Method for implementing gas diffusion model

Abstract

The present invention relates to a method for implementing a gas diffusion model, comprising the steps of: (a) setting a three-dimensional grid including a first voxel (v1) and a second voxel (v2); (b) allocating a first gas concentration value (d11; d21) of the first time (t1) to each of a first voxel (v1) and a second voxel (v2); (c) obtaining a twelfth gas concentration change value (Δf12) of the first voxel (v1) from the difference between a first gas concentration value (d11) of the first voxel (v1) and a first gas concentration value (d21) of the second voxel (v2); and (d) applying the 12th gas concentration change value (Δf12) of the first voxel (v1) to the first gas concentration change value (d11) of the first voxel (v1) so as to designate same as a second gas concentration value (d12) of the second time (t2) of the first voxel (v1).

Description

Method for implementing a gas diffusion model

[0001] The present invention relates to a method for implementing a gas diffusion model, and more specifically, to a method for implementing a gas diffusion model using a three-dimensional cellular automaton technique.

[0002] Specifically, the present invention relates to a method for implementing a prediction of atmospheric concentration changes over time using a 3D cellular automaton technique, which is necessary to implement 3D spatial information-based visualization of the diffusion of invisible gases, such as fog or pollutants, in resource-limited environments such as web services.

[0003] Precision gas diffusion models are executed using specialized tools that implement Computational Fluid Dynamics (CFD) based on mathematical models of gas diffusion. Because these specialized tools require significant computing power, they are not only expensive but also require high-performance hardware to run.

[0004] However, there are cases where it is necessary to implement a visualization of gas diffusion in three-dimensional space in situations where there is no gas diffusion prediction data produced by such tools and there is no environment to run such tools.

[0005] In such a limited resource environment, in order to provide a service for visualizing gas diffusion in three-dimensional space in a web browser, the visualization target, such as atmospheric gas diffusion prediction data, must be able to be produced with minimal resources. This is because web services running in a web browser have more constraints on resource usage compared to general applications.

[0006] Gas diffusion prediction data is usually described as three-dimensional grid data and produces a set of prediction data that changes over time.

[0007] A three-dimensional grid cell is called a voxel, and each voxel records information on the concentration or mass of the target gas.

[0008] 3D grid data of gas concentration can be represented similarly to actual gases using volume rendering technology. Volume rendering is a visualization technique that combines cross-sectional images of the human body, such as those taken by CT or MRI, to make them appear three-dimensional. Ultimately, 3D grid data is a data structure in which 2D grid data in a grid-like structure is stacked layer upon layer. Therefore, if the 2D grid data of each layer is used like a CT or MRI image, it can be displayed as a 3D image, and animation effects are generated by changing the corresponding 3D image over time.

[0009] Figure 1 schematically illustrates the principle of volume rendering.

[0010] Therefore, if the 'hourly virtual gas concentration 3D grid data' to be visualized can be created simply and plausibly with minimal resources, a web service that animates the diffusion of virtual gases in the atmosphere in 3D can be efficiently implemented.

[0011] [Prior Art Literature]

[0012] (Patent Document 1) Republic of Korea Registered Patent 10-1309773 (September 11, 2013)

[0013] One objective of the present invention is to provide a method for implementing a gas diffusion model that can efficiently provide a web service that animates the way gas diffuses in the atmosphere in 3D by utilizing virtual gas concentration 3D grid data over time in a limited resource environment.

[0014] The present invention relates to a method for implementing a gas diffusion model, comprising: (a) setting a three-dimensional grid including a first voxel (v1) and a second voxel (v2); and (b) a first gas concentration value (d) at a first time (t1) for each of the first voxel (v1) and the second voxel (v2). 11 ; d 21(c) a step of assigning ) a first gas concentration value (d) of the first voxel (v1); 11 ) and the first gas concentration value (d) of the second voxel (v2) 21 The 12th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 12 A step of obtaining ); and (d) a 12th gas concentration change value (Δf) of the 1st voxel (v1); 12 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 A method for implementing a gas diffusion model is provided, comprising the step of designating as ).

