Fluid simulation methods

Abstract

This invention provides a fluid simulation method that allows for easy comparison of fluid analysis results for multiple objects with different shapes. [Solution] This is a fluid simulation method. This method includes the step of calculating the physical quantities of a fluid using an object model 20 and a computational grid 30. The object model 20 includes a first object model 21 and a second object model. The first object model 21 has a first shape 11A and a first analytical coordinate system 21a. The second object model has a second shape and a second analytical coordinate system. The computational grid 30 includes a first computational grid 31 associated with the first object model 21 and a second computational grid associated with the second object model. When the first analytical coordinate system 21a and the second analytical coordinate system are aligned, the first computational grid 31 and the second computational grid include a common computational grid area 35 where nodes 26 or elements G(i) are in the same position relative to each other.

Description

[Technical Field]

[0001] This invention relates to a fluid simulation method. [Background technology]

[0002] Non-patent document 1 below describes a fluid analysis method. In this method, the mode with the lowest energy of the flow field is optimally extracted based on proper orthogonal decomposition (POD). [Prior art documents] [Patent Documents]

[0003] [Non-Patent Document 1] Kunihiko Taira, "Fluid Analysis by Intrinsic Orthogonal Decomposition: 1. Fundamentals," [online], Nagare, The Japan Society of Fluid Mechanics, Vol. 30, 2011, pp. 115-123, [Retrieved August 5, 2024], Internet<URL:https: / / www.nagare.or.jp / download / noauth.html?d=30-2rensai2.pdf&dir=54> [Overview of the project] [Problems that the invention aims to solve]

[0004] While the fluid analysis described above allows for fluid analysis around multiple objects with different shapes, comparing the results of these analyses has not been easy.

[0005] This invention was devised in view of the above-described circumstances, and its main objective is to provide a fluid simulation method that allows for easy comparison of fluid analysis results for multiple objects with different shapes. [Means for solving the problem]

[0006] The present invention is a fluid simulation method comprising the steps of: setting up an object model that mimics an object to be analyzed; setting up a computational grid having a plurality of nodes or a plurality of elements for calculating physical quantities of a fluid in the space surrounding the object model; and performing calculations of the physical quantities of the fluid using the object model and the computational grid under predetermined conditions, wherein the object model includes a first object model and a second object model, the first object model having a first shape and a first analytical coordinate system associated with the first shape, the second object model having a second shape different from the first shape and a second analytical coordinate system corresponding to the first analytical coordinate system, and the computational grid includes a first computational grid associated with the first object model and a second computational grid associated with the second object model, and when the first analytical coordinate system and the second analytical coordinate system are aligned, the first computational grid and the second computational grid include a common computational grid area where the nodes or elements are in the same position as each other. [Effects of the Invention]

[0007] By employing the above steps, the simulation method of the present invention makes it possible to easily compare the fluid analysis results of multiple objects with different shapes. [Brief explanation of the drawing]

[0008] [Figure 1] This is a block diagram showing an example of a fluid simulation device (computer). [Figure 2] Figures (a) to (e) show examples of objects to be analyzed. [Figure 3] A flowchart illustrating an example of the processing procedure for a fluid simulation method. [Figure 4] This figure shows an example of the first object model and space. [Figure 5] This figure shows an example of a second object model and space. [Figure 6] This figure shows an example of the first object model and the first computational grid. [Figure 7] This figure shows an example of the second object model and the second computational grid. [Figure 8] This flowchart shows an example of the processing procedure for the calculation step. [Figure 9] (a) is a contour plot showing an example of a physical quantity calculated in the first computational grid, and (b) is a contour plot showing an example of a physical quantity calculated in the second computational grid. [Figure 10] This figure shows an example of a physical quantity calculated using a computational grid. [Figure 11] This figure shows an example of the fluctuating components of a physical quantity. [Figure 12] (a) is a contour plot showing an example of a basis vector for the 0th mode, and (b) is a contour plot showing an example of a basis vector for the 2nd mode. [Figure 13] (a) is a graph showing the relationship between the coefficients of the basis vector for the 0th mode and the unit time of the simulation, and (b) is a graph showing the relationship between the coefficients of the basis vector for the 2nd mode and the unit time of the simulation. [Figure 14] This flowchart shows an example of a fluid simulation method according to another embodiment of the present invention. [Figure 15] This figure shows a first object model and a first computational grid according to another embodiment of the present invention. [Figure 16] This figure shows a second object model and a second computational grid according to another embodiment of the present invention. [Figure 17] This is a flowchart showing an example of the processing procedure for the transcription step. [Figure 18] (a) is a diagram showing an example of the first computational grid, and (b) is a diagram showing an example of the third computational grid. [Figure 19] (a) is a diagram showing an example of the second computational grid, and (b) is a diagram showing an example of the fourth computational grid. [Figure 20] This figure shows the nodes when the third computational grid is superimposed on the target region of the first computational grid. [Figure 21] This figure shows an example of a physical quantity of the transcribed computational grid. [Figure 22] This figure shows an example of a variation component of a physical quantity in another embodiment of the present invention. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings. It should be understood that the drawings contain exaggerations and representations that differ from the actual dimensional ratios of the structures in order to aid in understanding the content of the invention. Furthermore, the same or common elements are denoted by the same reference numerals throughout each embodiment, and redundant explanations are omitted. Moreover, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the content of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] In the fluid simulation method of this embodiment, a computer is used to perform the fluid simulation. In the fluid simulation method of this embodiment, the physical quantities of the fluid flowing around the object to be analyzed are calculated under predetermined conditions.

[0011] [Fluid Simulation Device] The computer in this embodiment is configured as a fluid simulation device 1A. Figure 1 is a block diagram showing an example of a fluid simulation device 1A (computer 1).

[0012] The fluid simulation device 1A of this embodiment is configured as a general-purpose computer 1. Examples of computers 1 include desktop PCs, laptop PCs, tablets, smartphones, and cloud servers.

[0013] The fluid simulation apparatus 1A of this embodiment includes an input device 3, an output device 4, and a calculation processing device 5.

[0014] [Input unit, output unit, arithmetic processing unit] Input device 3 is configured as an input device. An example of this input device is a keyboard or mouse. Output device 4 is configured as an output device. An example of this output device is a display device or printer. The arithmetic processing unit 5 is for performing fluid simulations. The arithmetic processing unit 5 of this embodiment is configured to include one or more processors (arithmetic units) 5A that perform various calculations, a storage unit 5B in which data and programs are stored, and a working memory 5C.

[0015] [Processor] In this embodiment, the processor 5A is configured as a central processing unit (CPU), but is not particularly limited and may be configured as a microprocessor or other processing unit, for example. In this embodiment, an example is shown in which the fluid simulation method is executed by one processor 5A, but it may also be executed by multiple processors (parallel processing).

[0016] [Storage] The storage unit 5B is a non-volatile information storage device, such as a magnetic disk, optical disk, or SSD. The storage unit 5B is provided with a data unit 7 and a program unit 8.

[0017] [Data Section] The data unit 7 of this embodiment is for storing data necessary for executing the fluid simulation method. The data unit 7 of this embodiment includes an object model storage unit 7A, a computation grid storage unit 7B, a physical quantity storage unit 7C, and a decomposition result storage unit 7D. The data unit 7 is not limited to this configuration, and may include storage units for other data as needed, or some of these may be omitted. The data stored in each storage unit 5B will be explained in each step of the fluid simulation method described later.

[0018] [Programming Department] The program unit 8 in this embodiment is a program (application) necessary for executing the fluid simulation method. When such a program unit 8 is executed by the processor (calculation unit) 5A, the computer 1 (fluid simulation device 1A) can be made to function as a specific means. The program unit 8 in this embodiment includes a model setting unit 8A, a computation grid setting unit 8B, a physical quantity calculation unit 8C, a comparison unit 8D, an evaluation unit 8E, and a transfer unit 8F. Note that the program unit 8 is not limited to this configuration; other programs may be included as needed, or some of these may be omitted. Furthermore, the functions of each program unit 8 will be explained in each step of the fluid simulation method described later.

[0019] [Object to be analyzed] The object to be analyzed is not particularly limited, as long as it is a target for calculating the physical quantities of the fluid flowing around it. Figures 2(a) to (e) show an example of an object 10 to be analyzed.

[0020] In this embodiment, the object to be analyzed 10 is exemplified as a columnar body 10A, but is not limited to this form. For example, it may be a sphere, a tire, a vehicle, etc. The columnar body 10A is constructed as a three-dimensional object enclosed by two parallel bottom surfaces 10a and a side surface (columnar surface) 10b connecting these bottom surfaces 10a. Such a columnar body 10A is formed of steel, but is not particularly limited and may be formed of, for example, a resin such as rubber, or wood, etc.

[0021] The object to be analyzed 10 in this embodiment includes a first object 11 shown in Figure 2(a) and a second object 12 shown in Figure 2(b). The first object 11 has a first shape 11A. In this embodiment, the first shape 11A is cylindrical. On the other hand, the second object 12 has a second shape 12A. In this embodiment, the second shape 12A is a square prism. Therefore, the first shape 11A and the second shape 12A are different from each other. Note that the first shape 11A and the second shape 12A are not limited to a cylindrical shape or a square prism, but may be, for example, a triangular prism or an elliptical prism.

[0022] In this embodiment, the object to be analyzed 10 includes, in addition to the first object 11 and the second object 12, the third object 13 shown in Figure 2(c), the fourth object 14 shown in Figure 2(d), and the fifth object 15 shown in Figure 2(e). Note that, depending on the purpose of the analysis, some of these objects may be omitted, or other objects (not shown) may be included in the object to be analyzed 10.

[0023] As shown in Figure 2(c), the third object 13 has a third shape 13A. The third shape 13A in this embodiment is an octagonal prism formed by chamfering the sides 10c of the square prism shown in Figure 2(a). As shown in Figure 2(d), the fourth object 14 has a fourth shape 14A. The fourth shape 14A in this embodiment is a regular octagonal prism. As shown in Figure 2(e), the fifth object 15 has a fifth shape 15A. The fifth shape 15A in this embodiment is an octagonal prism formed by chamfering the sides 10c of the square prism more significantly than the third shape 13A and the fourth shape 14A. Therefore, as shown in Figures 2(a) to (e), the first shapes 11A to the fifth shapes 15A are all different from each other.

[0024] [fluid] The fluid (not shown) is not particularly limited as long as it flows around the object 10 being analyzed, as shown in Figure 2. Examples of fluids include air and liquid (water). In this embodiment, the fluid is air.

[0025] The physical quantities of the fluid calculated in this embodiment are not particularly limited, as long as they act on the fluid (air) flowing around the object 10 being analyzed, as shown in Figure 2. The physical quantities in this embodiment include air pressure (Pa), velocity (velocity components in the x-axis and y-axis directions), or coefficients thereof. Examples of coefficients include pressure coefficients and total pressure coefficients. These pressures, velocities, and coefficients change depending on the shape of the object 10 being analyzed (e.g., first shape 11A, second shape 12A). Such pressures, velocities, and total pressure coefficients are useful, for example, for evaluating the air resistance of the object 10 being analyzed. In this embodiment, air pressure is calculated as a physical quantity.

[0026] [Fluid Simulation Method (First Embodiment)] Figure 3 is a flowchart showing an example of the processing procedure for a fluid simulation method. Each step of the fluid simulation method in this embodiment is performed by the processor (calculation unit) 5A included in the fluid simulation device 1A (computer 1) shown in Figure 1.

