WO2004088563A1 - Fluid analyzing method - Google Patents

Abstract

A first unknown physical property value in the vicinity of an inter-fluid interface is calculated using an advection equation and based on the known physical properties of respective fluids forming the interface, a first unknown fluid behavior value representing an behavior in the vicinity of an inter-fluid interface is calculated using the control equations of fluids and based on the calculated first unknown physical property, an interface function in the vicinity of an inter-fluid interface is calculated using a digitizer method and based on the calculated first unknown fluid behavior value, and the calculated interface function is converted using a smoothing method. A second unknown physical property in the vicinity of an inter-fluid interface is calculated using an advection equation and based on the known physical properties of respective fluids forming the interface and the converted interface function, and second unknown fluid behavior value representing an behavior in the vicinity of an inter-fluid interface is calculated using the control equations of fluids and based on the second unknown physical property and the first unknown fluid behavior value.

Description

 Specification

Fluid analysis method Technical field

 The present invention relates to a fluid analysis method, a fluid analysis program, and a fluid analysis device for performing a numerical simulation of a free surface flow based on an interface ίin capture method in a numerical solution method for a free surface problem. Background art

 The problem of a flow with a free surface is called the moving boundary problem as a more general classification, and the interface trapping method and the interface tracking method have been developed as methods for dealing with the moving boundary surface. The interface tracking method includes, for example, the ALE method developed by CW Hirt et al. In 1972 and the Space-Time method developed by R. Bonnerot et al. In 1977. .

 This interface tracking method is effective because it can represent the interface more accurately. However, since the computational mesh on the free surface (interface) moves along with the fluid particles, the free surface (interface) is used when expressing the moving boundary. If the moves greatly, the distortion of the calculation mesh becomes large, and the calculation becomes difficult. In addition, the computational mesh must be changed at every hour step, which complicates the algorithm (for example, the Numerical Computational Fluid Dynamics Editing Committee, 4 Moving Boundary Flow Analysis, The University of Tokyo Press, 199 March 10, 2005.)

On the other hand, the interface capture method uses a fixed computational mesh, a force S that requires special processing when expressing the moving boundary, and a simple algorithm because the computational mesh does not change every hour. This is advantageous for the phenomenon that the interface greatly fluctuates. As a typical solution to this interface capture method, for example, the VOF (Volume of Fluid) method was launched in 1981 by CW Hirt et al. (For example, CW H irtand BD N ichols

, Vo l ume o f F l u i d (VOF) Me t h o d f o r t h e

Dy n am i c s o f F r e B o un d a r i es, J o u r n a l o f Comp u t a t i o n a l Phy s i cs,. 1981, 39,.

201—See page 205. ).

 In the VOF method, in the Navier-Stokes equation (Equation (1) and Eq. (2)), which is the governing equation of a fluid, physical properties (density p, viscosity coefficient of fluid (fluid Α , The fluid Β), the advection equation (Equation (3)) below with the interface function Φ as an unknown quantity, the interface function φ is defined, and the physical property values are defined using the defined interface function φ. This is an interface capture method that calculates by the following equations (4) and (5) and determines the interface.

(1)

= 0 (2)

ρ = φρ _Α + (ΐ-φ) ρ _Β (4).

In the above equations (1) to (5), t represents time, and 1 ₁ represents the spatial direction (two-dimensional when i = 1, 2; three-dimensional when i = 1, 2, 3). The velocity component, p is pressure, and fi is external force. In Equations (4) and (5), p _A is the density of fluid A, p _B is the density of fluid B, / ^ is the viscosity coefficient of fluid A, and μ _{で あ} is the viscosity coefficient of fluid B. You.

 The interface function φ takes a value of 0 ≤ φ ≤ 1, and the fluid A and the fluid B use the interface function φ, as shown in Fig. 40, where the interface function φ of the fluid A is ψ = 1, and the fluid Β Is defined as φ = 0, and the part where the interface function φ = 0.5 is evaluated as the interface between different fluids A and B. .,

 Here, the advection equation in which the fluid A is φ = 1 and the fluid Β is ψ = 0 is to solve a function whose interface is discontinuous as shown in FIG. 41 by the above equation (3). In the solution based on these VOF methods, the problem is how to accurately obtain the interface function.