[0015] The method for implementing a gas diffusion model according to the present invention can efficiently provide a web service that animates the appearance of gas diffusion in the atmosphere in three dimensions in a limited resource environment.

[0016] Figure 1 schematically illustrates the principle of volume rendering.

[0017] Figure 2 schematically illustrates an example of a cellular automata technique.

[0018] Figure 3 schematically shows the flow of gas from a single voxel.

[0019] FIG. 4 schematically illustrates a method for implementing a gas diffusion model according to the present invention.

[0020] Figure 5 schematically illustrates the implementation method of the gas diffusion model presented in Figure 4 extended to three dimensions.

[0021] Figure 6 schematically illustrates a method for implementing a gas diffusion model representing voxels with adjacent faces touching.

[0022] FIG. 7 schematically illustrates a flowchart for performing the method of implementing the gas diffusion model of the present invention.

[0023] The national research and development projects that supported this invention are as follows.

[0024] Research Project Title (English): Spatial knowledge inference engine development

[0025] Research Project Title (Korean): Spatial Knowledge Inference Engine Technology Development Project

[0026] Specialized Agency: Korea Agency for Infrastructure Technology Advancement

[0027] Project No.: RS-2021-02317649 (NTIS: 1615012936)

[0028] The present invention will be described in detail below using the attached drawings.

[0029] Detailed descriptions of known technologies are omitted when describing the present invention.

[0030] A method for implementing a gas diffusion model according to the present invention generates three-dimensional grid data in which the concentration of a gas is recorded in each voxel over time to generate data that simulates gas diffusion prediction. To this end, the method of the present invention uses a three-dimensional cellular automaton.

[0031] An algorithm in which data in a two-dimensional grid structure is assigned arbitrary information to each grid, and when performing a process with the data, there is a rule for changing the information assigned to each grid, and the two-dimensional grid data of one step is determined based on the two-dimensional grid data of the previous step is called a cellular automata.

[0032] Figure 2 schematically illustrates an example of a cellular automata technique.

[0033] As illustrated in FIG. 2, let us assume that the information stored in the 2D grid data and the rules for change are as follows: i) The state information stored in each grid is the grid color, which is either white or black. ii) As the process step proceeds, the white grid remains unchanged, while the black grid changes to white and changes the color of the grids adjacent to the east and south to black. When such a cellular automaton is executed, the result is as shown in FIG. 2.

[0034] Ultimately, by assigning clear rules to how the virtual gas concentration assigned to each voxel of the 3D grid structure changes as the process steps proceed, it is possible to implement a cellular automaton extended to 3D using the time-dependent concentration 3D grid data.

[0035] Figure 3 schematically shows the flow of gas from a single voxel.

[0036] Referring to Fig. 3, one voxel is a cube, and in a three-dimensional lattice structure, one voxel is in contact with six adjacent voxels. It is assumed that the reason for the change in the concentration of one voxel is that gas inflow and outflow occurs through the six faces.

[0037] In one aspect, the present invention provides a method for implementing a gas diffusion model.

[0038] The method for implementing a gas diffusion model according to the present invention comprises: (a) a step in which a processor executes a program stored in an execution memory to set a three-dimensional grid including a first voxel (v1) and a second voxel (v2); and (b) a step in which a processor executes a program stored in an execution memory to set a first gas concentration value (d) at a first time (t1) in each of the first voxel (v1) and the second voxel (v2). 11 ; d 21 (c) a step of allocating ) and the processor executes a program stored in execution memory to obtain a first gas concentration value (d) of the first voxel (v1). 11 ) and the first gas concentration value (d) of the second voxel (v2) 21The 12th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 12 A step of obtaining ); and (d) the processor executes a program stored in the execution memory to obtain the 12th gas concentration change value (Δf) of the first voxel (v1). 12 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 Includes the step of designating as );

[0039] FIG. 4 schematically illustrates a method for implementing a gas diffusion model according to the present invention.