[0027] [Set object model] In the fluid simulation method of this embodiment, first, an object model that simulates the object to be analyzed 10 shown in Figure 2 is set (step S1).

[0028] In step S1 of this embodiment, first, the model setting unit 8A included in the program unit 8 shown in Figure 1 is loaded into the working memory 5C. The model setting unit 8A is a program for setting up an object model that simulates the object to be analyzed 10 shown in Figure 2. When this model setting unit 8A is executed by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for setting up the object model.

[0029] The object model of this embodiment includes a first object model and a second object model. Figure 4 shows an example of the first object model 21 and space 23. Figure 5 shows an example of the second object model 22 and space 23.

[0030] As shown in Figures 4 and 5, the object model 20 in this embodiment is set as a two-dimensional model, but it is not limited to this configuration. The object model 20 may be set as a three-dimensional model, for example.

[0031] As shown in Figure 4, the first object model 21 is modeled after the first object 11 shown in Figure 2(a). In this embodiment, the first shape 11A of the first object 11 is discretized using a finite number of elements F(i) (i=1, 2, ...). This allows for the creation of the first object model 21 having the first shape 11A.

[0032] In this embodiment, of the first shape 11A shown in Figure 2(a), only the contour of the bottom surface 10a of the first object 11 (first shape 11A) is discretized, but this is not particularly limited. For example, the entire bottom surface 10a may be discretized, or the contour of the side surface 10b of the first object 11 represented in a plane may be discretized. If the first object model 21 is set as a three-dimensional model, the entire first shape 11A may be discretized. Furthermore, it is preferable to use commercially available software (for example, "STAR-CCM+" from Siemens PLM Software) for discretization.

[0033] In this embodiment, each element F(i) is an Euler element capable of handling fluid (air) using the finite volume method. These elements F(i) are provided with multiple nodes 16 and are designed to be undeformable even when external forces are applied. These nodes 16 are fixed to coordinates in space 23.

[0034] The first object model 21 in this embodiment has a first analytical coordinate system 21a associated with the first shape 11A. This first analytical coordinate system 21a is used to align with the second analytical coordinate system 21b of the second object model 22 shown in Figure 5 when comparing the physical quantities calculated in the first computational grid with the physical quantities calculated in the second computational grid in step S4 described later. The first analytical coordinate system 21a can be set as appropriate, as long as it can be aligned with the second analytical coordinate system 21b. In this embodiment, the first analytical coordinate system 21a is identified as the centroid of the first shape 11A.

[0035] As shown in Figure 5, the second object model 22 is modeled after the second object 12 shown in Figure 2(b). In this embodiment, the second shape 12A of the second object 12 is discretized using a finite number of elements F(i) (i=1, 2, ...). This allows for the creation of a second object model 22 having the second shape 12A. In this embodiment, only the contour of the bottom surface 10a of the second object 12 is discretized, but this is not particularly limited. For example, the entire bottom surface 10a may be discretized, or the contour of the side surface 10b of the second object 12 shown in Figure 2(b) represented in a plane may be discretized. Furthermore, if the second object model 22 is set as a three-dimensional model, the entire second shape 12A may be discretized. Details of the elements F(i) and discretization are as described above.

[0036] The second object model 22 of this embodiment has a second analytical coordinate system 21b that corresponds to the first analytical coordinate system 21a. The second analytical coordinate system 21b of this embodiment is associated with the second shape 12A and can be identified as the centroid of the second shape 12A.

[0037] In step S1 of this embodiment, a third object model (not shown), a fourth object model (not shown), and a fifth object model (not shown) are set up based on the same procedure as for the first object model 21 and the second object model 22. The third object model is a replica of the third object 13 shown in Figure 2(c). The fourth object model is a replica of the fourth object 14 shown in Figure 2(d). The fifth object model is a replica of the fifth object 15 shown in Figure 2(e).

[0038] The third object model (not shown) has a third shape 13A (shown in Figure 2(c)) and a third analytical coordinate system (not shown) corresponding to the first analytical coordinate system 21a shown in Figure 4. The third analytical coordinate system in this embodiment is associated with the third shape 13A and can be identified as the centroid of the third shape 13A.

[0039] The fourth object model (not shown) has a fourth shape 14A (shown in Figure 2(d)) and a fourth analytical coordinate system (not shown) corresponding to the first analytical coordinate system 21a shown in Figure 4. The fourth analytical coordinate system in this embodiment is associated with the fourth shape 14A and can be identified as the centroid of the fourth shape 14A.

[0040] The fifth object model (not shown) has a fifth shape 15A (shown in Figure 2(e)) and a fifth analytical coordinate system (not shown) corresponding to the first analytical coordinate system 21a shown in Figure 4. The fifth analytical coordinate system in this embodiment is associated with the fifth shape 15A and can be identified as the centroid of the fifth shape 15A.

[0041] The first object model 21 to the fifth object model (not shown) can be aligned based on the first analytical coordinate system 21a to the fifth analytical coordinate system (not shown). The object model 20 (in this example, the first object model 21 to the fifth object model (not shown)) is input to the object model storage unit 7A.

[0042] [Set the calculation grid] Next, in the fluid simulation method of this embodiment, a computational grid having multiple nodes or multiple elements for calculating the physical quantities of the fluid is set up in the space 23 surrounding the object model 20 shown in Figures 4 and 5 (step S2). The computational grid of this embodiment has both multiple nodes and multiple elements, but it may have only one of them.

[0043] In step S2 of this embodiment, first, the object model 20 (shown in Figures 4 and 5) input into the object model storage unit 7A shown in Figure 1, and the computation grid setting unit 8B included in the program unit 8 are loaded into the working memory 5C. The computation grid setting unit 8B is a program for setting a computation grid in the space 23 surrounding the object model 20. When this computation grid setting unit 8B is executed by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for setting the computation grid.

[0044] Figure 6 shows an example of the first object model 21 and the first computational grid 31. Figure 7 shows an example of the second object model 22 and the second computational grid 32. In Figures 6 and 7, the virtual region 36, which will be described later, is shown with a white frame.

[0045] As shown in Figures 6 and 7, the computational grid 30 in this embodiment is set as a two-dimensional model, similar to the object model 20, but is not limited to this configuration. The computational grid 30 may, for example, be set as a three-dimensional model. The computational grid 30 in this embodiment includes a first computational grid 31 (shown in Figure 6) and a second computational grid 32 (shown in Figure 7).

[0046] As shown in Figure 6, the first computational grid 31 is set in the space 23 surrounding the first object model 21 shown in Figure 4. In this embodiment, the first computational grid 31 is set excluding the area occupied by the first object model 21 from the space 23, but the embodiment is not limited to this. The first computational grid 31 may be set including, for example, the area occupied by the first object model 21.

[0047] As shown in Figure 4, the space 23 in this embodiment is large enough to completely surround the first object model 21, but it is not limited to this configuration. For example, the space 23 may be large enough to surround only a portion of the first object model 21, as long as it includes the region to be analyzed.

[0048] Although the space 23 in this embodiment is formed in a rectangular shape, it is not limited to this configuration. Depending on the purpose of fluid analysis, the space 23 may be formed in a circular or triangular shape, for example.

[0049] In the space 23 of this embodiment, the first length L1, which is the length in the direction of fluid flow (in this example, the x-axis direction), is set to be greater than the second length L2, which is the length in the direction perpendicular to the flow direction (in this example, the y-axis direction). These first length L1 and second length L2 can be set as appropriate depending on the object to be analyzed and the purpose of the fluid analysis. The first length L1 can be set, for example, to 5 to 100 times the maximum width (not shown) of the bottom surface 10a of the object model 20 (first object model 21 and second object model 22). The second length L2 can be set, for example, to 5 to 100 times the maximum width of the bottom surface 10a.

[0050] In this embodiment, a predetermined reference position 24 is set in space 23. The reference position 24 is set at any position within space 23, for example, at the origin of space 23 (where both the x-axis and y-axis coordinates are zero). A predetermined position 25 is identified relative to this reference position 24. The first object model 21 is set within space 23 such that the first analytical coordinate system 21a is located at this position 25. Then, the space 23 surrounding the first object model 21 is discretized by a finite number of elements G(i) (i=1, 2, ...) as shown in Figure 6. This sets up the first computational grid 31 (shown in Figure 6) associated with the first object model 21.

[0051] In this embodiment, each element G(i), like element F(i), uses an Euler element capable of handling fluid (air) using the finite volume method. Each element G(i) can be assigned the fluid (air) velocity, characteristics, etc. Each element G(i) is provided with multiple nodes 26. In this embodiment, the space 23 is discretized so that the nodes 26 of the first computational grid 31 and the nodes 16 of the first object model 21 (shown in Figure 4) are shared. Furthermore, physical quantities in the fluid (pressure in this example) can be calculated at each node 26. Note that the physical quantities are not limited to those calculated at each node 26, but may also be calculated at each element G(i).

[0052] The first computational grid 31 can be appropriately configured based on, for example, a known method (e.g., the procedure for setting up a sound space region described in the Patent Document (Japanese Patent No. 4792049)). Furthermore, the above-mentioned software can be used for discretization.

[0053] As shown in Figure 7, the second computational grid 32 is set in the space 23 surrounding the second object model 22 shown in Figure 5. In this embodiment, the second computational grid 32 is set excluding the area occupied by the second object model 22, but it is not limited to this configuration, and for example, the second computational grid 32 may be set including the area occupied by the second object model 22.

[0054] As shown in Figure 5, the space 23 in this embodiment, like the space 23 shown in Figure 4, has a size that completely surrounds the second object model 22, but is not limited to this configuration. For example, the space 23 may have a size that surrounds only a part of the second object model 22, as long as it includes the region to be analyzed. Furthermore, the space 23 is set up, for example, in the same way as the space 23 of the first computational grid 31, and the details, including the first length L1 and the second length L2, are as described above.

[0055] In this embodiment, the space 23 is defined by the aforementioned reference position 24 and the aforementioned position 25 relative to the reference position 24. The second object model 22 is set up in space 23 such that the second analytical coordinate system 21b is located at this position 25. As a result, the first analytical coordinate system 21a of the first object model 21 shown in Figure 4 and the second analytical coordinate system 21b of the second object model 22 are located at the same position 25 in each of the spaces 23. The space 23 surrounding the second object model 22 is then discretized by a finite number of elements G(i) (i=1, 2, ...) shown in Figure 7. This sets up the second computational grid 32 (shown in Figure 7) associated with the second object model 22. Details of the elements G(i) are as described above. Furthermore, in this embodiment, the space 23 is discretized so that the nodes 26 of the second computational grid 32 and the nodes 16 of the second object model 22 (shown in Figure 4) are shared.

[0056] As described above, the first shape 11A of the first object model 21 associated with the first computational grid 31 shown in Figure 6 and the second shape 12A of the second object model 22 associated with the second computational grid 32 shown in Figure 7 are different from each other. Therefore, at least some of the nodes 26 of the first computational grid 31 that are shared with the nodes 16 of the first object model 21 (shown in Figure 4) and the nodes 26 of the second computational grid 32 that are shared with the nodes 16 of the second object model 22 (shown in Figure 5) have different relative positions in space 23.