 It should be noted that there is no solution that can accurately analyze the advection equation of the above equation (3) by numerical calculation using a function having a discontinuous distribution as shown in FIGS. 41 and 42. When a solution such as the stabilized finite element method (for example, the stabilized bubble function method) is used, the calculation results shown in Fig. 43 are obtained (for example, Junichi Matsumoto, Go Umezu, Mutsuto Kawahara, stabilization for shallow water long wave equation) See the finite element method and the stabilized bubble function method, Journal of Applied Mechanics, Japan Society of Civil Engineers, 2002, Vol. 5, pp. 235-242.) As one of the interface capturing methods based on the VOF method, the S FEZ IC method was developed in 2000 by S. Aliabadi et al. This SFE / IC? Le 'method is a method of remodeling a function with a broken discontinuous distribution obtained by numerical calculation into a sharp distribution (for example, S. Aliabadiand TE Te du duar, S tabi—lized—F inite—Ele ment / lnterface—Capturing Te chnique for Pararel C omp utationof Un steady F lows with Interface, Computer Me thodsin Ap plied Me chanicsand Eng ineering, 2000, 190, pp. 243—see pp. 261.).

Further, in 1994, Sussman et al. Developed the Le vel Set method as one of the interface trapping methods based on the VOF method. Le vel S e The t method is a method to evaluate interfaces by introducing a distance function with a smooth distribution instead of solving an interface function with a discontinuous distribution. Since this solution calculates a smooth function, it is possible to evaluate the interface with high accuracy (for example, M. Susman, P. Smereka, and S. O sher, A. evel S et Ap proach for Computing S o1 utionsto Incos ressible Two—Phase Flow, Journal of Computational Physics, 1994, 114, pp. 146—pp. 159).

 Also, as one of the fluid analysis methods, a CIP (Cubic-InterpolpalatepRopatagation) method has been developed. The digitizer method proposed in 1993 by Yabe et al. In this solution using the CIP method uses a discrete tangent transformation function instead of solving the actual discontinuous interface function. Functions such as T. Ya beand F. Xiao, De scription of Complexandsharp I nterface du ring Shock Wave I nteractionwith L i quid Drop, Journalof Physical So ciety of Japan, 1993, 62, pp. 2537—pp. 2540.).

'However, when the interface function φ is calculated for one period around the origin from the initial conditions shown in Fig. 43 (a), the distribution of the interface function φ gradually collapses as shown in Fig. 43 (b). After 5 cycles, the portion where the discontinuous interface function 分布 is distributed becomes narrower and becomes almost conical as shown in Fig. 43 (c). Thus, even if the stabilized finite element method, which was considered effective at the moment, is used, if there is a time change, the interface state of the interface function Ψ cannot be maintained, and the The evaluation of the discontinuous surface was insufficient, and the interface function φ could not be calculated accurately. When the ordinary finite element method is used, as shown in Fig. 44 (a), after 1/4 period, the distribution of the interface function φ is changed to the stabilized finite state shown in Fig. 44 (b). Element method 9

5, the evaluation of the discontinuous surface of the interface function Φ became much more insufficient, and the interface function Φ could not be calculated with high accuracy.

 Here, the effect of the calculation results when the evaluation of the interface function Φ on the discontinuous surface when the VOF method is applied will be described using a model shown in FIG. 45. In this model, the air in the water rises toward the free surface (water surface). The calculation results of the analysis model in FIG. 45 are as shown in FIG. In other words, in Fig. 46, the accuracy of the interface function having a discontinuous distribution is poor, and as the calculation proceeds, the interface force S between two fluids, that is, air and water, is blurred, and exactly two This means that the fluid interface has not been calculated.

 In addition, as shown in Fig. 47, the SFE / IC method is remodeled from the distribution of the broken interface function φ, and is gradually affected by the broken distribution. As shown in FIG. 47 (a), from the initial conditions shown in FIG. 47 (a), the distribution shape is deformed as shown in FIGS. 47 (b) and 47 (c), and the interface function Ψ The shape could not be maintained, and the interface function φ could not be calculated accurately.