[0040] Referring to FIG. 4, in one embodiment, the method for implementing a gas diffusion model of the present invention, in step (a), a processor executes a program stored in an execution memory to set a three-dimensional grid including a first voxel (v1) and a second voxel (v2). Then, in step (b), the processor executes a program stored in an execution memory to set a first gas concentration value (d) at a first time (t1) in each of the first voxel (v1) and the second voxel (v2). 11 ; d 21 ) is assigned. FIG. 4 (A) shows a first gas concentration value (d) to each of the first voxel (v1) and the second voxel (v2) at the first time (t1). 11 ; d 21 It schematically represents a portion of the 3D grid to which ) is assigned.

[0041] In the subsequent step (c), the processor executes a program stored in the execution memory to obtain the first gas concentration value (d) of the first voxel (v1). 11 ) and the first gas concentration value (d) of the second voxel (v2) 21 The 12th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 12 ) is calculated. Specifically, the first gas concentration value (d) of the first voxel (v1) 11 The first gas concentration value (d) of the second voxel (v2) in ) 21The value obtained by subtracting ) is the 12th gas concentration change value (Δf) of the 1st voxel (v1). 12 ...is set as ). Here, the 12th gas concentration change value (Δf 12 If ) has a positive (+) value, gas is leaked, and if it has a negative (-) value, gas is leaked. The same applies below.

[0042] Meanwhile, when calculating the change in gas concentration of a single target voxel, the concentration of adjacent voxels can be assumed to be 0 and only the outflow can be calculated. This is because when an adjacent voxel becomes the target of calculation, calculating only the outflow in the same way will eventually result in a settlement and the calculation of the net outflow.

[0043] Figures 4(A1) and 4(A2) schematically illustrate this calculation method.

[0044] Specifically, when the first voxel (v1) is the turn to be calculated, the first gas concentration value (d) of the adjacent second voxel (v2) 21 Assuming ) is 0, the outflow amount of gas (f) moving from the first voxel (v1) to the second voxel (v2) 12 Calculate )

[0045] Likewise, when the second voxel (v2) is the turn to be calculated, the first gas concentration value (d) of the adjacent first voxel (v1) 11 Assuming ) is 0, the outflow amount of gas (f) moving from the second voxel (v2) to the first voxel (v1) 21 Calculate )

[0046] Subsequently, the outflow of the two gases (f 12 ; f 21 If you settle ) in each voxel, you can calculate the net outflow.

[0047] Subsequently, in step (d), the processor executes a program stored in the execution memory to obtain the 12th gas concentration change value (Δf) of the 1st voxel (v1). 12 ) is the first gas concentration value (d) of the first voxel (v1). 11Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 Designate as ).

[0048] Figure 5 schematically illustrates the implementation method of the gas diffusion model presented in Figure 4 extended to three dimensions.

[0049] Figure 6 schematically illustrates a method for implementing a gas diffusion model representing voxels with adjacent faces touching.

[0050] Referring to FIG. 5, in one embodiment, the three-dimensional grid in step (a) further includes a third voxel (v3), a fourth voxel (v4), a fifth voxel (v5), a sixth voxel (v6), and a seventh voxel (v7). Here, the second voxel (v2), the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7) each surround the first voxel (v1) with one of the faces as a boundary.

[0051] Meanwhile, step (b) is a first gas concentration value (d) at the first time (t1) for each of the third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7). 31 ; d 41 ; d 51 ; d 61 ; d 71 Includes the step of allocating ).

[0052] Step (c) is the first gas concentration value (d) of the first voxel (v1). 11 ) and the first gas concentration value (d) of each of the third voxel (v3) to the seventh voxel (v7). 31 to d 71 ) From the respective differences, the 13th to 17th gas concentration change values ​​(Δf) of the 1st voxel (v1) 13 Δf 17 Includes the step of obtaining ).