[0057] In general, in fluid analysis, it is important to compare physical quantities calculated at the same location for multiple objects 10 (shown in Figure 2) with different shapes (i.e., physical quantities with the same weight in space 23). For this reason, if the locations of the nodes 26 or elements G(i) where the fluid's physical quantities are calculated differ in the analysis regions of the first computational grid 31 and the second computational grid 32 shown in Figures 6 and 7, it is not easy to compare the fluid analysis results.

[0058] In this embodiment, when the first analytical coordinate system 21a shown in Figure 6 and the second analytical coordinate system 21b shown in Figure 7 are aligned, the first computational grid 31 and the second computational grid 32 include a common computational grid area 35 (shown in Figures 6 and 7) where the nodes 26 or elements G(i) (in this example, the nodes 26 where physical quantities are calculated) are located at the same positions. In these common computational grid areas 35, the physical quantities of the fluid are calculated at the same positions in the first computational grid 31 and the second computational grid 32, respectively, making it possible to easily compare the fluid analysis results.

[0059] The common computational grid area 35 can be set as appropriate. In this embodiment, prior to the discretization of the first computational grid 31 and the second computational grid 32 by element G(i), virtual regions 36 having the same shape as the common computational grid area 35 are set in the respective spaces 23 shown in Figures 4 and 5. At this time, each virtual region 36 is positioned spaced apart from the first object model 21 and the second object model 22, and is positioned at the same position with respect to the reference position 24 in each space 23.

[0060] Next, when the first analytical coordinate system 21a and the second analytical coordinate system 21b are aligned, each virtual region 36 (common computational grid area 35) is discretized by element G(i) such that the nodes 26 or elements G(i) (in this example, the nodes 26 for which physical quantities are calculated) within each virtual region 36 are in the same position. As described above, since each virtual region 36 is located spaced apart from the first object model 21 and the second object model 22, it can be discretized by element G(i) without being shared with the nodes 16 of the first object model 21 and the second object model 22 shown in Figures 4 and 5. For this reason, each virtual region 36 (common computational grid area 35) can be easily discretized by element G(i) such that the nodes 26 or elements G(i) (in this example, the nodes 26 for which physical quantities are calculated) within each virtual region 36 are in the same position. As a result, a common computational grid area 35 is set in the first computational grid 31 and the second computational grid 32, respectively. Such discretization can be easily performed by adjusting the parameters of the software described above.

[0061] As shown in Figures 4 to 7, the common computational grid area 35 (virtual region 36) in this embodiment is preferably set downstream (to the right in the figures) in the direction of fluid flow with respect to the first object model 21 and the second object model 22. Such a common computational grid area 35 makes it possible to analyze the physical quantities of the fluid after it has collided with and been affected by the first object 11 (first object model 21) and the second object 12 (second object model 22). In this embodiment, the common computational grid area 35 (virtual region 36) is set in a U-shape surrounding the first object model 21 and the second object model 22, but it is not limited to this configuration, and may be set in an inverted C-shape, for example.

[0062] Next, as shown in Figure 6, in the space 23 where the common computational grid area 35 is set, the region between the first object model 21 and the common computational grid area 35 (i.e., the region other than the common computational grid area 35) is discretized by element G(i). Similarly, as shown in Figure 7, in the space 23 where the common computational grid area 35 is set, the region between the second object model 22 and the common computational grid area 35 (i.e., the region other than the common computational grid area 35) is discretized by element G(i). At this time, in each space 23, the nodes 26 of element G(i) are shared with the nodes 16 (shown in Figure 4) that constitute the contour of the first shape 11A of the first object model 21 and the nodes 16 (shown in Figure 5) that constitute the contour of the second shape 12A of the second object model 22. These first shape 11A and second shape 12A are different from each other. Therefore, when the first analytical coordinate system 21a and the second analytical coordinate system 21b are aligned, the first computational grid 31 and the second computational grid 32 each contain non-common computational grid areas 37 in which the node 26 or element G(i) (in this example, node 26) is located at different positions.

[0063] In this embodiment, the non-common computational grid area 37 is provided adjacent to the first object model 21 in the first computational grid 31, as shown in Figure 6, while it is provided adjacent to the second object model 22 in the second computational grid 32, as shown in Figure 7. In these non-common computational grid areas 37, the physical quantities of the fluid are calculated at nodes 26 or elements G(i) (node ​​26 in this example) located at different positions between the first computational grid 31 and the second computational grid 32. For this reason, the non-common computational grid area 37 is not suitable for comparing fluid analysis results.

[0064] In step S2 of this embodiment, the fifth computational grid (not shown), the sixth computational grid (not shown), and the seventh computational grid (not shown) are set up based on the same procedure as for the first computational grid 31 (shown in Figure 6) and the second computational grid 32 (shown in Figure 7).

[0065] The fifth computational grid is associated with a third object model (not shown) that mimics the third object 13 shown in Figure 2(c). Furthermore, when the first analytical coordinate system 21a (shown in Figure 6) and the third analytical coordinate system (not shown) are aligned, the first computational grid 31 (shown in Figure 6) and the fifth computational grid each contain a common computational grid area 35 and a non-common computational grid area 37, respectively.

[0066] The sixth computational grid is associated with a fourth object model (not shown) that mimics the fourth object 14 shown in Figure 2(d). Furthermore, when the first analytical coordinate system 21a (shown in Figure 6) and the fourth analytical coordinate system (not shown) are aligned, the first computational grid 31 (shown in Figure 6) and the sixth computational grid each contain a common computational grid area 35 and a non-common computational grid area 37, respectively.

[0067] The seventh computational grid is associated with a fifth object model (not shown) that mimics the fifth object 15 shown in Figure 2(e). Furthermore, when the first analytical coordinate system 21a (shown in Figure 6) and the fifth analytical coordinate system (not shown) are aligned, the first computational grid 31 (shown in Figure 6) and the seventh computational grid each contain a common computational grid area 35 and a non-common computational grid area 37, respectively.

[0068] In this embodiment, when the first analytical coordinate system 21a (shown in Figure 6), the second analytical coordinate system 21b (shown in Figure 7), and the third to fifth analytical coordinate systems (not shown) are aligned, the first computational grid 31 (shown in Figure 6), the second computational grid 32 (shown in Figure 7), and the fifth to seventh computational grids (not shown) include a common computational grid area 35 in which the nodes 26 or elements G(i) (in this example, the nodes 26 for which physical quantities are calculated) are located at the same positions. Each computational grid 30 is input to the computational grid storage unit 7B shown in Figure 1.

[0069] [Calculate the physical quantities of the fluid using the object model and computational grid (calculation step)] Next, in the fluid simulation method of this embodiment, under predetermined conditions, the physical quantities of the fluid are calculated using the object model 20 and computational grid 30 shown in Figures 6 and 7 (calculation step S3). The conditions are not particularly limited as long as they are used for calculating the physical quantities of the fluid. The conditions in this embodiment include the fluid velocity. The velocity is set appropriately according to the purpose of the analysis, for example, to 5 to 30 m / s (10 m / s in this example).

[0070] In the calculation step S3 of this embodiment, first, the object model 20 (shown in Figures 6 and 7) input to the object model storage unit 7A shown in Figure 1, and the calculation grid 30 (shown in Figures 6 and 7) input to the calculation grid storage unit 7B, are loaded into the working memory 5C. Furthermore, the physical quantity calculation unit 8C included in the program unit 8 is loaded into the working memory 5C. The physical quantity calculation unit 8C is a program that calculates the physical quantities of the fluid using the object model 20 and the calculation grid 30. By executing this physical quantity calculation unit 8C by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for calculating the physical quantities of the fluid. Figure 8 is a flowchart showing an example of the processing procedure in the calculation step S3.

[0071] First, in calculation step S3 of this embodiment, the physical quantity of the fluid (in this example, the pressure of the air) is calculated using the first object model 21 and the first calculation grid 31 shown in Figure 6 (first calculation step S31). In this embodiment, in the first calculation grid 31, the inflow F1 of the fluid (air) is defined on the front wall 30f on one side in the fluid flow direction (x-axis direction). Furthermore, the outflow F2 of the fluid (air) is defined on the rear wall 30b on the other side in the fluid flow direction (x-axis direction). As a result, in the first calculation grid 31, the fluid flowing along the flow direction is calculated for the first object model 21, and a simulation can be performed in which the fluid (air) is in contact with the first object 11 shown in Figure 2(a). Note that the inflow F1 and outflow F2 of the fluid are not limited to this configuration, and for example, they may be defined by swapping the front wall 30f and the rear wall 30b, or they may be defined in the vertical or diagonal direction.

[0072] In this embodiment, the motion of the fluid (air) flowing through the first object model 21 can be calculated at each unit time (small time interval) of the simulation. For such simulations, commercially available fluid analysis application software such as STAR-CD from CD-adapco or FLUNET from ANSYS can be used.

[0073] At each node 26 or element G(i) (node ​​26 in this example) that constitutes the first computational grid 31, a physical quantity (air pressure in this example) is calculated. The physical quantity is calculated at each unit time (infinite time) from the start to the end of the simulation. The unit time is set to, for example, 0.5 to 5.0 microseconds (1.0 microsecond in this example). Also, from the start (t=t0) to the end (t=t0) of the simulation n The time until ) is set to 1.0 to 10.0 seconds (1.5 seconds in this example). The physical quantities calculated at each node 26 or each element G(i) (each node 26 in this example) of the first computation grid 31 can be input to the physical quantity storage unit 7C shown in Figure 1 at intervals of unit time from the start to the end of the simulation.

[0074] Next, in calculation step S3 of this embodiment, based on the procedure described above, the physical quantities of the fluid are calculated using the second object model 22 and the second computational grid 32 shown in Figure 7 (second calculation step S32). The physical quantities calculated at each node 26 or each element G(i) (in this example, each node 26) of the second computational grid 32 can be input into the physical quantity storage unit 7C shown in Figure 1 at intervals of unit time from the start to the end of the simulation.

[0075] Figure 9(a) is a contour plot showing an example of a physical quantity C1 calculated in the first computational grid 31 (hereinafter referred to as the "first physical quantity"). In Figure 9(a), the first physical quantity C1 is shown in a part of the first computational grid 31, including the common computational grid area 35 shown in Figure 6. Figure 9(b) is a contour plot showing an example of a physical quantity C2 calculated in the second computational grid 32 (hereinafter referred to as the "second physical quantity"). In Figure 9(b), the second physical quantity C2 is shown in a part of the second computational grid 32, including the common computational grid area 35 shown in Figure 7. As shown in Figures 9(a) and (b), the trends of the fluid flow field (first physical quantity C1 and second physical quantity C2) are different from each other, influenced by the first shape 11A and the second shape 12A, which are different from each other.

[0076] Figure 10 shows an example of physical quantities calculated in the computational grid 30. In Figure 10, the first physical quantity C1, the second physical quantity C2, and the seventh physical quantity C7 are shown as representative examples. Also, in Figure 10, the physical quantities are shown in a simplified form (sign only). The first physical quantity C1 is a physical quantity calculated in the common computational grid area 35 of the first computational grid 31 shown in Figure 6. The second physical quantity C2 is a physical quantity calculated in the common computational grid area 35 of the second computational grid 32 shown in Figure 7. The seventh physical quantity C7 is a physical quantity calculated in the common computational grid area of ​​the seventh computational grid, which is not shown.