 In the Level Set method, a function that satisfies the definition of the distance function (| VF | = 1) is obtained by iterative calculation.If the fluid behavior is complicated, the calculation result does not always converge even after repeated iterations. Absent. Even if the solution can be calculated, a large amount of labor (computation cost) is required if the number of iterations is very large.

 On the other hand, if the digitizer method used in the above-mentioned CIP method is incorporated into the solution of the finite element method, the interface function φ under the initial conditions shown in Fig. 48 (a) becomes as shown in Fig. 48 (b). Even after one cycle, the shape of the interface function Φ is maintained even after five cycles, as shown in Fig. 48 (c), and accurate calculations can be performed for the discontinuous function. be able to.

However, for the analytical model shown in Fig. 45, the interface function obtained via the digitizer method described above shows that the value of the interface function φ corresponding to fluids A and B is , 1 and 0, which are extremely discontinuous functions. Since the finite element method divides an arbitrary region into a mesh with a finite shape such as a triangle or a tetrahedron, if this function is evaluated as an interface as it is, the interface between the two fluids, air and water, This results in a rattling interface as shown in Fig. 49.

 As shown in Fig. 49, considering the interface between two actual fluids, the interface has a smooth distribution with a certain curvature due to the effect of surface tension. Due to this surface tension, when an extremely discontinuous interface function is used, the interface is rattled, and the evaluation taking into account the effect of the surface tension on the interface cannot be performed. As a result, the calculation becomes rather unstable. However, the obtained result does not represent the actual phenomenon. In addition, if iterative calculation was performed using this method, calculation could not be performed, and there was a problem that fluid analysis could not be performed. The present invention solves the above-mentioned problems of the prior art by accurately calculating an interfacial function having a discontinuous distribution by a simple and versatile method, and furthermore, a surface between fluids having different physical properties. An object of the present invention is to provide a fluid analysis method, a fluid analysis program, and a fluid analysis device that can incorporate the smoothness of an interface caused by tension into an interface function. Disclosure of the invention

In order to solve the above-described problems and achieve the object, a fluid analysis method according to the present invention uses advection equations based on known physical property values of each fluid forming an interface, to obtain a first fluid near an interface between the fluids. A first unknown physical property value calculating step of calculating the first unknown physical property value, and a first unknown physical property value calculated in the first unknown physical property value calculating step, using a governing equation of a fluid. A first unknown fluid behavior value calculation step of calculating a first unknown fluid behavior value representing a behavior in the vicinity of the interface between the fluids, and a first unknown fluid behavior value calculation step of using a digitizer method Calculating an interface function in the vicinity of the interface between the fluids based on the first unknown fluid behavior value calculated by the interface function calculating step; and calculating the interface function using the smoothing method. And an interface function conversion step of converting the obtained interface function. According to the present invention, an interface function having a discontinuous distribution can be converted into an interface function corresponding to an actual interface state between fluids.

 Further, the above-mentioned fluid analysis method uses the advection equation to calculate the following based on known physical property values of each of the fluids forming the interface, and an interface function converted in the interface function conversion step. Calculating a second unknown property value in the vicinity of the interface between the fluids, a second unknown property value calculation step, and a second unknown property value calculated in the second unknown property value calculation step using the governing equation of the fluid. A second unknown fluid behavior representing a behavior in the vicinity of the interface between the fluids, based on the unknown physical property value and the first unknown fluid behavior value calculated in the first unknown fluid behavior value calculation step And a second unknown fluid behavior value calculating step of calculating the value.

 According to the present invention, it is possible to reproduce the behavior near the interface between fluids that changes with time.

 Further, the above-mentioned fluid analysis method uses the advection equation to calculate a first unknown property value near the interface between the fluids based on the known property values of the respective fluids forming the interface. A first unknown physical property value calculated in the first unknown physical property value calculating step using a physical property value calculating step and a governing equation of the fluid; a surface tension coefficient of one of the fluids; and the interface A first unknown fluid behavior value calculation step of calculating a first unknown fluid behavior value representing a behavior in the vicinity of the interface between the fluids, based on a curvature function representing a curvature of and a digitizer method. An interface function calculating step of calculating an interface function near an interface between the fluids based on the first unknown fluid behavior value calculated in the first unknown fluid behavior value calculating step; The said world The interface function conversion step of converting the interface function calculated by the function calculation process, it is also possible that contains.

According to the present invention, an interface function having a discontinuous distribution can be converted into an interface function corresponding to an actual interface state between fluids affected by surface tension. '' Further, the above-described fluid analysis method according to the third aspect of the present invention, The second unknown in the vicinity of the interface between the fluids, based on the known physical property values of each of the fluids forming the interface and the interface function converted in the interface function conversion step, using the advection equation A second unknown property value calculating step of calculating a property value; a second unknown property value calculated in the second unknown property value calculating step using the governing equation of the fluid; and A first unknown fluid behavior value calculated in the unknown fluid behavior value calculation step, a surface tension coefficient of one of the fluids, a curvature at an interface between the fluids obtained from the converted interface function, And a second unknown fluid behavior value calculating step of calculating a second unknown fluid behavior value representing a behavior near the interface between the fluids based on a curvature function representing the curvature of the interface. And as Is also good.

 According to the present invention, it is possible to reproduce a behavior taking into account the effect of surface tension in the vicinity of the interface between fluids that changes over time.

 Further, a fluid analysis program causes a computer to execute the fluid analysis method according to any one of the above.

 According to the present invention, the fluid analysis method according to any one of the above aspects can be realized by computer processing.

In addition, the fluid analysis device includes a data storage unit for storing a known physical property value representing a property of the fluid for each fluid, and two fluids to be analyzed, and the known physical property value of the selected fluid is determined. A fluid for calculating a fluid behavior value representing a behavior in the vicinity of the interface between the fluids based on physical properties in the vicinity of the interface of the fluid, using data extraction means extracted from the data storage means and a fluid control equation; A behavior value calculation unit; an interface function calculation unit that calculates an interface function near the interface between the fluids based on the fluid behavior value calculated by the fluid behavior value calculation unit using a digitizer method; and a smoothing method. An interface function conversion means for converting the interface function calculated by the interface function calculation means, and an advection equation, and A material for calculating a physical property value in the vicinity of the interface between the fluids based on the physical property value of the extracted fluid and the interface function converted by the interface function converting unit. And a calculating means.

 According to the present invention, an interface function having a discontinuous distribution can be converted into an interface function corresponding to an actual interface state between fluids.

 Further, in the above-described fluid analysis device, the data storage unit further stores a surface tension coefficient for each of the fluids, and the data extraction unit further includes a data storage unit for the fluid selected by the fluid selection unit. One of the surface tension coefficients is extracted from the data storage means, and the fluid behavior value calculation means uses the governing equation of the fluid, and further, any one of the surface tension coefficients is extracted from the data extraction means. Near the interface between the fluids, based on the surface tension coefficient of the fluid, the interface function converted by the interface function conversion means, and the curvature at the interface between the fluids obtained from the converted interface function. The method is characterized by calculating a fluid behavior value representing the behavior at.

 According to the present invention, an interface function having a discontinuous distribution can be converted into an interface function corresponding to an actual interface state between fluids affected by surface tension.

 '

Brief description of the drawings ''

FIG. 1 is a block diagram showing a hardware configuration of a fluid analysis device according to the embodiment of the present invention, and FIG. 2 is a functional configuration of the fluid analysis device according to the embodiment of the present invention. FIG. 3 is a block diagram illustrating a fluid information table stored in a data storage unit in the fluid analyzing apparatus according to the embodiment of the present invention. FIG. 4 is a block diagram of the present invention. FIG. 5 is a flowchart showing a pre-processing procedure in the fluid analysis device according to the embodiment; FIG. 5 is a flowchart showing a fluid analysis processing procedure in the fluid analysis device according to the embodiment of the present invention; FIG. 5 is a flowchart showing a fluid analysis processing procedure in the fluid analysis device according to the embodiment of the present invention. FIG. 7 is a flowchart showing the VOF method using the analysis model of FIG. 45 as an example. A comparison view of the fluid analysis according to VOF method + Dejitiza method and the present embodiment, FIG. 8 is an analysis model of the fourth 5 view the example, VO F method and VOF FIG. 9 is a comparison diagram between the flow model and the digitizer method and the fluid analysis according to the present embodiment. FIG. 9 shows an example of the analysis model shown in FIG. Fig. 10 is a comparison diagram of the VOF method, the VOF method + the digitizer method, and the fluid analysis according to the present embodiment, taking the analysis model of Fig. 45 as an example. Yes, FIG. 11 is a comparison diagram of the VOF method, the VOF method + the digitizer method, and the fluid analysis according to the present embodiment, taking the analysis model of FIG. 45 as an example, and FIG. Fig. 13 is a comparison diagram of the VOF method, the VOF method + the digitizer method, and the fluid analysis according to the present embodiment, taking the analysis model of the figure as an example.Fig. 13 shows the analysis model of Fig. 45 as an example. FIG. 14 is a comparison diagram of the VOF method, the VOF method + the digitizer method, and the fluid analysis according to the present embodiment. FIG. 14 shows the analysis model of FIG. Fig. 15 is a comparison diagram between the VOF method, the VOF method + the digitizer method, and the fluid analysis according to the present embodiment, and Fig. 15 shows the VOF method and the VO method using the analysis model in Fig. 45 as an example. Fig. 16 is a comparison diagram between the F method + digitizer method and the fluid angle drought according to the present embodiment. Fig. 16 shows the VOF method, VOF method + digitizer method, FIG. 17 is a comparison diagram with the fluid analysis according to the embodiment of the present invention. FIG. 17 shows an example of the VOF method, the VOF method and the digitizer method, and the fluid analysis according to the present embodiment. Fig. 18 is an explanatory diagram showing an analysis model of the bubble flow in water. Fig. 19 is a case where the bubble shape (Spherica 1) is taken as an example in the analysis model of Fig. 18. Fig. 20 is an explanatory diagram showing the behavior of the fluid. Fig. 20 shows an example of the bubble shape (Sk irted) in the analysis model of Fig. 18. Fig. 21 is an explanatory diagram showing the behavior of the fluid in the case.Fig. 21 is an explanation showing a model for analyzing the behavior of the fluid inside the converter in which pure oxygen gas flows at high speed from the lance to produce metals such as iron and copper. FIG. 22 is an explanatory diagram showing the flow velocity vector inside the converter in the analysis model of FIG. 21. FIG. 23 is a diagram showing the flow velocity inside the converter in the analysis model of FIG. FIG. 24 is an explanatory diagram showing a vector, FIG. 24 is an explanatory diagram showing a flow velocity vector inside a converter in the analysis model of FIG. 21, and FIG. 25 is a diagram showing a conversion vector in the analysis model of FIG. FIG. 26 is an explanatory diagram showing flow velocity vectors inside the furnace. 9

Fig. 11 is an explanatory diagram showing the flow velocity vector inside the converter in the analysis model of Fig. 21.Fig. 27 shows the flow velocity vector inside the converter in the analysis model of Fig. 21. Fig. 28 is an explanatory diagram showing the flow velocity vector inside the converter in the analysis model of Fig. 21. Fig. 29 is an explanatory diagram of the analysis model of Fig. 21. FIG. 30 is an explanatory diagram showing a flow velocity vector inside the converter. FIG. 30 is an explanatory diagram showing a flow velocity vector inside the converter in the analysis model of FIG. 21. FIG. 3 is an explanatory diagram showing a model for analyzing the behavior of a fluid that ejects ink from a force. FIG. 32 is a mesh diagram divided into fixed meshes in the angular analysis model of FIG. . FIG. 33 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. 31; FIG. 34 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. 31; FIG. 35 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. 31. FIG. 36 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. FIG. 37 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. 31. FIG. 38 is an explanatory diagram showing a gas-liquid interface in the analysis model of FIG. FIG. 39 is an explanatory diagram showing a gas-liquid interface in the analytical model of FIG. 31. FIG. 40 is an explanatory diagram showing an analytical model of an interface between fluids and fluids. The figure is an explanatory view showing a function as an example of analysis in FIG. 40, and FIG. 42 is a graph obtained by expanding the function in FIG. 41 into xy coordinates. Yes, FIG. 43 is an explanatory diagram showing a function as an example of analysis when the stabilized bubble function method is applied in the analysis model of FIG. 40, and FIG. In the analysis model shown in the figure, it is an explanatory diagram showing a function as an example of analysis when the finite element method is applied.Fig. 45 is an explanatory diagram showing an analytical model showing a flow state of bubbles in water. FIG. 46 is an explanatory diagram showing a gas-liquid interface and a flow velocity vector when the VOF method + stabilized bubble function method is applied in the analysis model of FIG. 45. FIG. 48 is an explanatory diagram showing a function that is an example of analysis when the SF EZ IC method is applied to the analysis model of FIG. 40. FIG. 48 is a diagram illustrating the VO F in the analysis model of FIG. FIG. 49 is an explanatory diagram showing a function which is an example of analysis when the method + digitizer method is applied. F method + Digi T / JP2004 / 004529