[0053] Specifically, step (c) is a first gas concentration value (d) of the first voxel (v1). 11) and the first gas concentration value (d) of the third voxel (v3) 31 The 13th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 13 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fourth voxel (v4) 41 The 14th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 14 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fifth voxel (v5) 51 The 15th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 15 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 6th voxel (v6) 61 The 16th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 16 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 7th voxel (v7) 71 The 17th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 17 Includes the step of obtaining ).

[0054] Meanwhile, step (d) is the 12th gas concentration change value (Δf) of the 1st voxel (v1). 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14 ), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 Includes the step of designating as ).

[0055] In one embodiment, step (a) further includes the step of designating one or more of the second voxel (v2), third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7) as gas impermeable voxels.

[0056] Meanwhile, step (c) is the firstn change in gas concentration value (Δf) of the first voxel (v1) for the voxel designated as a gas impermeable voxel among the second voxel (v2), third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7). 1n , where n is an integer from 2 to 7) further includes the step of assigning 0.

[0057] The advantage of 3D cellular automata is that it can apply areas where gas cannot pass through due to the presence of buildings or terrain. For example, voxels included in a building area can be designated as gas-impermeable voxels. In this case, surfaces in contact with gas-impermeable voxels can be excluded from the calculation of gas outflow. That is, the change in gas concentration value (Δf) can be set to 0 and excluded from the calculation of gas outflow.

[0058] In one embodiment, the second gas concentration value (d) at the second time (t2) 12 ) can be performed using the following formula.

[0059] d 12 = d 11 + C·Σ(Δf1)

[0060] Here, d 11 is the first gas concentration value (d) of the first voxel (v1) at the first time (t1). 11 ) and; d 12 is the second gas concentration value (d) of the first voxel (v1) at the second time (t2). 12 ) and; Σ(Δf1) is the 12th gas concentration change value (Δf) of the 1st voxel (v1) 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 It is the sum of ); and C is a proportionality constant.

[0061] Therefore, the change in concentration due to gas leakage through six planes in a single target voxel is calculated by setting the concentration of the six adjacent voxels in contact with those six planes to zero and calculating only the change in concentration in the direction of outflow, and by calculating for all voxels, the total change in concentration of each voxel can be obtained.

[0062] The proportionality constant C increases the diffusion rate when it increases and decreases it when it decreases, so the developer adjusts it according to the purpose of visualization. For example, when visualizing a diffusion prediction that is one hour long, it is not possible to actually perform the animation for one hour, so the diffusion rate must be exaggerated to be performed within a few seconds to a few tens of seconds; in this case, C can be increased appropriately.

[0063] Meanwhile, the rule for calculating the outflow is derived from the gas state equation to plausibly simulate the reality. The gas state equation is as follows.

[0064] P·V = n·R·T

[0065] (P is pressure, V is volume, n is the number of gas molecules in mol, R is the gas constant, T is the absolute temperature)

[0066] However, if the molecular weight of a hypothetical gas molecule is specified, and the total mass of all gas molecules contained in that volume is denoted as m, it can be expressed as P·V = k1·m·T (where k1 is a proportionality constant). If the temperature is fixed, it can be expressed as P = k2·(m / V) (where k2 is a proportionality constant).

[0067] However, since m / V represents density, rearranging it, it can be expressed as P = k·d (where d is the density of the gas and k is the proportionality constant), and ΔP = k·Δd.

[0068] This formula implies that if there is a concentration difference between two adjacent voxels, there exists a pressure difference of the corresponding gas between them. Since the inflow and outflow rates are proportional to this pressure difference, and the concentration of the voxel changes in proportion to these rates, if the outflow side is designated as the positive direction, it can be expressed as follows.

[0069] d = d0+ C·Σd

[0070] Here, d is the concentration of the next time zone, d0 is the concentration of the current time zone, C is a proportionality constant, and Σd is the value obtained by subtracting the concentration of the current target voxel from the concentration of the 6 adjacent voxels.

[0071] Meanwhile, a gas generation grid (source, implementable by assigning an increase in concentration per hour; both fixed values ​​and variable methods based on time can be applied) can be applied to simulate a phenomenon where gas is continuously generated in the atmosphere at a specific point, such as in a gas pipeline leak accident, or conversely, a gas extinction grid (sink, implementable by assigning an increase in concentration per hour; both fixed values ​​and variable methods based on time can be applied) can be applied to simulate a phenomenon where gas concentration decreases, such as in a ventilation fan.

[0072] In addition, if the outermost plane of the 3D grid is designated as a gas impermeable plane, it can be simulated under conditions where the gas within the gas diffusion prediction area does not disappear and continues to exist, and conversely, if it is set to be permeable, it can be simulated under conditions where the gas concentration within the prediction area eventually converges to zero over time.

[0073] In one embodiment, the method for implementing a gas diffusion model of the present invention, in step (e), a processor executes a program stored in an execution memory, and the first gas concentration value (d) of the second voxel (v2) 21 ) and the first gas concentration value (d) of the first voxel (v1) 11 The 21st gas concentration change value (Δf) of the 2nd voxel (v2) from the difference of ) 21) obtains.

[0074] In this way, the change in gas concentration (Δf) is calculated for all voxels at the first time (t1).

[0075] In the subsequent step (f), the processor executes a program stored in the execution memory to change the 21st gas concentration value (Δf) of the second voxel (v2). 21 ) is the first gas concentration value (d) of the second voxel (v2). 21 By applying to ) the second gas concentration value (d) of the second voxel (v2) at the second time (t2). 22 Designate as ).

[0076] In this way, the gas concentration change value (Δf) is applied to all voxels and designated as the second gas concentration value (d2) of the second time (t2) for all voxels.

[0077] In one embodiment, the method for implementing a gas diffusion model of the present invention, in step (g), a processor executes a program stored in an execution memory, and the first gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the first time (t1) 11 ; d 21 Specify the first three-dimensional grid data including ).

[0078] In this way, for all voxels, first three-dimensional grid data including the first gas concentration value (d1) at the first time (t1) is specified.

[0079] Meanwhile, in step (h), the processor executes a program stored in the execution memory to obtain the second gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the second time (t2). 12 ; d 22 Specify the second three-dimensional grid data including ).

[0080] In this way, for all voxels, second three-dimensional grid data including the second gas concentration value (d2) at the second time (t2) is specified.

[0081] In the subsequent step (i), the processor executes a program stored in the execution memory to implement a gas diffusion model using the first three-dimensional grid data and the second three-dimensional grid data.

[0082] FIG. 7 schematically illustrates a flowchart for performing the method of implementing the gas diffusion model of the present invention.

[0083] Here, the process is performed in the following order: initialization, setting the concentration prediction target area, setting the side length of a single voxel (automatically determining the number of horizontal / vertical / height grids of the grid data and creating the first edition of the 3D grid data), initializing the concentration of all voxels of the generated 3D grid data to 0, specifying the proportionality constant C of the formula d = d0+ C·ΣΔd, setting the initial concentration value for voxels that do not have an initial concentration of 0, designating voxels to be deactivated by building / terrain effects, designating voxels to be used as source / sink and assigning creation / destruction rate values, and setting whether the outermost surface of the grid data is permeable or impenetrable.

[0084] Various embodiments of the present invention are described below.

[0085] Example 1. A method for implementing a gas diffusion model, comprising: (a) setting a three-dimensional grid including a first voxel (v1) and a second voxel (v2); (b) a first gas concentration value (d) at a first time (t1) for each of the first voxel (v1) and the second voxel (v2). 11 ; d 21 (c) a step of assigning ) a first gas concentration value (d) of the first voxel (v1); 11 ) and the first gas concentration value (d) of the second voxel (v2) 21 The 12th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 12 A step of obtaining ); and (d) a 12th gas concentration change value (Δf) of the 1st voxel (v1); 12 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12A method for implementing a gas diffusion model including the step of designating as ).