[0077] In Figure 10, in the common computational grid area 35 of the first computational grid 31 shown in Figure 6, the first physical quantity C1 of node 26 at the smallest coordinate values ​​(x1, y1) is calculated for each unit time t. 1t From there, the largest coordinate value (x z , y zThe first physical quantity C1 of the node 26 in zt are arranged vertically in ascending order. Further, these first physical quantities C1 1t ~C1 zt are arranged horizontally in ascending order from the smallest unit time (t = t0) to the largest unit time (t = t n ). As a result, for all the nodes 26 in the common calculation grid area 35 of the first calculation grid 31, the first physical quantities C1 10 ~C1 zn calculated from the start to the end of the simulation can be specified as a matrix 27A (multidimensional data of the first physical quantity C1). Note that the arrangement of the first physical quantity C1 is not limited to such an order and can be arranged in any order.

[0078] Furthermore, in FIG. 10, similar to the first calculation grid 31, for all the nodes 26 or each element G(i) (in this example, each node 26) in the common calculation grid area 35 of the second calculation grid 32 shown in FIG. 7, the second physical quantity C2 10 ~C2 zn calculated from the start to the end of the simulation can be specified as a matrix 27B (multidimensional data of the second physical quantity C2). The arrangement order of this second physical quantity C2 10 ~C2 zn is the same as the arrangement order of the first physical quantity C1 10 ~C1 zn .

[0079] As shown in FIGS. 6 and 7, when the first analysis coordinate system 21a and the second analysis coordinate system 21b are aligned, the first calculation grid 31 and the second calculation grid 32 include a common calculation grid area 35 where the nodes 26 or each element G(i) (in this example, each node 26) are at the same position. The first physical quantity C1 and the second physical quantity C2 (shown in FIG. 10) of the nodes 26 (or each element G(i)) at the same position (coordinates) in these common calculation grid areas 35 can be compared respectively. As a result, the fluid analysis results of the first object 11 (the first object model 21) and the second object 12 (the second object model 22) with different shapes can be easily compared.

[0080] Furthermore, in calculation step S3 of this embodiment, as shown in Figure 8, the physical quantities of the fluid are calculated using a third object model (not shown) and a fifth computational grid based on the procedure described above (third calculation step S33). Furthermore, the physical quantities of the fluid are calculated using a fourth object model (not shown) and a sixth computational grid (fourth calculation step S34). Furthermore, the physical quantities of the fluid are calculated using a fifth object model (not shown) and a seventh computational grid (fifth calculation step S35). The physical quantities calculated at each node or element (in this example, the node where the physical quantity is calculated) of the fifth computational grid, the sixth computational grid, and the seventh computational grid can be input to the physical quantity storage unit 7C shown in Figure 1 at intervals of unit time from the start to the end of the simulation.

[0081] In Figure 10, similar to the first computational grid 31, for each common computational grid area 35 of the fifth computational grid (not shown) to the seventh computational grid (not shown), the matrices 27E to 27G (fifth physical quantity C5 to seventh physical quantity C7) calculated at all nodes 26 or elements G(i) (node ​​26 in this example) from the start to the end of the simulation are shown. 10 ~C5 zn ~7th physical quantity C7 10 ~C7 zn Each of the multidimensional data (of which) can be identified. Fifth physical quantity C5 10 ~C5 zn The order of the items, the sixth physical quantity C6 10 ~C6 zn The order of the elements, and the seventh physical quantity C7 10 ~C7 zn The order of these is: First physical quantity C1 10 ~C1 zn This is considered to be the same as the order of the following:

[0082] As described above, when the first analytical coordinate system 21a (shown in Figure 6) to the fifth analytical coordinate system (not shown) are aligned, the first computational grid 31 (shown in Figure 6), the second computational grid 32 (shown in Figure 7), and the fifth to seventh computational grids (not shown) include common computational grid areas 35 where nodes 26 or elements G(i) (node ​​26 in this example) are in the same position. The first physical quantities C1 to C7 of nodes 26 or elements G(i) in the same position in these common computational grid areas 35 can be compared. This makes it possible to easily compare the fluid analysis results of multiple objects 10 with different shapes (first objects 11 to fifth objects 15 shown in Figures 2(a) to (e)).

[0083] [Comparing physical quantities in the common computational grid area] Next, in the fluid simulation method of this embodiment, physical quantities calculated in the common computational grid area 35 of the computational grid are compared (step S4). In step S4 of this embodiment, as shown in Figure 10, a physical quantity (first physical quantity) C1 calculated in the common computational grid area 35 of the first computational grid 31 is compared with a physical quantity (second physical quantity) C2 calculated in the common computational grid area 35 of the second computational grid 32.

[0084] In this implementation, in addition to the first physical quantity C1 and the second physical quantity C2, the fifth physical quantity C5 (not shown), the sixth physical quantity C6 (not shown), and the seventh physical quantity C7 mentioned above are compared, but are not particularly limited. The fifth physical quantity C5 is a physical quantity calculated in the common computational grid area 35 (not shown) in the fifth computational grid associated with the third object model (not shown), which mimics the third object 13 shown in Figure 2(c). The sixth physical quantity C6 is a physical quantity calculated in the common computational grid area 35 (not shown) in the sixth computational grid associated with the fourth object model (not shown), which mimics the fourth object 14 shown in Figure 2(d).

[0085] In step S4 of this embodiment, first, the physical quantities of the common calculation grid area 35 (including the first physical quantity C1 and the second physical quantity C2 shown in Figure 10) input to the physical quantity storage unit 7C shown in Figure 1, and the comparison unit 8D included in the program unit 8 are loaded into the working memory 5C. The comparison unit 8D is a program for comparing the physical quantity (first physical quantity) C1 calculated in the common calculation grid area 35 of the first calculation grid 31 with the physical quantity (second physical quantity) C2 calculated in the common calculation grid area 35 of the second calculation grid 32. When this comparison unit 8D is executed by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for comparing physical quantities (including the first physical quantity C1 and the second physical quantity C2).

[0086] Comparison of physical quantities can be performed as appropriate. As shown in Figures 6 and 7, when the first analytical coordinate system 21a and the second analytical coordinate system 21b are aligned, the first computational grid 31 and the second computational grid 32 include a common computational grid area 35 in which the nodes 26 or elements G(i) (node ​​26 in this example) are at the same positions. As described above, in fluid analysis, it is important to compare physical quantities calculated at the same positions for multiple objects 10 with different shapes. For this reason, the first physical quantity C1 and the second physical quantity C2 (shown in Figures 9 and 10) calculated at each node 26 or element G(i) (node ​​26 in this example) in these common computational grid areas 35 may be output to the output device 4 shown in Figure 1. This makes it possible to easily compare the results of fluid analysis of the first object 11 and the second object 12 (shown in Figures 2(a) and (b)) with different shapes.

[0087] Step S4 of this embodiment may include a step of performing an intrinsic orthogonal decomposition on the first physical quantity C1 and the second physical quantity C2 shown in Figure 10.

[0088] Proper Orthogonal Decomposition (POD) is a method for extracting low-dimensional components from multidimensional data such as the first physical quantity C1 to the seventh physical quantity C7 shown in Figure 10. This proper orthogonal decomposition is also called Principal Component Analysis (PCA), and it can decompose the first physical quantity C1 to the seventh physical quantity C7 into multiple basis vectors that indicate the direction of large variance, and the coefficients of each of these basis vectors. These basis vectors are extracted for each of the multiple modes (principal components).

[0089] In proper orthogonal decomposition, by comparing coefficients for multiple basis vectors (i.e., basis vectors for multiple modes), it becomes possible to identify regions where the variance of a physical quantity is large (i.e., regions where the flow is characteristic). Furthermore, by summing the values ​​obtained by multiplying these basis vectors by coefficients, the original physical quantity can be restored. Details of proper orthogonal decomposition are as described in Non-Patent Document 1 above.

[0090] For example, when the first physical quantity C1 and the second physical quantity C2 are independently decomposed into their intrinsic orthogonal vectors, different basis vectors are calculated for each mode. This is because the trends of the fluid flow field (first physical quantity C1 and second physical quantity C2) shown in Figure 9 differ due to the difference between the first shape 11A of the first object model 21 (shown in Figure 6) and the second shape 12A of the second object model 22 (shown in Figure 7). Thus, when the basis vectors of each mode differ, the parts where the variance of the first physical quantity C1 and the second physical quantity C2 is large (i.e., the parts where the flow is characteristic) also differ. For this reason, it is difficult to quantitatively compare the physical quantities (first physical quantity C1 and second physical quantity C2) because coefficients with different basis vectors cannot be simply compared.

[0091] In this embodiment, a known Global POD (hereinafter sometimes referred to as "G-POD") is performed, which is a method for aligning the basis vectors of each mode (for example, mode 0 to mode 40) (obtaining a common basis vector). In this embodiment, prior to performing G-POD, the fluctuation component obtained by subtracting the physical quantity by the average value of the physical quantity may be calculated. By performing G-POD on such a fluctuation component, characteristic parts of the flow can be extracted more efficiently compared to, for example, when G-POD is performed on the physical quantity as is. Figure 11 is a diagram showing an example of the fluctuation component of a physical quantity.

[0092] In this embodiment, the first physical quantity C1 is measured at each unit time shown in Figure 10. 10 ~C1 zn The average value of the first physical quantity C1 10 ~C1 zn The first variable component D1 obtained by subtracting each of the above. 10 ~D1 zn This is obtained. This generates a matrix 28A of the first variation component D1, in which the coordinate values ​​and unit time are arranged in ascending order. Furthermore, using the same procedure as for the matrix 28A of the first variation component D1, the second physical quantity C2 is obtained for each time interval shown in Figure 10. 10 ~C2 zn The average value of the second physical quantity C2 10 ~C2 zn The second variable component D2 obtained by subtracting each of the above. 10 ~D2 znThis is obtained. As a result, a matrix 28B of the second variation component D2 is generated in which the coordinate values ​​and unit time are arranged in ascending order. In this embodiment, the first physical quantity C1 and the second physical quantity C2 shown in Figure 10 are calculated in a common computational grid area 35 where the nodes 26 or elements G(i) (node ​​26 in this example) are at the same position, so the weights in space 23 of the first variation component D1 in matrix 28A shown in Figure 11 and the second variation component D2 in matrix 28B are common. These matrices 28A of the first variation component D1 and 28B of the second variation component D2 are arranged, for example, in the direction of the time series of unit time (horizontal direction in Figure 10) and merged, and an intrinsic orthogonal decomposition is performed on the resulting matrix. As a result, the matrix 28A of the first variation component D1 and the matrix 28B of the second variation component D2 can be decomposed into a plurality of basis vectors common to the first variation component D1 and the second variation component D2 (i.e., basis vectors common to each mode) and the coefficients of each of the plurality of basis vectors.

[0093] In this embodiment, the fifth physical quantity C5 (not shown) is calculated at each unit time using the same procedure as for matrix 28A of the first variation component D1. 10 ~C5 zn The average value of the fifth physical quantity C5 10 ~C5 zn The fifth variable component D5 obtained by subtracting each of the above. 10 ~D5 zn This is obtained. This generates a matrix 28E of the fifth variation component D5, in which the coordinate values ​​and unit time are arranged in ascending order. Furthermore, for each unit time, the sixth physical quantity C6 (not shown) is obtained. 10 ~C6 zn The average value of the sixth physical quantity C6 10 ~C6 zn The sixth variable component D6 obtained by subtracting each of the above. 10 ~D6 zn This is obtained. This generates a matrix 28F of the sixth variation component D6, in which the coordinate values ​​and unit time are sorted in ascending order. Furthermore, for each unit time, the seventh physical quantity C7 10 ~C7 zn The average value of the seventh physical quantity C7 10 ~C7 zn The seventh variable component D7 obtained by subtracting each of the above. 10~D7 zn This is obtained. This generates a matrix 28G of the seventh variation component D7, in which the coordinate values ​​and unit time are arranged in ascending order. Then, an intrinsic orthogonal decomposition is performed on the matrix obtained by combining the matrix 28A of the first variation component D1, the matrix 28B of the second variation component D2, the matrix of the fifth variation component D5, the matrix of the sixth variation component D6, and the matrix 28G of the seventh variation component D7. As a result, the first variation component D1, the second variation component D2, the fifth variation component D5, the sixth variation component D6, and the seventh variation component D7 can be decomposed into a plurality of common basis vectors (i.e., common basis vectors in each mode) and the coefficients of each of the plurality of basis vectors.

[0094] Figure 12(a) is a contour plot showing an example of a basis vector for the 0th mode. Figure 12(b) is a contour plot showing an example of a basis vector for the 2nd mode. In Figure 12, the coordinate values ​​of the first analytical coordinate system 21a (shown in Figure 6) and the second analytical coordinate system 21b (shown in Figure 7) are set to (0,0). Figure 13(a) is a graph showing the relationship between the coefficients of the basis vector for the 0th mode and the unit time of the simulation. Figure 13(b) is a graph showing the relationship between the coefficients of the basis vector for the 2nd mode and the unit time of the simulation.

[0095] In step S4 of this embodiment, intrinsic orthogonal decomposition (G-POD in this example) is performed on the first physical quantity C1 and the second physical quantity C2 shown in Figure 10 (in this example, the first fluctuation component D1 and the second fluctuation component D2 shown in Figure 11). As a result, the first physical quantity C1 and the second physical quantity C2 (first fluctuation component D1 and second fluctuation component D2) can be decomposed into a common basis vector (shown in Figure 12) and the coefficients of each basis vector (shown in Figure 13). Since the basis vector shown in Figure 12 shows a characteristic part common to the first physical quantity C1 and the second physical quantity C2 (the part with large variance), the first physical quantity C1 and the second physical quantity C2 can be quantitatively compared based on the coefficients of each mode shown in Figure 13. This makes it possible to easily compare the fluid analysis results for the first object 11 and the second object 12 (shown in Figures 2(a) and (b)), which have different shapes.

[0096] Furthermore, in step S4 of this embodiment, intrinsic orthogonal decomposition (G-POD in this example) is performed on the first physical quantity C1, second physical quantity C2, fifth physical quantity C5, sixth physical quantity C6, and seventh physical quantity C7 shown in Figure 10 (in this example, the first fluctuation component D1, second fluctuation component D2, fifth fluctuation component D5, sixth fluctuation component D6, and seventh fluctuation component D7 shown in Figure 11). This makes it possible to easily compare the fluid analysis results for the first object 11, second object 12, third object 13, fourth object 14, and fifth object 15 (shown in Figures 2(a) to (e)), which have different shapes. The basis vectors and coefficients are input to the decomposition result storage unit 7D shown in Figure 1.

[0097] In step S4, the difference between the coefficients of the first physical quantity C1, the second physical quantity C2, the fifth physical quantity C5, the sixth physical quantity C6, and the seventh physical quantity C7 shown in Figure 13 may be calculated for each mode. This allows for a quantitative comparison of the fluid analysis results of the objects 10 (first object 11 to fifth object 15) shown in Figures 2(a) to (e).

[0098] [Evaluating the physical quantities of the object being analyzed] Next, in the fluid simulation method of this embodiment, the quality of the physical quantities of the object to be analyzed 10 shown in Figure 2 is evaluated (step S5). The quality of the physical quantities may be evaluated by the fluid simulation device 1A (computer 1) shown in Figure 1, or by an operator or the like. Furthermore, the quality of the physical quantities in this embodiment is performed based on basis vectors (shown in Figure 12) and coefficients (shown in Figure 13), but is not limited to this configuration. For example, the quality of the physical quantities may be evaluated based on the physical quantities (shown in Figure 10) calculated at each node 26 or each element G(i) (in this example, each node 26) of the common computational grid area 35 shown in Figures 6 and 7.

[0099] In step S5 of this embodiment, first, the basis vectors (shown in Figure 12) and coefficients (shown in Figure 13) input to the decomposition result storage unit 7D shown in Figure 1, and the evaluation unit 8E included in the program unit 8 are loaded into the working memory 5C. The evaluation unit 8E is a program for evaluating the quality of the physical quantities of the object to be analyzed 10. When this evaluation unit 8E is executed by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for evaluating physical quantities.

[0100] The quality of the physical quantities of the object being analyzed 10 can be evaluated as appropriate. In this embodiment, the first physical quantity C1, the second physical quantity C2, and the fifth to seventh physical quantities C5 to C7 (in this example, the first variation component D1, the second variation component D2, and the fifth to seventh variation components D7 shown in Figure 11) are decomposed into a plurality of basis vectors (shown in Figure 12) and coefficients (shown in Figure 13). In this case, for example, the physical quantity restored by multiplying the basis vector selected according to the purpose of the analysis by the coefficient may be judged as good if it is less than a predetermined threshold. The threshold can be set as appropriate, for example, according to the performance required of the object being analyzed (e.g., air resistance).

[0101] If the physical quantities of the object to be analyzed 10 are deemed to be good (Yes in step S5), the object to be analyzed 10 deemed to be good (shown in Figure 2) is manufactured (step S6). On the other hand, if the physical quantities of the object to be analyzed 10 are deemed to be unsatisfactory (No in step S5), the shape of the object to be analyzed 10 is changed (step S7), and steps S1 to S5 are repeated. In this embodiment, when air pressure or its coefficient is calculated as a physical quantity, the shape of the part that is increasing those physical quantities is changed in step S7. Such changes may be made by an operator or the like, or by a computer 1 based on a known optimization method or the like. This ensures that the object to be analyzed 10 with reduced air resistance is reliably designed and manufactured.

[0102] [Fluid Simulation Method (Second Embodiment)] In the fluid simulation method of the previous embodiment, a first computational grid 31 and a second computational grid 32, including the common computational grid area 35 shown in Figures 6 and 7, were set up, and the physical quantities calculated in each common computational grid area 35 were compared. However, the invention is not limited to this configuration. For example, physical quantities calculated in a first computational grid and a second computational grid with different grid divisions (i.e., not including the common computational grid area 35) may be transferred to a third computational grid and a fourth computational grid, and the resulting physical quantities may be compared. These third and fourth computational grids are grid-divided separately from the first and second computational grids and have the same grid division structure. Figure 14 is a flowchart showing an example of a fluid simulation method of another embodiment of the present invention.

[0103] [Setting the object model (Second embodiment)] In the fluid simulation method of this embodiment, first, an object model 20 that mimics the object 10 to be analyzed shown in Figure 2 is set (step S1).

[0104] In this embodiment, as in previous embodiments, a first object model 21 having the first shape 11A shown in Figure 4 and a second object model 22 having the second shape 12A shown in Figure 5 are set. Note that, as in previous embodiments, a first analytical coordinate system 21a and a second analytical coordinate system 21b are set for the first object model 21 and the second object model 22, but these may be omitted.

[0105] Furthermore, in this embodiment, as in previous embodiments, a third object model (not shown) having the third shape 13A shown in Figure 2(c) is set. Furthermore, a fourth object model (not shown) having the fourth shape 14A shown in Figure 2(d) is set. Furthermore, a fifth object model (not shown) having the fifth shape 15A shown in Figure 2(e) is set. Note that, as in previous embodiments, a third analytical coordinate system (not shown) to a fifth analytical coordinate system is set for the third to fifth object models, but these may be omitted. The object models 20 (in this example, the first object model 21 to the fifth object model (not shown)) are input to the object model storage unit 7A shown in Figure 1.

[0106] [Setting up the computational grid (second embodiment)] Next, in the fluid simulation method of this embodiment, a computational grid 30 having multiple nodes 26 or multiple elements G(i) for calculating the physical quantities of the fluid is set up in the space 23 surrounding the object model 20 shown in Figures 4 and 5 (step S2). Figure 15 shows a first object model 21 and a first computational grid 31 of another embodiment of the present invention. Figure 16 shows a second object model 22 and a second computational grid 32 of another embodiment of the present invention.

[0107] In this embodiment, as in previous embodiments, a first computational grid 31 associated with the first object model 21 shown in Figure 4 (shown in Figure 15) and a second computational grid 32 associated with the second object model 22 shown in Figure 5 (shown in Figure 16) are set up. However, in this embodiment, unlike previous embodiments, the second computational grid 32 has a different grid division than the first computational grid 31 (i.e., it does not include the common computational grid area 35 shown in Figures 6 and 7).

[0108] The first computational grid 31 and the second computational grid 32 can be set as appropriate, provided that they have different grid divisions. In this embodiment, unlike the previous embodiments shown in Figures 4 and 5, a common computational grid area 35 (virtual region 36) is not set in the space 23 surrounding the first object model 21 and the second object model 22, respectively. Then, without distinguishing the common computational grid area 35 (virtual region 36), each space 23 is discretized collectively using a finite number of elements G(i). As a result, each space 23 is independently grid-divided according to the nodes 16 of the first object model 21 having a first shape 11A (shown in Figure 4) and the nodes 16 of the second object model 22 having a second shape 12A (shown in Figure 5). At least some of the nodes 26 or elements G(i) of the first computational grid 31 (shown in Figure 15) and the nodes 26 or elements G(i) of the second computational grid 32 (shown in Figure 16) are in different relative positions in space 23. Therefore, the first computational grid 31 and the second computational grid 32 in this embodiment mainly include non-common computational grid areas 37.

[0109] In this embodiment, the first computational grid 31 and the second computational grid 32 have different grid divisions (in this example, mainly non-common computational grid area 37 is included). As a result, unlike previous embodiments which include a common computational grid area 35 as shown in Figures 6 and 7, the first computational grid 31 and the second computational grid 32 in this embodiment can discretize the space 23 all at once, thus shortening the setup time for the computational grid 30. On the other hand, in the first computational grid 31 and the second computational grid 32 in this embodiment, the positions of the nodes 26 or elements G(i) (node ​​26 in this example) where the physical quantities of the fluid are calculated are different, making it difficult to compare the fluid analysis results.

[0110] In this embodiment, in the transfer step S8 described later, the first physical quantity of each node 26 or element G(i) (in this example, node 26) of the first computational grid 31 and the second physical quantity of each node 26 or element G(i) (in this example, node 26) of the second computational grid 32 are transferred to the third and fourth computational grids, respectively, which have the same grid division structure. This makes it possible to easily compare the fluid analysis results based on the physical quantities of each node or element (in this example, element) of the third computational grid (hereinafter sometimes referred to as the "third physical quantity") and the physical quantities of each node or element (in this example, element) of the fourth computational grid (hereinafter sometimes referred to as the "fourth physical quantity").