FIG. 12 is an explanatory diagram showing a flow velocity vector when the Tiza method is applied. BEST MODE FOR CARRYING OUT THE INVENTION

 Preferred embodiments of a fluid analysis method, a fluid angle analysis program, and a fluid analysis device according to the present invention will be described below in detail with reference to the accompanying drawings. In this embodiment, the VOF method is used to handle complex interfaces, and the CIP method is proposed to calculate an accurate free surface.'The digitizer method adopted is a finite element method (stabilized bubble function Method). Also, when incorporating the digitizer method using the finite element method, a smoothing method that can accurately represent the interface evaluation method when calculating using the finite element method is adopted.

 (Hardware configuration of fluid analyzer)

 First, the hardware configuration of the fluid angle analyzer 1 according to the present embodiment will be described with reference to FIG. The fluid analyzer 1 includes a CPU 101, a ROM 102, a RAM 03, an HDD (hard disk drive) 104, an HD (hard disk) 105, an FDD (flexible disk drive) 106, and an example of a removable recording medium. An FD (flexible disk) 107, a display 108, an IZF (interface) 109, a keyboard 110, a mouse 111, a scanner 112, and a printer 113 are provided. Each component is connected by a bus 100.

 Here, the CPU 101 governs overall control of the fluid analysis device 1. The ROM 102 stores programs such as a boot program. RAMI 03 is used as a work area of CPU 101. The HDD 104 controls read / write Z of data to / from the HD 105 under the control of the CPU 101. The HD 105 stores data written under the control of the HDD 104.

The FDD 106 controls reading / writing of data from / to the FD 107 under the control of the CPU 101. The FD 107 stores the data written under the control of the FDD 106 and reads the data stored in the FD 107 into the fluid analysis device 1. Or take it. The removable recording medium may be a CD-ROM (CD-R, CD-RW), MO, DVD (Digital Versati 1 e Disk), a memory card, or the like. The display 108 displays data such as a document, an image, and function information, including a cursor, an icon, or a tool box. As the display 108, for example, a CRT, a TFT liquid crystal display, a plasma display, or the like can be adopted.

 The IZF 109 is connected to a network such as the Internet via a communication line, and is connected to other devices via this network. The IZF 109 manages a network and an internal interface, and controls input / output of data from an external device. As the I / F 109, for example, a modem or a LAN adapter can be used.

 The keyboard 110 has keys for inputting letters, numbers, various instructions, and the like, and performs data input. Further, it may be a touch panel type input pad / numeric keypad. The mouse 111 is used to move the cursor, select a region, or move and change the size of the window ゥ. A trackball, a joystick, or the like may be used as long as the pointing device has the same function.

 The scanner 112 optically reads an image and takes in the image data into the fluid analyzer 1. The printer 113 prints image data and document data. As the printer 113, for example, a laser printer or an ink jet printer can be employed.

 (Functional configuration of fluid analyzer 1)

Next, a functional configuration of the fluid analysis device 1 according to the present embodiment will be described. As shown in FIG. 2, the fluid analysis device 1 includes a data storage unit 2, a data extraction unit 3, an initial setting unit 4, a fluid analysis unit 5, and a display control unit 6. As shown in Fig. 3, data storage unit 2 stores fluid ID, fluid name, fluid property values (density, viscosity coefficient, surface tension coefficient), initial fluid behavior value ( 2004/004529

14 and an analysis start pressure). Although not shown, the data storage unit 2 also stores, as initial setting information, information such as the time increment and the number of calculation steps for performing the sequential analysis calculation in the time direction.