[0086] Example 2. In Example 1, the three-dimensional grid in step (a) further comprises a third voxel (v3), a fourth voxel (v4), a fifth voxel (v5), a sixth voxel (v6), and a seventh voxel (v7), wherein the second voxel (v2), the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7) each surround the first voxel (v1) with one of the faces as a boundary, and in step (b), a first gas concentration value (d) of a first time (t1) at each of the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7). 31 ; d 41 ; d 51 ; d 61 ; d 71 It includes a step of assigning ), wherein step (c) is a first gas concentration value (d) of the first voxel (v1). 11 ) and the first gas concentration value (d) of the third voxel (v3) 31 The 13th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 13 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fourth voxel (v4) 41 The 14th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 14 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fifth voxel (v5) 51 The 15th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 15 Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 6th voxel (v6) 61 The 16th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 16Step of obtaining ); first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 7th voxel (v7) 71 The 17th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 17 The method includes a step of obtaining ); and step (d) is a 12th gas concentration change value (Δf) of the 1st voxel (v1). 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14 ), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 A method for implementing a gas diffusion model including the step of designating as ).

[0087] Example 3. In Example 2, step (a) further comprises the step of designating one or more of the second voxel (v2), the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7) as gas-impermeable voxels; and step (c) further comprises the firstn change in gas concentration value (Δf) of the first voxel (v1) for the voxel designated as a gas-impermeable voxel among the second voxel (v2), the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7). 1n A method for implementing a gas diffusion model, further comprising the step of assigning 0 to , where n is an integer from 2 to 7.

[0088] Example 4. In Example 2, step (d) is performed using the following formula, and d 12 = d 11 + C·Σ(Δf1), where d 11is the first gas concentration value (d) of the first voxel (v1) at the first time (t1). 11 ) and, d 12 is the second gas concentration value (d) of the first voxel (v1) at the second time (t2). 12 ) and Σ(Δf1) is the 12th gas concentration change value (Δf) of the 1st voxel (v1) 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14 ), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 A method for implementing a gas diffusion model, which is the sum of ) and where C is a proportionality constant.

[0089] Example 5. In Example 1, (e) the first gas concentration value (d) of the second voxel (v2). 21 ) and the first gas concentration value (d) of the first voxel (v1) 11 The 21st gas concentration change value (Δf) of the 2nd voxel (v2) from the difference of ) 21 A step of obtaining ); and (f) a 21st gas concentration change value (Δf) of the 2nd voxel (v2); 21 ) is the first gas concentration value (d) of the second voxel (v2). 21 By applying to ) the second gas concentration value (d) of the second voxel (v2) at the second time (t2). 22 A method for implementing a gas diffusion model, further comprising the step of designating as ).

[0090] Example 6. In Example 5, (g) a first gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the first time (t1). 11 ; d 21 (h) a step of specifying first three-dimensional grid data including ); a second gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the second time (t2). 12 ; d 22A method for implementing a gas diffusion model, comprising: a step of specifying a second three-dimensional grid data including ); and a step of implementing a gas diffusion model using the first three-dimensional grid data and the second three-dimensional grid data.

