grid point adjustment unit according to the embodiment.

FIG. 5 is a flowchart illustrating an operation of a shape approximating unit according to the present embodiment.

FIG. 6 is a diagram showing an example in which a three-dimensional analysis target area is set based on topographic data.

FIG. 7 is a diagram illustrating an example in which an initial grid is generated for an analysis target area.

FIG. 8 is a diagram showing an example in which an initial lattice is divided for each layer region.

FIG. 9 is a diagram illustrating an example in which a reference point is specified on one surface of a layer area.

FIG. 10 is a diagram showing an example of a case where a contour partial curve can be approximated by a second-order polynomial and an example of a case where it cannot be approximated.

FIG. 11 is a diagram showing an example in which a calculation cell is divided into four parts.

FIG. 12 is a diagram illustrating a method of defining an attribute of a grid point based on a relative position with respect to a reference point, and illustrating an example in which the attribute is a spatial attribute.

FIG. 13 is a diagram illustrating a method of defining an attribute of a grid point based on a relative position with respect to a reference point, and illustrating an example in which the attribute is a soil attribute.

FIG. 14 is a diagram showing an example of calculation cells having different space occupancies.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Initial grid generation part 20 Secondary grid generation part 30 Grid point adjustment part 30 40 Shape approximation part 50 Grid data output part 100 Storage device 110 Terrain data 111 Contour data

──────────────────────────────────────────────────続 き Continued on front page (58) Field surveyed (Int. Cl. ⁷ , DB name) G06F 17/50 612

Claims (4)

(57) [Claims] 1. An orthogonal difference grid generating apparatus for generating an orthogonal difference grid used in a finite difference method for a three-dimensional analysis region including a predetermined terrain, comprising the steps of: An initial grid generating unit that generates an initial grid in the analysis area using the setting conditions of the difference grid, and the initial grid generated by the initial grid generating unit is located at a contour line position indicated by the contour data. Dividing by the corresponding grid lines to form a plurality of layer regions having a thickness equal to the height interval of the contour lines, and for each layer region,
Generating a grid that reflects the initial grid and subdividing the grid generated in the layer area according to the contour shape included in the division plane of the layer area to generate a secondary grid 2
A secondary lattice generation unit, and a grid point newly set in the secondary lattice generated for each of the layer regions by the secondary lattice generation unit is reflected in all of the layer regions, so that the An orthogonal difference grid generating apparatus, comprising: a grid point adjusting unit for matching a secondary grid. 2. The secondary grid generating means further determines, for all grid points forming the secondary grid, whether the grid points are located in a space or a point located in soil, and a determination result is provided. Is defined as an attribute of the lattice point, and the lattice point adjusting means is further positioned in space with respect to all lattice points newly set when the secondary lattices of the respective layer regions are matched. The orthogonal difference grid generation device according to claim 1, wherein it is determined whether the grid point is a point located on the soil or not, and a determination result is defined as an attribute of the grid point. 3. The secondary grid generating means designates an arbitrary point on a division plane of the layer area as a reference point, and designates each grid point on the division plane of the layer area relative to the reference point. It is determined whether the grid point is located in the space or the soil based on the natural position, the grid point adjusting means is newly set when matching the secondary grid of each layer region The orthogonal difference grid generation according to claim 2, wherein it is determined whether the grid points are located in a space or a soil based on a relative position of the grid points with respect to all the grid points. apparatus. 4. A space occupancy calculating means for inputting the secondary grid, whose lattice points have been matched by the grid point adjusting means, and calculating a spatial occupancy in a small area formed by the secondary grid. The orthogonal difference grid generation device according to claim 1, further comprising: