Fluid analysis method, fluid analysis device, and program

Abstract

To solve the problem that a highly precise calculation cannot be performed efficiently since a time increment required from local spatial resolution becomes much smaller than an essentially required time scale and hence many repeated computations are required for the entire analysis period and computation time becomes enormous in a variation analysis of an environment fluid including a local component expressing a fast component of time variation and an average component expressing a slow component of time variation.SOLUTION: Computation considering a change in an actual time scale is performed by amplifying an average component of the amount of variation in a next time step by a constant on the basis of the amount of variation of an environment fluid in a current time step so as to reduce calculation time by calculating a short period obtained by reducing the time scale of an actual phenomenon as an object to 1 / constant, and a time change in various calculated variation amounts is extended by a multiple of a constant, thus speedily and precisely calculating a time change in the amount of variation in an actual time scale.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a fluid analysis method and the like, and more particularly to a fluid analysis method, a fluid analysis device, and a program for analyzing state fluctuations of environmental fluids such as rivers, oceans, and the atmosphere. [Background technology]

[0002] In recent years, with the development of computer technology, numerical analysis of environmental fluids such as rivers, oceans, and the atmosphere has come to be applied practically in a wide range of fields. For example, the importance of analyzing flood flow and inundation flow is increasing in relation to heavy rain disasters, the frequency of which is increasing with climate change.

[0003] To perform accurate numerical analysis of environmental fluids, it is necessary to increase the spatial resolution of the analysis target area so that complex boundary shapes, vortices, and wave motion can be calculated, and to reduce the time step of the calculation set based on the spatial resolution. However, when analyzing environmental fluids such as rivers, oceans, and the atmosphere, the analysis target area generally targets long-time-scale phenomena that occur at a spatial scale much larger than the analysis resolution of several kilometers or more, so if the spatial resolution is increased and the time step is reduced accordingly, the calculation load increases and the time required for calculation increases dramatically.

[0004] As a method for efficiently performing calculations related to fluid analysis, for example, Patent Document 1 discloses a method for stably and efficiently performing analysis of differential equations governing flow using the finite difference method by using two types of time integration methods.

[0005] Moreover, Patent Document 2 discloses a method for reducing memory capacity and calculation time in the computational fluid analysis of a fluid including a moving boundary. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Publication No. 8-263470 [Patent Document 2] Japanese Patent Application Publication No. 6-75938 Summary of the Invention [Problem to be solved by the invention]

[0007] For example, in the analysis of environmental fluids, including the above-mentioned analysis of flood flow and inundation flow, the time scale actually required as an analysis result is often a gradual change over a period of about 10 minutes during flood or inundation durations of days or more, whereas a spatial resolution of a few meters or less is required to calculate the boundaries of structures and other local flow changes, and the time scale required for this is seconds or less. Therefore, the time interval required from the local spatial resolution is far smaller than the time scale actually required, and many repeated calculations are required over the entire analysis period, resulting in enormous calculation times.

[0008] Both Patent Documents 1 and 2 relate to techniques for numerically and efficiently solving equations. However, it is difficult to bridge the gap between the time step of calculations determined by the required spatial resolution and the time resolution required for the analysis results. In other words, since the time scale considering the local spatial scale is small compared to the large time scale required for the analysis results, it is difficult to perform calculations for the entire period in a short time.

[0009] The present invention has been made in consideration of the above circumstances, and an object of the present invention is to provide a fluid analysis method, a fluid analysis device, and a program that are capable of performing environmental fluid analysis efficiently with high accuracy. [Means for solving the problem]

[0010] In order to achieve the above object, a first aspect of the present invention provides an environmental fluid analysis method, comprising: An environmental fluid analysis method for performing a fluctuation analysis of an environmental fluid including a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation, comprising: an acceleration calculation step of calculating a time change of the fluctuation amount by repeatedly executing a next-time fluctuation amount calculation process in which the fluctuation amount at the next time step is calculated by accelerating the analysis based on an actual time scale based on the fluctuation amount of the environmental fluid at the current time step; and an expansion step of calculating a time change of the amount of fluctuation based on the time change of the amount of fluctuation calculated in the acceleration calculation step so as to return the amount of fluctuation to an actual time scale, In the acceleration calculation step, Calculating a difference between the amount of change in a next time step and the amount of change in the current time step; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; calculating the amount of change in the next time step by the sum of the amount of change in the current time step, the difference, and the acceleration average value; In the stretching calculation step, The time change of the amount of fluctuation calculated in the acceleration calculation step is stretched based on the constant, thereby calculating the time change of the amount of fluctuation on an actual time scale.