[0111] In step S2 of this embodiment, a fifth computational grid (not shown), a sixth computational grid (not shown), and a seventh computational grid (not shown) are set up based on the same procedure as for the first computational grid 31 (shown in Figure 15) and the second computational grid 32 (shown in Figure 16).

[0112] In this embodiment, the fifth computational grid (not shown) is associated with a third object model (not shown) that mimics the third object 13 shown in Figure 2(c), and has a different grid division than the first computational grid 31 (shown in Figure 15). The sixth computational grid (not shown) is associated with a fourth object model (not shown) that mimics the fourth object 14 shown in Figure 2(d), and has a different grid division than the first computational grid 31. The seventh computational grid (not shown) is associated with a fifth object model (not shown) that mimics the fifth object 15 shown in Figure 2(e), and has a different grid division than the first computational grid 31.

[0113] Thus, the first computational grid 31, the second computational grid 32, and the fifth to seventh computational grids of this embodiment mainly include non-common computational grid areas 37 in which the nodes 26 or elements G(i) (nodes 26 in this example) are located at different positions from each other. Each computational grid 30 is input to the computational grid storage unit 7B shown in Figure 1.

[0114] [Calculate the physical quantities of the fluid using the object model and computational grid] Next, in the fluid simulation method of this embodiment, similar to previous embodiments, the physical quantities of the fluid are calculated under predetermined conditions using the object model 20 and computational grid 30 shown in Figures 15 and 16 (calculation step S3).

[0115] In the calculation step S3 of this embodiment, as in previous embodiments, the first calculation step S31, the second calculation step S32, the third calculation step S33, the fourth calculation step S34, and the fifth calculation step S35 are performed, as shown in Figure 8.

[0116] In the first calculation step S31, the fluid's physical quantity (first physical quantity) C1 is calculated using the first object model 21 and the first computational grid 31 shown in Figure 15. In the second calculation step S32, the fluid's physical quantity (second physical quantity C2) is calculated using the second object model 22 and the second computational grid 32 shown in Figure 16. The physical quantities (first physical quantity C1 and second physical quantity C2) calculated at each node 26 or element G(i) (node ​​26 in this example) of the first computational grid 31 and the second computational grid 32 can be input into the physical quantity storage unit 7C shown in Figure 1 at intervals of unit time from the start to the end of the simulation.

[0117] In the third calculation step S33, the physical quantities of the fluid (fifth physical quantity C5) are calculated using a third object model (not shown) and a fifth computational grid. In the fourth calculation step S34, the physical quantities of the fluid (sixth physical quantity C6) are calculated using a fourth object model (not shown) and a sixth computational grid. In the fifth calculation step S35, the physical quantities of the fluid (seventh physical quantity C7) are calculated using a fifth object model (not shown) and a seventh computational grid. The physical quantities calculated at each node or element (node ​​in this example) of the fifth computational grid, sixth computational grid, and seventh computational grid can be input into the physical quantity storage unit 7C shown in Figure 1 at intervals of unit time from the start to the end of the simulation.

[0118] [Transferring physical quantities at each node onto the computational grid (transfer step)] Next, in the fluid simulation method of this embodiment, the physical quantities of each node 26 or element G(i) (node ​​26 in this example) of the computational grid 30 obtained in calculation step S3 are transferred to a computational grid (not shown) that is divided into a grid separately from the computational grid 30 using interpolation (transfer step S8).

[0119] In the transfer step S8 of this embodiment, first, the physical quantities of each node 26 or element G(i) (in this example, node 26) of the computational grid 30, which are input to the physical quantity storage unit 7C shown in Figure 1, and the transfer unit 8F included in the program unit 8 are loaded into the working memory 5C. The transfer unit 8F is a program for transferring the physical quantities of each node 26 or element G(i) (in this example, node 26) of the computational grid 30 obtained in the calculation step S3 onto a computational grid (not shown) that has been grid-divided separately from the computational grid 30, using interpolation processing. By executing this transfer unit 8F by the processor 5A, the computer 1 (fluid simulation device 1A) can be made to function as a means for transferring physical quantities. Figure 17 is a flowchart showing an example of the processing procedure of the transfer step S8.

[0120] The transfer step S8 of this embodiment includes a first transfer step S81 and a second transfer step S82. In the first transfer step S81, the physical quantity (first physical quantity) C1 of each node 26 or element G(i) (in this example, node 26) obtained in the first calculation step S31 is transferred to a third calculation grid that is grid-divided separately from the first calculation grid 31 (shown in Figure 15) using interpolation. In the second transfer step S82, the physical quantity (second physical quantity) C2 of each node 26 or element G(i) (in this example, node 26) obtained in the second calculation step S32 is transferred to a fourth calculation grid that is grid-divided separately from the second calculation grid 32 (shown in Figure 16) using interpolation. Figure 18(a) shows an example of the first calculation grid 31. Figure 18(b) shows an example of the third calculation grid 33. Figure 19(a) shows an example of the second calculation grid 32. Figure 19(b) shows an example of the fourth computational grid 34.

[0121] The third computational grid 33 shown in Figure 18(b) and the fourth computational grid 34 shown in Figure 19(b) have the same grid division structure. Therefore, the third computational grid 33 and the fourth computational grid 34 have the same shape (contour). The third computational grid 33 and the fourth computational grid 34 can be set up by discretizing these contours with a finite number of elements H(i) (i=1, 2, ...). When the contours of the third computational grid 33 and the fourth computational grid 34 are superimposed so that they are aligned, the nodes 46 or elements H(i) (node ​​46 in this example) of the third computational grid 33 and the nodes 46 or elements H(i) (node ​​46 in this example) of the fourth computational grid 34 are discretized to be in the same position. Such discretization can be easily performed by adjusting the parameters of the software described above.

[0122] The third computational grid 33 shown in Figure 18(b) has the same shape as the target region 45 (shown by a white frame in the figure) to which the first physical quantity C1 of the first computational grid 31 shown in Figure 18(a) is transferred. The fourth computational grid 34 shown in Figure 19(b) has the same shape as the target region 45 (shown by a white frame in the figure) to which the second physical quantity C2 of the second computational grid 32 shown in Figure 19(a) is transferred. These target regions 45 are preferably set downstream (to the right in the figure) in the direction of fluid flow with respect to the first object model 21 and the second object model 22, similar to the common computational grid area 35 (virtual region 36) shown in Figures 6 and 7. This makes it possible to analyze the physical quantities of the fluid after it has collided with and fluctuated against the first object 11 (first object model 21) and the second object 12 (second object model 22), respectively. The contours of the target region 45 (third computation grid 33 and fourth computation grid 34) shown in Figures 18(a) and 19(b), respectively, are set in a U-shape surrounding the first object model 21 and the second object model 22, but the configuration is not limited to this. For example, the target region 45 may be set in an inverted C-shape or a rectangular shape. Also, the third computation grid 33 may be divided into smaller or larger grid sections than the first computation grid 31, depending on the computation time and analysis accuracy, for example. Similarly, the fourth computation grid 34 may be divided into smaller or larger grid sections than the second computation grid 32.

[0123] [First transcription step] In the first transfer step S81, the physical quantities of each node 26 or element G(i) (in this example, node 26) obtained in the first calculation step S31 are transferred onto the third calculation grid 33 shown in Figure 18(b) using interpolation. The interpolation can be performed as appropriate once the physical quantities (first physical quantities) C1 of each node 26 or element G(i) (in this example, node 26) obtained in the first calculation step S31 have been transferred onto the third calculation grid 33. The interpolation in this embodiment is performed based on at least one of linear interpolation and spline interpolation. Figure 20 shows the nodes 26 and 46 when the third calculation grid 33 shown in Figure 18(b) is superimposed on the target region 45 of the first calculation grid 31 shown in Figure 18(a). In Figure 20, the elements G(i) and node 26 of the first computational grid 31 are shown with dashed lines, and the elements H(i) and node 46 of the third computational grid 33 are shown with solid lines.

[0124] In this embodiment, based on linear interpolation, the first physical quantity C1 of node 26 (of the first computational grid 31) obtained in the first calculation step S31 is transferred to the third computational grid 33. In this case, as shown in Figure 20, one node 46 of the third computational grid 33 to which the first physical quantity C1 is transferred (hereinafter referred to as "target node 46a") and the nodes 26 of the first computational grid 31 surrounding the target node 46a (in this example, the first node 26a to the fourth node 26d) are identified. The coordinate values ​​of the target node 46a, the coordinate values ​​of the first node 26a to the fourth node 26d, and the first physical quantity C1 of the first node 26a to the fourth node 26d are as follows. Coordinate values: Coordinate values ​​of target node 46a: (x i , y i ) Coordinate values ​​of node 1, 26a: (x1, y1) Coordinates of node 26b: (x2, y1) Coordinate values ​​of node 3, 26c: (x1, y2) Coordinate values ​​of node 4, 26d: (x², y²) Physical quantity: First physical quantity at node 26a: C1 a The first physical quantity at node 26b: C1 b The first physical quantity at node 3, 26c: C1 c The first physical quantity at node 4, 26d: C1 d

[0125] Next, the coordinate values ​​of the first node 26a to the fourth node 26d, the coordinate value of the target node 46a, and the first physical quantity C1 of each node 26 (first node 26a to fourth node 26d) of the first computational grid 31. a ~C1 d The third physical quantity C3 of the target node 46a can be calculated by substituting these values ​​into the following equation (1).

[0126]

number

[0127] In this embodiment, all nodes 46 of the third computational grid 33 shown in Figures 18(b) and 20 are identified as target nodes 46a, and the first nodes 26a to the fourth nodes 26d of the first computational grid 31 surrounding these target nodes 46a are identified. Then, based on the linear interpolation described above, the third physical quantity C3 of the target nodes 46a can be calculated from the first physical quantity C1 of each node 26 (of the first computational grid 31) obtained in the first calculation step S31. The calculated third physical quantity C3 is then transferred to each of the target nodes 46a.

[0128] Thus, in this embodiment, the first physical quantity C1 of node 26 or element G(i) (node ​​26 in this example) obtained in the first calculation step S31 can be easily transferred to the third calculation grid 33 by performing the interpolation process based on linear interpolation. Alternatively, instead of linear interpolation, the interpolation process may be performed based on known spline interpolation. Compared to linear interpolation, such spline interpolation allows the first physical quantity C1 to be transferred to the third calculation grid 33 with greater accuracy.

[0129] In this embodiment, the first physical quantity C1 calculated at each unit time from the start to the end of the simulation can be transferred to the third computational grid 33. The third physical quantity C3 transferred to the third computational grid 33 can be input to the physical quantity storage unit 7C shown in Figure 1.

[0130] Figure 21 shows an example of physical quantities transferred to a computational grid. In Figure 21, the third physical quantity C3, the fourth physical quantity C4, and the tenth physical quantity C10 are shown as representative examples. The third physical quantity C3 is a physical quantity transferred to the third computational grid 33 (shown in Figure 18(b)). The fourth physical quantity C4 is a physical quantity transferred to the fourth computational grid 34 (shown in Figure 19(b)). The tenth physical quantity C10 is a physical quantity transferred to the tenth computational grid (not shown).