Claims

1. Regarding the method for implementing a gas diffusion model, (a) A step in which a processor executes a program stored in an execution memory to set a three-dimensional grid including a first voxel (v1) and a second voxel (v2); (b) The processor executes a program stored in the execution memory to obtain a first gas concentration value (d) of the first time (t1) in each of the first voxel (v1) and the second voxel (v2). 11 ; d 21 Step of assigning ); (c) The processor executes a program stored in the execution memory to obtain the first gas concentration value (d) of the first voxel (v1). 11 ) and the first gas concentration value (d) of the second voxel (v2) 21 The 12th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 12 Step of obtaining ); and (d) The processor executes a program stored in the execution memory to change the 12th gas concentration value (Δf) of the 1st voxel (v1). 12 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 Step of designating as ); Includes, In step (a), the three-dimensional grid further includes a third voxel (v3), a fourth voxel (v4), a fifth voxel (v5), a sixth voxel (v6), and a seventh voxel (v7), and Here, the second voxel (v2), the third voxel (v3), the fourth voxel (v4), the fifth voxel (v5), the sixth voxel (v6), and the seventh voxel (v7) each surround the first voxel (v1) with one of the faces as a boundary, and Step (b) is a first gas concentration value (d) at the first time (t1) for each of the third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7). 31 ; d 41 ; d 51 ; d 61 ; d 71 It includes a step of assigning ), Step (c) is The first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the third voxel (v3) 31 The 13th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 13 Step of finding ) The first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fourth voxel (v4) 41 The 14th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 14 Step of finding ) The first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the fifth voxel (v5) 51 The 15th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 15 Step of finding ) The first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 6th voxel (v6) 61 The 16th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 16 Step of finding ) The first gas concentration value (d) of the first voxel (v1) 11 ) and the first gas concentration value (d) of the 7th voxel (v7) 71 The 17th gas concentration change value (Δf) of the 1st voxel (v1) from the difference of ) 17 Step of finding ) Includes, Step (d) is the 12th gas concentration change value (Δf) of the 1st voxel (v1). 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14 ), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 ) is the first gas concentration value (d) of the first voxel (v1). 11 Applying to ) the second gas concentration value (d) of the first voxel (v1) at the second time (t2) 12 Step of designating as ); A method for implementing a gas diffusion model including 2. In Claim 1, Step (a) is a step of designating one or more of the second voxel (v2), third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7) as gas impermeable voxels; Including further, Step (c) is the firstn change in gas concentration value (Δf) of the first voxel (v1) for the voxel designated as a gas impermeable voxel among the second voxel (v2), third voxel (v3), fourth voxel (v4), fifth voxel (v5), sixth voxel (v6), and seventh voxel (v7). 1n A method for implementing a gas diffusion model, further comprising the step of assigning 0 to , where n is an integer from 2 to 7.

3. In Claim 1, Step (d) is performed using the following formula, and d 12 = d 11 + C·Σ(Δf1) Here d 11 is the first gas concentration value (d) of the first voxel (v1) at the first time (t1). 11 ) and, d 12 is the second gas concentration value (d) of the first voxel (v1) at the second time (t2). 12 ) and, Σ(Δf1) is the 12th gas concentration change value (Δf) of the 1st voxel (v1) 12 ), 13. Change in gas concentration (Δf 13 ), 14th change in gas concentration (Δf 14 ), 15th change in gas concentration (Δf 15 ), 16th change in gas concentration (Δf 16 ), and the 17th change in gas concentration (Δf 17 It is the sum of ), and A method for implementing a gas diffusion model where C is a proportionality constant.

4. In Claim 1, (e) The processor executes a program stored in the execution memory, and the first gas concentration value (d) of the second voxel (v2) 21 ) and the first gas concentration value (d) of the first voxel (v1) 11 The 21st gas concentration change value (Δf) of the 2nd voxel (v2) from the difference of ) 21 Step of obtaining ); and (f) The processor executes a program stored in the execution memory, and the 21st gas concentration change value (Δf) of the 2nd voxel (v2) 21 ) is the first gas concentration value (d) of the second voxel (v2). 21 By applying to ) the second gas concentration value (d) of the second voxel (v2) at the second time (t2). 22 Step of designating as ); A method for implementing a gas diffusion model that further includes 5. In Claim 4, (g) The processor executes a program stored in the execution memory to obtain a first gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the first time (t1). 11 ; d 21 A step of specifying first three-dimensional grid data including ); (h) The processor executes a program stored in the execution memory to obtain the second gas concentration value (d) of each of the first voxel (v1) and the second voxel (v2) at the second time (t2). 12 ; d 22 A step of specifying second three-dimensional grid data including ); and (i) A step in which a processor executes a program stored in execution memory to implement a gas diffusion model using first three-dimensional grid data and second three-dimensional grid data; A method for implementing a gas diffusion model that further includes

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