[0011] In addition, the average is a spatial average of a part or the whole of the analysis area. This may also be the case.

[0012] Moreover, the average is an average of the time change of the fluctuation amount. This may also be the case.

[0013] The environmental fluid is water flowing in a river, The amount of change is the water depth of the river. This may also be the case.

[0014] Further, an environmental fluid analysis apparatus according to a second aspect of the present invention comprises: An environmental fluid analysis device that performs a fluctuation analysis of an environmental fluid including a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation, an acceleration calculation unit that calculates a time change of the fluctuation amount by repeatedly executing a next-time fluctuation amount calculation process that calculates the fluctuation amount at a next time step by accelerating the fluctuation amount at a next time step based on the fluctuation amount of the environmental fluid at a current time step with respect to an analysis based on an actual time scale; and an expansion calculation unit that calculates a time change of the amount of fluctuation based on the time change of the amount of fluctuation calculated by the acceleration calculation unit so as to return the amount of fluctuation to an actual time scale, The acceleration calculation unit is Calculating a difference between the amount of change in a next time step and the amount of change in the current time step; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; calculating the amount of change in the next time step by the sum of the amount of change in the current time step, the difference, and the acceleration average value; The stretching calculation unit includes: The time change of the amount of fluctuation calculated by the acceleration calculation unit is stretched based on the constant, thereby calculating the time change of the amount of fluctuation on an actual time scale.

[0015] Moreover, the program according to the third aspect of the present invention comprises: Computer, Calculating a difference between an amount of fluctuation of an environmental fluid at a next time step and an amount of fluctuation of the environmental fluid at a current time step, the amount of fluctuation being a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; an acceleration calculation unit that calculates the change over time of the amount of variation by repeatedly executing a next-time variation calculation process in which the amount of variation at the next time step is calculated by adding the amount of variation at the current time step, the difference, and the accelerated average value, thereby accelerating and calculating the amount of variation at the next time step with respect to an analysis based on an actual time scale; an extension calculation unit that calculates the time change of the fluctuation amount calculated by the acceleration calculation unit by extending the time change of the fluctuation amount based on the constant so as to return the time change to an actual time scale; Function as. Effect of the Invention

[0016] According to the environmental fluid analysis method, environmental fluid analysis device, and program of the present invention, the calculation of the fluctuation amount at each time step is accelerated using the average difference value obtained by multiplying the average value of the differences in the fluctuation amount at each time step by a constant, making it possible to perform environmental fluid analysis efficiently with high accuracy. [Brief description of the drawings]

[0017] [Figure 1] 1 is a functional block diagram of an environmental fluid analysis apparatus according to an embodiment of the present invention. [Diagram 2] 4 is a flowchart showing a flow of environmental fluid analysis according to the embodiment. [Diagram 3] FIG. 1A is a graph showing the concept of accelerated calculation according to an embodiment, and FIG. 1B is an enlarged view showing the fluctuation of local components in FIG. [Figure 4] Graph (A) shows an example of the case where the time axis of the input is shortened, and graph (B) shows an example of the calculation result of (A) being stretched without accelerating the average component. [Diagram 5] 13 is a graph showing the results of a numerical example. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] Hereinafter, a fluid analysis device 1 according to an embodiment of the present invention will be described with reference to the drawings. In this embodiment, the environmental fluid analyzed by the fluid analysis device 1 is water flowing in a river. Assuming a flood flow caused by a rise in the water level of the river, a case will be described in which the flood flow of the river is analyzed with the water depth of the river as the amount of fluctuation.

[0019] As shown in the functional block diagram of FIG. 1, the fluid analysis device 1 includes a control unit 11, a storage unit 12, a display unit 13, and an input unit .