[0131] As shown in Figure 21, in this embodiment, in the third computational grid 33 shown in Figure 18(b), for each unit time t, the third physical quantity C3 of node 46 at the smallest coordinate value (x1, y1) is measured. 1t From there, the largest coordinate value (x z , y z The third physical quantity C3 at node 46 in ) zt They are arranged vertically in the order up to this point. Furthermore, these third physical quantity C3 1t ~C3 zt However, from the smallest unit time (t=t0) to the largest unit time (t=t0) n They are arranged horizontally in the order (ascending). As a result, at all nodes 46 of the third computation grid 33, the third physical quantity C3 is transferred from the first physical quantity C1 from the start to the end of the simulation. 10 ~C3 zn The matrix 29C (multidimensional data of the third physical quantity C3) can be identified.

[0132] [Second transcription step] In the second transfer step S82, based on the same procedure as in the first transfer step S81, the physical quantities of each node 26 or element G(i) (in this example, the node 26 shown in Figure 16) obtained in the second calculation step S32 are transferred onto the fourth calculation grid 34 shown in Figure 19(b) using interpolation.

[0133] In this embodiment, the second physical quantity C2 calculated at each unit time from the start to the end of the simulation can be transferred to the fourth computational grid 34. The fourth physical quantity C4 transferred to the fourth computational grid 34 can be input to the physical quantity storage unit 7C shown in Figure 1.

[0134] As shown in Figure 21, in this embodiment, in the fourth computational grid 34 shown in Figure 19(b), for each unit time t, the fourth physical quantity C4 of node 46 at the smallest coordinate value (x1, y1) 1t From there, the largest coordinate value (x z , y z The fourth physical quantity C4 at node 46 in ) zt They are arranged vertically in the order up to this point. Furthermore, these fourth physical quantity C4 1t ~C4 zt However, from the smallest unit time (t=t0) to the largest unit time (t=t0) n They are arranged horizontally in the order (ascending). As a result, at all nodes 46 of the fourth computation grid 34, the fourth physical quantity C4 is transferred from the second physical quantity C2 from the start to the end of the simulation. 10 ~C4 zn The matrix 29D (multidimensional data of the fourth physical quantity C4) can be identified.

[0135] As described above, the third computational grid 33 (shown in Figure 18(b)) and the fourth computational grid 34 (shown in Figure 19(b)) have the same grid division structure. By comparing the third physical quantity C3 of each node 46 or each element H(i) (in this example, each node 46) of the third computational grid 33 with the fourth physical quantity C4 of each node 46 or each element H(i) (in this example, each node 46) of the fourth computational grid 34, the first physical quantity C1 and the second physical quantity C2 at the same positions in the first computational grid 31 (shown in Figure 15) and the second computational grid 32 (shown in Figure 16) can be pseudo-compared.

[0136] The third computational grid 33 and the fourth computational grid 34 of this embodiment are grid-divided smaller than the first computational grid 31 and the second computational grid 32. With such third and fourth computational grids 33 and 34, the first physical quantity C1 of the first computational grid 31 and the second physical quantity C2 of the second computational grid 32 can be transferred with high resolution.

[0137] The transfer step S8 of this embodiment further includes a third transfer step S83, a fourth transfer step S84, and a fifth transfer step S85.

[0138] [Third Transfer Step] In the third transfer step S83, the physical quantity (fifth physical quantity) C5 of each node 26 or each element G(i) (in this example, each node 26) obtained in the third calculation step S33 is transferred onto an eighth computational grid (not shown) that is grid-divided separately from the fifth computational grid (not shown) using interpolation processing. As a result, an eighth physical quantity C8 is calculated (transferred) for each node or each element (in this example, each node) of the eighth computational grid.

[0139] In this embodiment, during the period from the start to the end of the simulation, the fifth physical quantity C5 calculated for each unit time can be transferred to an eighth computational grid not shown respectively. The eighth physical quantity C8 transferred to the eighth computational grid can be input to the physical quantity storage unit 7C shown in FIG. 1. In this embodiment, in the eighth computational grid not shown, for each unit time t, the eighth physical quantity C8 of the node 46 at the smallest coordinate values (x1, y1) 1t from, the largest coordinate values (x z , y z ) of the node 46 zt of the eighth physical quantity C8 are arranged vertically in order. Further, these eighth physical quantities C8 1t ~C8 zt are arranged horizontally in order (ascending order) from the smallest unit time (t = t0) to the largest unit time (t = t n ). As a result, for all nodes 46 of the eighth computational grid, the eighth physical quantity C8 transferred from the fifth physical quantity C5 from the start to the end of the simulation 10 ~C8 znThe matrix 29H (multidimensional data of the eighth physical quantity C8) can be specified.

[0140] [Fourth transfer step] In the fourth transfer step S84, the physical quantity (sixth physical quantity) C6 of each node 26 or each element G(i) (in this example, each node 26) obtained in the fourth calculation step S34 is transferred onto a ninth calculation grid (not shown) that is grid-divided separately from the sixth calculation grid (not shown) using interpolation processing. As a result, the ninth physical quantity C9 is calculated (transferred) for each node or each element (in this example, each node) of the ninth calculation grid.

[0141] In this embodiment, during the period from the start to the end of the simulation, the sixth physical quantity C6 calculated for each unit time can be transferred to a ninth calculation grid (not shown) respectively. The ninth physical quantity C9 transferred to the ninth calculation grid can be input to the physical quantity storage unit 7C shown in FIG. 1. In this embodiment, in the ninth calculation grid (not shown), for each unit time t, the ninth physical quantity C9 of the node 46 at the smallest coordinate values (x1, y1) 1t to z the ninth physical quantity C9 of the node 46 at the largest coordinate values (x z ) zt are arranged vertically in order. Furthermore, these ninth physical quantities C9 1t ~C9 zt are arranged horizontally in order (ascending order) from the smallest unit time (t = t0) to the largest unit time (t = t n ). As a result, for all nodes 46 of the ninth calculation grid, the ninth physical quantities C9 10 ~C9 zn transferred from the sixth physical quantity C6 from the start to the end of the simulation, i.e., the matrix 29I (multidimensional data of the ninth physical quantity C9), can be specified.

[0142] [Fifth transfer step] In the fifth transfer step S85, the physical quantity (seventh physical quantity) C7 of each node 26 or each element G(i) (in this example, each node 26) obtained in the fifth calculation step S35 is transferred using interpolation to the tenth calculation grid (not shown), which is grid-divided separately from the seventh calculation grid (not shown). As a result, the tenth physical quantity C10 is calculated (transferred) to each node or each element (in this example, each node) of the tenth calculation grid.

[0143] In this embodiment, the seventh physical quantity C7 calculated at each unit time from the start to the end of the simulation can be transferred to the tenth computational grid (not shown). The tenth physical quantity C10 transferred to the tenth computational grid can be input to the physical quantity storage unit 7C shown in Figure 1. As shown in Figure 21, in this embodiment, at each unit time t in the tenth computational grid (not shown), the tenth physical quantity C10 of node 46 at the smallest coordinate value (x1, y1) 1t From there, the largest coordinate value (x z , y z The tenth physical quantity C10 at node 46 in ) zt They are arranged vertically in the order up to [the specified order]. Furthermore, these 10th physical quantity C10 1t ~C10 zt However, from the smallest unit time (t=t0) to the largest unit time (t=t0) n They are arranged horizontally in the order (ascending). As a result, at all 46 nodes of the 10th computational grid, the 10th physical quantity C10 is transferred from the 7th physical quantity C7 from the start to the end of the simulation. 10 ~C10 zn The matrix 29J (multidimensional data of the fourth physical quantity C4) can be identified.

[0144] The third computational grid 33 (shown in Figure 18(b)), the fourth computational grid 34 (shown in Figure 19(b)), the eighth computational grid, the ninth computational grid, and the tenth computational grid have the same grid division structure. In these computational grids, the physical quantities C3-C4 and C8-C10 are compared. This allows for a pseudo-comparison of the physical quantities C1-C2 and C5-C7 calculated at the same position in the first computational grid 31 (shown in Figure 18(b)), the second computational grid 32 (shown in Figure 19(b)), the fifth computational grid, the sixth computational grid, and the seventh computational grid. Therefore, it becomes possible to easily compare the fluid analysis results of multiple analysis targets 10 with different shapes (the first target 11 to the fifth target 15 shown in Figures 2(a)-(e)).

[0145] [Comparing physical quantities in the common computational grid area] Next, in the fluid simulation method of this embodiment, the physical quantities of each node or element (each node in this example) of the transferred computational grid are compared (step S9). In step S9 of this embodiment, as shown in Figure 21, the physical quantity (third physical quantity) C3 of each node 46 or element F(i) (each node 46 in this example) of the third computational grid 33 is compared with the physical quantity (fourth physical quantity) C4 of each node or element (each node in this example) of the fourth computational grid 34.

[0146] In this implementation, in addition to the third physical quantity C3 and the fourth physical quantity C4, the eighth physical quantity C8 of each node or element (each node in this example) of the eighth computational grid (not shown), the ninth physical quantity C9 of each node or element (each node in this example) of the ninth computational grid (not shown), and the tenth physical quantity C10 of each node or element (each node in this example) of the tenth computational grid (not shown) are compared.

[0147] Comparison of physical quantities can be performed as appropriate. As shown in Figures 18(b) and 19(b), the third computational grid 33 and the fourth computational grid 34 have the same grid division structure. As mentioned above, in fluid analysis, it is important to compare physical quantities calculated at the same location for multiple objects 10 with different shapes. In this embodiment, the first physical quantity C1 and the second physical quantity C2 calculated in the first computational grid 31 (shown in Figure 15) and the second computational grid 32 (shown in Figure 16), respectively, are transferred to each node 46 or element H(i) (in this example, each node 46) of the third computational grid 33 and the fourth computational grid 34. The third physical quantity C3 and the fourth physical quantity C4 transferred to the third computational grid 33 and the fourth computational grid 34 make it possible to easily compare the results of fluid analysis of the first object 11 and the second object 12 (shown in Figures 2(a) and (b)), which have different shapes.

[0148] Step S9 of this embodiment may include a step of performing intrinsic orthogonal decomposition on the third physical quantity C3 and the fourth physical quantity C4 shown in Figure 21. In this embodiment, in addition to the third physical quantity C3 and the fourth physical quantity C4, Global POD (G-POD) is performed on the eighth physical quantity C8 (not shown), the ninth physical quantity C9 (not shown), and the tenth physical quantity C10 based on the procedure described above. At this time, as in previous embodiments, G-POD may be performed on the fluctuating components obtained by subtracting the physical quantities by the average value of the physical quantities. This allows for the efficient extraction of characteristic parts of the flow. Figure 22 is a diagram showing an example of the fluctuating components of physical quantities in another embodiment of the present invention.

[0149] In this embodiment, the matrix 40C represents the third variation component D3, the matrix 40D represents the fourth variation component D4, the matrix 40H represents the eighth variation component D8, the matrix 40I represents the ninth variation component D9, and the matrix 40J represents the tenth variation component D10.