[0020] The control unit 11 is composed of a central processing unit (CPU), a graphics processing unit (GPU), a read only memory (ROM), a random access memory (RAM), etc., and controls the operation of the fluid analysis device 1. The control unit 11 also analyzes the environmental fluid based on set analysis conditions. The control unit 11 loads various operation programs and data stored in the ROM, storage unit 12, etc. of the control unit 11 into the RAM and operates the CPU and GPU, thereby realizing each function of the control unit 11 shown in FIG. 1. In this way, the control unit 11 operates as a condition setting unit 111, an acceleration calculation unit 112, and an enlargement calculation unit 113.

[0021] The condition setting unit 111 sets various conditions related to the environmental fluid analysis. Specifically, the condition setting unit 111 reads the physical properties, boundary conditions, initial conditions, time intervals of the calculation, and other conditions such as the altitude and roughness of the calculation mesh set by the user, and sets the conditions necessary for the calculation related to the analysis. The analysis of the environmental fluid handled in this embodiment is an analysis of the fluctuation of the environmental fluid including a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation. Specifically, the analysis according to this example includes a local water depth fluctuation that is required to be calculated on a time scale of seconds or less as a local component representing a component with a relatively fast time fluctuation. In addition, the analysis according to this example includes a wide range of water depth fluctuation such as flood flow, for which a calculation result is required for a period of days or more, as an average component representing a component with a relatively slow time fluctuation.

[0022] The acceleration calculation unit 112 performs calculations on the state fluctuations of the environmental fluid based on the analysis calculation conditions set by the condition setting unit 111. In the analysis according to this embodiment, accelerated calculations are performed to perform calculations on average components, which require calculation results on a large spatiotemporal scale, with high accuracy and at high speed while performing calculations on local components, which require small calculation time intervals. Details of the calculation process related to the accelerated calculations will be described later. The acceleration calculation unit 112 also stores the results of the calculations it has performed in the memory unit 12.

[0023] The stretching calculation unit 113 stretches the accelerated calculation result obtained by the acceleration calculation unit 112 along the time axis, and derives the analysis result on the actual time scale.

[0024] The storage unit 12 is a non-volatile memory such as a hard disk or a flash memory, and stores set analysis conditions, programs for performing acceleration calculations in the acceleration calculation unit 112 and expansion calculations in the expansion calculation unit 113, analysis calculation results, and the like.

[0025] The display unit 13 is a display device, such as a liquid crystal display, provided in the fluid analysis apparatus 1. The display unit 13 displays information such as the analysis results of the fluctuation amounts calculated by the acceleration calculation unit 112 and the stretching calculation unit 113.

[0026] The input unit 14 is an input device for inputting various analysis conditions related to the environmental fluid analysis, etc. The input unit 14 is a keyboard, a touch panel, a mouse, etc., provided in the fluid analysis apparatus 1.

[0027] Next, environmental fluid analysis using the fluid analysis device 1 will be described with reference to the flowchart in Fig. 2. As described above, in this embodiment, the environmental fluid is water flowing in a river, a flood flow caused by rising water levels in the river is assumed, and the water depth of the river is analyzed as a fluctuation amount.

[0028] First, in the analysis condition setting process, the conditions such as the physical properties of the environmental fluid, boundary conditions, and the time interval of the calculation set by the user are read, and the conditions necessary for the calculation related to the analysis are set (step S11). In the flood flow phenomenon, the time change of the local water depth h is x i Direction (i=1,2) depth average current velocity u i Unit width discharge u multiplied by water depth h i It is expressed as the divergence of h.

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[0029] In the numerical analysis, the differential equation (1) above is calculated by numerical integration using the following equation (2), and the water depth for each time and location is predicted by calculating the state at the next time step (t=n+1) from the state at the current time step (t=n).

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[0030] Also, the water depth change Δh occurs when i Flow rate in unit width u i For h, see the following x i It is calculated by solving the equation of motion for the direction.

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[0031] To calculate the water depth h, it is necessary to simultaneously solve the above equations (2) and (3). In general, the calculation time step Δt is required to be set in a range where the physical information transmission during that time step does not exceed the size of the calculation mesh. For example, in order to take into account the shape of the river, the shape of structures, local flows, etc., it is necessary to use a small calculation mesh, so it is necessary to reduce the calculation time step, which results in a drastic increase in the time required for calculation.

[0032] In this embodiment, the difference between the time increment (time resolution) ΔT representing the time scale of the flood waveform obtained in the water flow analysis and the time increment (time resolution) Δt corresponding to the time scale required by the computational mesh causes a problem in that the calculation time becomes too long for the time scale related to the results desired to be obtained by the analysis.When analyzing a river flood flow, the change in the flow rate of the desired flood flow fluctuates relatively slowly over time, and the change in flow due to the change in flow rate is smaller than the change in local flow over time at the spatial resolution of the analysis.

[0033] In this embodiment, the analytical calculation is performed by compressing the time axis of the time change in the flow rate of the environmental fluid related to the input within a range where the time step Δt set based on the local calculation mesh has a sufficiently small resolution compared to the time step ΔT required for the output (Figure 3(A)), and the calculation time is shortened while maintaining the calculation accuracy by amplifying the average component of the time change in water depth by the amount of the compression and stretching the time axis of the output waveforms of the water depth, flow velocity, flow rate, etc. related to the analysis result.

[0034] If the analysis is performed by shortening the time axis of the time change of the flow rate related to the input to 1 / α without amplifying the average component, the amount of water flowing into the analysis domain will be smaller, and the calculated water depth in the analysis domain will be smaller. As a result, the time change of the water depth at the desired point will differ from the water depth waveform of a flood solved using the input related to the original time scale, as shown in Figure 4 (B). More specifically, in the propagation of flood flow, the greater the water depth, the greater the flow velocity and the greater the propagation speed, so the shorter the flood period, the less water flows into the river channel, and as a result, the water depth will be lower, so the arrival of the flood flow at the desired point will be delayed, and the difference will be that the change in water depth during the flood period will be sudden.

[0035] One way to resolve the above discrepancy is to amplify the change in water depth h in equation (2). However, simply amplifying the change in water depth h is equivalent to increasing the calculation time step Δt, which makes the solution unstable and makes it impossible to perform an appropriate analysis.

[0036] Here, the time change in water depth h is composed of small time-scale components (local components) such as local eddies and waves, and large time-scale components (average components) related to rainfall runoff. When the fluctuations in water depth h are averaged, the influence of the fluctuations in the local components disappears, and only the influence of the average component remains. Therefore, in this embodiment, as shown in the following equation (4), by amplifying only the average component of the time change in water depth h by a factor of α, it is possible to avoid problems such as those shown in Figure 4(B) even in an analysis in which the time axis related to the time change in the input water flow rate is shortened, and appropriate calculations of the time change in the actual phenomenon are performed.

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[0037] As a specific calculation flow (FIG. 2), in the acceleration calculation step, the difference between the amount of change in the environmental fluid at the current time step and the amount of change in the environmental fluid at the next time step is calculated based on the formulas (2) and (3) (step S12). Next, the acceleration calculation unit 112 calculates the average difference value, which is the average of the water depth change amount Δh, which is the difference in the amount of change. - Δh is calculated (step S13).

[0038] Here, since it is assumed that the average component does not affect the local component, the method of calculating the difference average value is important for improving the accuracy of the analysis. In flood flow analysis, if the average component is calculated by time averaging using past analysis results, a time delay occurs in the water depth fluctuation, so if the fluctuation of the average component is amplified, the solution may oscillate and appropriate calculation may not be possible. In the river flow analysis according to this embodiment, since the river, which is the analysis target area, is long and narrow, and the flow rate of the boundary condition is a first-order quantity, the average component is calculated by a spatial averaging operation that vertically averages the cross-sectional average value of the change in the fluctuation amount (water depth) shown in the following formula instead of the time averaging. As a result, there is no time delay, which was a problem when using the time averaging, and the occurrence of oscillation of the average component is suppressed, making it possible to perform an appropriate analysis. The area in which the spatial averaging is performed may be a part of the analysis area or the entire area.