[0150] Matrix 40C, as shown in Figure 21, represents the third physical quantity C3 at each unit time interval. 10 ~C3 zn The average value of the third physical quantity C3 10 ~C3 zn The third variable component D3 obtained by subtracting each of the above.10 ~D3 zn This is what was obtained. Matrix 40D is obtained for each unit time shown in Figure 21, for the fourth physical quantity C4 10 ~C4 zn The average value of the fourth physical quantity C4 10 ~C4 zn The fourth variable component D4 obtained by subtracting each of the above. 10 ~D4 zn This is what was obtained. Matrix 40H is obtained for each unit time, the 8th physical quantity C8 10 ~C8 zn The average value of the eighth physical quantity C8 10 ~C8 zn The eighth variation component D8 obtained by subtracting each of the above. 10 ~D8 zn This is what was obtained. Matrix 40I is obtained for each unit time, the 9th physical quantity C9 10 ~C9 zn The average value of the 9th physical quantity C9 10 ~C9 zn The 9th variation component D9 obtained by subtracting each of the above. 10 ~D9 zn This is what was obtained. Matrix 40J is obtained by the 10th physical quantity C10 at each unit time. 10 ~C10 zn The average value of the 10th physical quantity C10 10 ~C10 zn The 10th variation component D10 obtained by subtracting each of the above. 10 ~D10 zn This is what was obtained.

[0151] In step S9 of this embodiment, an intrinsic orthogonal decomposition (G-POD in this example) is performed on the third physical quantity C3 and the fourth physical quantity C4 (in this example, the third and fourth variation components D3 and D4 shown in Figure 22). Since the third and fourth physical quantities C3 and C4 are transferred to the third and fourth computational grids 33 and 34, which have the same lattice division structure, their weights in space 23 are common. By performing an intrinsic orthogonal decomposition on such a third and fourth physical quantity C3 and C4 (in this example, the third and fourth variation components D3 and D4 shown in Figure 22), they can be decomposed into a common basis vector (for example, shown in Figure 12) and the coefficients of each basis vector (for example, shown in Figure 13) in each mode. Since these basis vectors show a common characteristic part (a part with large variance) in the third and fourth physical quantities C3 and C4, the third and fourth physical quantities C3 and C4 can be quantitatively compared based on the coefficients of each mode. This makes it possible to easily compare the fluid analysis results for the first object 11 and the second object 12 (shown in Figures 2(a) and (b)), which have different shapes.

[0152] Furthermore, in step S9 of this embodiment, intrinsic orthogonal decomposition (G-POD in this example) is performed on the third physical quantity C3, fourth physical quantity C4, eighth physical quantity C8, ninth physical quantity C9, and tenth physical quantity C10 shown in Figure 21 (in this example, the third variable component D3, fourth variable component D4, eighth variable component D8, ninth variable component D9, and tenth variable component D10 shown in Figure 22). This makes it possible to easily compare the fluid analysis results for the first object 11, second object 12, third object 13, fourth object 14, and fifth object 15 (shown in Figures 2(a) to (e)), which have different shapes. The basis vectors and coefficients are input to the decomposition result storage unit 7D shown in Figure 1.

[0153] In step S9, the difference between the coefficients of the third physical quantity C3, the fourth physical quantity C4, the eighth physical quantity C8, the ninth physical quantity C9, and the tenth physical quantity C10 may be calculated for each mode. This allows for a quantitative comparison of the fluid analysis results of the objects 10 (first object 11 to fifth object 15) shown in Figures 2(a) to (e).

[0154] [Evaluating the physical quantities of the object being analyzed] Next, in the fluid simulation method of this embodiment, the quality of the physical quantities of the object to be analyzed is evaluated, as in previous embodiments (step S5). If the physical quantities of the object to be analyzed 10 are judged to be good (Yes in step S5), the object to be analyzed 10 judged to be good is manufactured (step S6). On the other hand, if the physical quantities of the object to be analyzed 10 are judged to be unsatisfactory (No in step S5), the shape of the object to be analyzed 10 is changed (step S7), and steps S1 to S5 are performed again. This ensures that the object to be analyzed 10 with reduced air resistance is reliably designed and manufactured.

[0155] Although particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be implemented in various modified forms.

[0156] [Note] The present invention includes the following embodiments.

[0157] [Invention 1] A fluid simulation method, The steps include setting up an object model that simulates the object to be analyzed, The steps include setting up a computational grid having multiple nodes or multiple elements for calculating the physical quantities of the fluid in the space surrounding the object model, The process includes the step of calculating the physical quantities of the fluid using the object model and the computational grid under predetermined conditions, The object model includes a first object model and a second object model. The first object model has a first shape and a first analytical coordinate system associated with the first shape, The second object model has a second shape different from the first shape, and a second analytical coordinate system corresponding to the first analytical coordinate system. The aforementioned computational grid is The first computational grid associated with the first object model, A second computational grid associated with the second object model, When the first analytical coordinate system and the second analytical coordinate system are aligned, the first computational grid and the second computational grid include a common computational grid area where the nodes or elements are in the same position as each other. Fluid simulation methods. [Invention 2] When the first analytical coordinate system and the second analytical coordinate system are aligned, the first computational grid and the second computational grid include non-common computational grid areas where the nodes or elements are located at different positions from each other. The fluid simulation method according to the present invention 1, wherein the non-common computational grid area is provided adjacent to the first object model in the first computational grid and adjacent to the second object model in the second computational grid. [Invention 3] A fluid simulation method according to invention 1 or 2, further comprising the step of comparing the physical quantity calculated in the common computational grid area of ​​the first computational grid with the physical quantity calculated in the common computational grid area of ​​the second computational grid. [4th Invention] The fluid simulation method according to the present invention, wherein the comparison step includes performing an intrinsic orthogonal decomposition on the physical quantity calculated in the common computational grid area of ​​the first computational grid and the physical quantity calculated in the common computational grid area of ​​the second computational grid to decompose them into a plurality of basis vectors and the coefficients of each of the plurality of basis vectors. [5th ​​Invention] The fluid includes air, The fluid simulation method according to any one of inventions 1 to 4, wherein the physical quantity includes the air pressure or its coefficient. [Invention 6] A fluid simulation method, A step of setting up a first object model and a second object model that mimic the object to be analyzed, wherein the first object model has a first shape and the second object model has a second shape different from the first shape, A step of setting up a first computational grid and a second computational grid having a plurality of nodes or a plurality of elements for calculating the physical quantities of a fluid in the respective spaces surrounding the first object model and the second object model, wherein the first computational grid is associated with the first object model, the second computational grid is associated with the second object model, and the second computational grid has a different grid division than the first computational grid, A first calculation step in which the physical quantities of the fluid are calculated using the first object model and the first computational grid under predetermined conditions, A second calculation step in which the physical quantities of the fluid are calculated using the second object model and the second computational grid under predetermined conditions, A step of transferring the physical quantities of each node or element obtained in the first calculation step onto a third calculation grid that is grid-divided separately from the first calculation grid, using interpolation processing, The process includes the step of transferring the physical quantities of each node or element obtained in the second calculation step onto a fourth calculation grid that is grid-divided separately from the second calculation grid, using interpolation. The third computational grid and the fourth computational grid have the same grid division structure as each other. Fluid simulation methods. [7th Invention] The fluid simulation method according to the present invention, wherein the interpolation process is performed based on at least one of linear interpolation and spline interpolation. [8th Invention] The fluid simulation method according to claim 6 or 7 of the present invention, further comprising the step of comparing the physical quantities of each node or element of the third computational grid with the physical quantities of each node or element of the fourth computational grid. [Invention 9] The fluid simulation method according to the present invention, wherein the comparison step includes performing an intrinsic orthogonal decomposition on the physical quantities of each node in the third computational grid and the physical quantities of each node or element in the fourth computational grid to decompose them into a plurality of basis vectors and the coefficients of each of the plurality of basis vectors. [Invention 10] The fluid includes air, The fluid simulation method according to any one of claims 6 to 9 of the present invention, wherein the physical quantity includes the air pressure or its coefficient. [Explanation of Symbols]

[0158] 11A First Shape 20 Object Models 21. First Object Model 21a First analytical coordinate system 26 nodes 30 Computational grid 31 1st calculation grid 35 Common Computation Grid Area G(i) element

Claims

1. A fluid simulation method, The steps include setting up an object model that simulates the object to be analyzed, The steps include setting up a computational grid having multiple nodes or multiple elements for calculating the physical quantities of the fluid in the space surrounding the object model, The process includes the step of calculating the physical quantities of the fluid using the object model and the computational grid under predetermined conditions, The object model includes a first object model and a second object model. The first object model has a first shape and a first analytical coordinate system associated with the first shape, The second object model has a second shape different from the first shape, and a second analytical coordinate system corresponding to the first analytical coordinate system. The aforementioned computational grid is The first computational grid associated with the first object model, The second computational grid associated with the second object model, When the first analytical coordinate system and the second analytical coordinate system are aligned, the first computational grid and the second computational grid include a common computational grid area where the nodes or elements are in the same position as each other. Fluid simulation methods.

2. When the first analytical coordinate system and the second analytical coordinate system are aligned, the first computational grid and the second computational grid include non-common computational grid areas where the nodes or elements are in different positions from each other. The fluid simulation method according to claim 1, wherein the non-common computational grid area is provided adjacent to the first object model in the first computational grid and adjacent to the second object model in the second computational grid.

3. The fluid simulation method according to claim 1, further comprising the step of comparing the physical quantity calculated in the common computational grid area of ​​the first computational grid with the physical quantity calculated in the common computational grid area of ​​the second computational grid.

4. The fluid simulation method according to claim 3, wherein the comparison step includes performing an intrinsic orthogonal decomposition on the physical quantity calculated in the common computational grid area of ​​the first computational grid and the physical quantity calculated in the common computational grid area of ​​the second computational grid to decompose them into a plurality of basis vectors and the coefficients of each of the plurality of basis vectors.

5. The fluid includes air, The fluid simulation method according to claim 1, wherein the physical quantity includes the air pressure or its coefficient.

6. A fluid simulation method, A step of setting up a first object model and a second object model that mimic the object to be analyzed, wherein the first object model has a first shape and the second object model has a second shape different from the first shape, A step of setting up a first computational grid and a second computational grid having a plurality of nodes or a plurality of elements for calculating the physical quantities of a fluid in the respective spaces surrounding the first object model and the second object model, wherein the first computational grid is associated with the first object model, the second computational grid is associated with the second object model, and the second computational grid has a different grid division than the first computational grid, A first calculation step in which the physical quantities of the fluid are calculated using the first object model and the first computational grid under predetermined conditions, A second calculation step in which the physical quantities of the fluid are calculated using the second object model and the second computational grid under predetermined conditions, A step of transferring the physical quantities of each node or element obtained in the first calculation step onto a third calculation grid that is grid-divided separately from the first calculation grid, using interpolation processing, The process includes the step of transferring the physical quantities of each node or element obtained in the second calculation step onto a fourth calculation grid, which is grid-divided separately from the second calculation grid, using interpolation. The third computational grid and the fourth computational grid have the same grid division structure as each other. Fluid simulation methods.

7. The fluid simulation method according to claim 6, wherein the interpolation process is performed based on at least one of linear interpolation and spline interpolation.

8. The fluid simulation method according to claim 6, further comprising the step of comparing the physical quantities of each node or element of the third computational grid with the physical quantities of each node or element of the fourth computational grid.

9. The fluid simulation method according to claim 8, wherein the comparison step includes performing an intrinsic orthogonal decomposition on the physical quantities of each node in the third computational grid and the physical quantities of each node or element in the fourth computational grid to decompose them into a plurality of basis vectors and the coefficients of each of the plurality of basis vectors.

10. The fluid includes air, The fluid simulation method according to claim 6, wherein the physical quantity includes the air pressure or its coefficient.

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