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[0039] Next, as shown in equation (4), the difference average value calculated in step S13 is calculated using a constant α that reduces the time change of the input flow rate. - The amplified average component value (acceleration average value) is calculated by multiplying Δh by α-1 (step S14). Then, the water depth h, which is the amount of fluctuation at the current time step, the water depth change amount Δh, which is the difference between the amount of fluctuation, and the amplified average component value - The amount of change in the environmental fluid (water depth) at the next time step is calculated by adding Δh·(α-1) (step S15). This avoids the problem of flood flow propagation differing from reality due to a small amount of water as shown in Figure 4(B) by multiplying the average component by α, reduces the input conditions to 1 / α, and enables analysis at an analysis speed that is α times faster.

[0040] The acceleration calculation unit 112 repeatedly executes the next time variation calculation process of steps S12 to S15 until the analysis time set in advance as an analysis condition ends (NO in step S16). Then, when the predetermined analysis time ends (YES in step S16), the process proceeds to the next process, which is the stretching process.

[0041] Next, as the stretching process, the stretching calculation unit 113 stretches the time axis of the analysis results calculated in the acceleration calculation process based on a constant α that shortens the time change of the input flow rate, and calculates the changes in various fluctuation quantities of the environmental fluid (water depth, flow velocity, flow rate) on the actual time scale (step S17).

[0042] The enlargement calculation unit 113 stores the analysis result in the storage unit 12 and displays it on the display unit 13 (step S18), and ends the analysis process.

[0043] (Numerical example) Figure 5 shows an example of the analytical calculation results when analytical calculation is performed using the above formulas (4) and (5). As shown in Figure 5, the graph when accelerated calculation is performed matches well with the graph when accelerated calculation is not performed. Therefore, it can be seen that even when the average component is amplified and the time axis of the time change of the flow rate related to the input is shortened to perform accelerated calculation, the calculation results are roughly the same as when analytical calculation is performed using the input of the original time scale.

[0044] (Application example) In the above embodiment, the case of analyzing flood flow assuming an increase in the water level of a river has been described, but the environmental fluid according to the present invention is not limited to water flowing in a river, and ocean currents, waves, and atmospheric motions can be treated as environmental fluid motions. More specifically, an analysis target in which there is a large gap between the time scale required for the analysis calculation and the time scale required by the computational mesh, and in which the interaction between local components and average components is not easily observed, can be selected as an environmental fluid motion suitable for the present invention, and the analysis calculation using formula (4) can be accelerated. For example, erosion by water currents and waves, such as bedrock erosion and beach topography change, is a phenomenon in which minute changes due to flow and sediment transport accumulate, so it is generally required to calculate on a time scale that is extremely long compared to the scale of the flow. In this case, if the acceleration calculation of the present invention is used for the local topography change amount Δz, with the change amount being the ground height z, the acceleration calculation can be performed as shown in the following formula (6).

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[0045] Equation (6) acts on the fluid motion related to the first term on the right-hand side of the equation of motion in equation (3), etc. In general, the amount of topographical change Δz at each time step is small compared to the change in fluid motion, and its average value is even smaller. Unlike flood phenomena with large waveforms, wave erosion is considered to be a periodic phenomenon on a short time scale, so by expressing the average component as a time average, it is believed that it will be possible to analyze localized long-term phenomena.

[0046] In addition, the present invention can be applied to the calculation of equation (2) included in an existing calculation program by writing the averaging corresponding to equation (4) into the existing program, so it can be easily used in conjunction with existing fluid analysis methods and can be easily implemented. Therefore, it can be used for various environmental fluid simulations.

[0047] As described above, in the environmental fluid analysis method using the fluid analysis device according to the present embodiment, in order to obtain the same solution in an analysis in which the calculation period is shortened to 1 / α, the average value of the difference in the amount of fluctuation for each calculation step is multiplied by α-1, thereby shortening the time required for the overall analysis and enabling efficient and appropriate calculations. Furthermore, since the analysis is performed without amplifying local components that represent components with fast time fluctuations in the calculation of each time step, it is possible to perform environmental fluid analysis with high accuracy at the time interval required for spatial resolution.

[0048] Furthermore, the environmental fluid analysis apparatus according to the above embodiment can be realized by using a normal computer system. For example, a computer program for performing the environmental fluid analysis according to the above embodiment can be distributed via a network such as the Internet, and the computer program can be installed in a computer to cause the computer to function as the environmental fluid analysis apparatus that performs the above environmental fluid analysis. [Industrial Applicability]

[0049] The present invention is suitable for analyzing fluctuations in environmental fluids having different spatiotemporal scales. [Explanation of symbols]

[0050] 1 Fluid analysis device, 11 Control unit, 111 Image acquisition unit, 112 Vibration analysis unit, 113 Display image generation unit, 12 Storage unit, 13 Display unit, 14 Input unit

Claims

1. An environmental fluid analysis method for performing a fluctuation analysis of an environmental fluid including a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation, comprising: an acceleration calculation step of calculating a time change of the fluctuation amount by repeatedly executing a next-time fluctuation amount calculation process in which the fluctuation amount at the next time step is calculated by accelerating the analysis based on an actual time scale based on the fluctuation amount of the environmental fluid at the current time step; and an expansion step of calculating a time change of the amount of fluctuation based on the time change of the amount of fluctuation calculated in the acceleration calculation step so as to return the amount of fluctuation to an actual time scale, In the acceleration calculation step, Calculating a difference between the amount of change in the next time step and the amount of change in the current time step; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; calculating the amount of change in the next time step by the sum of the amount of change in the current time step, the difference, and the acceleration average value; In the stretching calculation step, The time change of the fluctuation amount calculated in the acceleration calculation step is stretched based on the constant, thereby calculating the time change of the fluctuation amount on an actual time scale. An environmental fluid analysis method comprising:

2. The average is a spatial average of part or all of the analysis area; 2. The environmental fluid analysis method according to claim 1,

3. The average is an average of the time change of the fluctuation amount.

2. The environmental fluid analysis method according to claim 1,

4. the environmental fluid is water flowing in a river, The amount of change is the water depth of the river.

2. The environmental fluid analysis method according to claim 1,

5. An environmental fluid analysis device that performs a fluctuation analysis of an environmental fluid including a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation, an acceleration calculation unit that calculates a time change of the fluctuation amount by repeatedly executing a next-time fluctuation amount calculation process that calculates the fluctuation amount at a next time step by accelerating the fluctuation amount at a next time step based on the fluctuation amount of the environmental fluid at a current time step with respect to an analysis based on an actual time scale; and an expansion calculation unit that calculates a time change of the amount of fluctuation based on the time change of the amount of fluctuation calculated by the acceleration calculation unit so as to return the amount of fluctuation to an actual time scale, The acceleration calculation unit is Calculating a difference between the amount of change in the next time step and the amount of change in the current time step; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; calculating the amount of change in the next time step by the sum of the amount of change in the current time step, the difference, and the acceleration average value; The stretching calculation unit includes: The time change of the fluctuation amount calculated by the acceleration calculation unit is stretched based on the constant, thereby calculating the time change of the fluctuation amount on an actual time scale. An environmental fluid analysis device comprising:

6. Computer, Calculating a difference between an amount of fluctuation of an environmental fluid at a next time step and an amount of fluctuation of the environmental fluid at a current time step, the amount of fluctuation being a local component representing a component with a fast time fluctuation and an average component representing a component with a slow time fluctuation; Calculating an average difference value obtained by averaging the differences; calculating an accelerated average value by multiplying the difference average value by a constant that is determined in advance within a range in which the fluctuation of the environmental fluid due to the average component is sufficiently small relative to the fluctuation of the environmental fluid due to the local component; an acceleration calculation unit that calculates the change over time of the amount of variation by repeatedly executing a next-time variation calculation process in which the amount of variation at the next time step is calculated by adding the amount of variation at the current time step, the difference, and the accelerated average value, thereby accelerating and calculating the amount of variation at the next time step with respect to an analysis based on an actual time scale; an extension calculation unit that calculates the time change of the fluctuation amount calculated by the acceleration calculation unit by extending the time change of the fluctuation amount based on the constant so as to return the time change to an actual time scale; A program that functions as a

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