 Furthermore, mesh information such as the division width, the number of nodes, and the number of meshes of the fixed mesh divided and formed in the analysis target range is also stored. This fixed mesh is composed of triangles or grids when the analysis target area is a two-dimensional space, and finite hollows such as tetrahedrons or cubes when the analysis target area is a three-dimensional space. The mesh information can also be captured by reading with the scanner 112. Specifically, the function of the data storage unit 2 is realized by, for example, the RAM 103, the HD 105, or the FD 107 shown in FIG.

 The data extraction unit 3 selects the fluid ID of the fluid to be analyzed, and from the data storage unit 2, the fluid name and known physical properties (density, viscosity coefficient, surface tension coefficient) associated with the selected fluid ID ) Extract the initial fluid behavior values (analysis start flow velocity and analysis start pressure). Specifically, the data extraction unit 3 executes the programs stored in, for example, the ROM 102, the RAMI 03, the HD 105, and the FD 107 shown in FIG. The IZF 109 shown implements that function.

 After the extraction of each data by the data extraction unit 3, the initial setting unit 4 assigns the analysis start interface function φ to one of the selected fluids. (Interface function φ at time t == 0) φ = 1, Analysis start interface function Φ for the other fluid selected. Is set as φ = 0. In addition, when the two selected fluids are a gas and a liquid, the initial setting unit 4 outputs the surface tension coefficient of the liquid to the fluid behavior value calculation unit 8. Specifically, the initial setting unit 4 executes the program stored in the ROM 102, RAMI 03, HD 105, FD 107, or the like shown in FIG. The function is realized by the I / F 109 shown in FIG.

The fluid analysis unit 5 includes a physical property value calculation unit 7, a fluid behavior value calculation unit 8, and an interface function calculation unit. 2004/004529

15

9, an interface function conversion unit 10, and a force. The fluid analysis unit 5 analyzes the behavior of the fluid for each fixed mesh stored in the data storage unit 2. Specifically, the fluid analysis unit 5 executes the program stored in, for example, the ROM 102, the RAMI 03, the HD 105, and the FD 107 shown in FIG. The IZF 109 shown implements that function. The physical property value calculation unit 7 calculates the interface function φ converted by the interface function conversion unit 10 and the density of the fluid extracted from the data extraction unit 3 using the advection equations of the following equations (6) and (7). The unknown density p and the unknown viscosity coefficient // at the interface between the fluids are calculated based on and the viscosity coefficient and (hereinafter, the calculated unknown density p is referred to as the “calculated density, and the calculated unknown viscosity coefficient μ is referred to as “calculated viscosity coefficient /”. ρ = φρ _Α + (1-φ) ρ _Β

μ = φμ _Α + (ΐ-φ) μ _Β ■ ■ · (7)

Where ρ _Α is the density of fluid Α and p _B is the density of fluid B. _A is the viscosity coefficient of fluid A, and _μΒ is the viscosity coefficient of fluid B. It should be noted that the physical property value calculation unit 7 is realized by the CPU 101 executing a program stored in, for example, the ROM 102, the RAMI 03, the HD 105, the FD 107 shown in FIG. The function is realized by the I / F 109 shown in FIG.

The fluid behavior value calculation unit 8 uses the Na Vier-S tokes equation shown in the following equation (8) and equation (9) to calculate the fluid density based on the calculated density and the calculated viscosity coefficient at the interface between the fluids. Calculate unknown flow velocity u, V, w at the interface. At the same time, the unknown pressure p is calculated (hereinafter, the calculated unknown velocities u, V, w are referred to as “calculated flow velocities u, V, wj”, and the calculated unknown pressure p is referred to as “calculated pressure p”. ). 2004/004529

16

dp d ^ Uj

P ~~ ^L + U ~ ^L + ι ι j 6Xj

 V dt J no

Or (8)

= 0 (9)

dx: where i and j are natural numbers selected from 1 to 3. I and j are numbers representing dimensions in the spatial direction of the analysis target range. When U i -U i, the calculated flow velocity u of the fluid in the X-axis direction is expressed.When U i = u ₂ , represents a calculated flow velocity V of the fluid in the Y-axis direction, when the U i = u _3, represents the calculated flow velocity w of the fluid definitive in the Z-axis direction.

Also, I ₅ represents an external force, is set Te cowpea the analysis scope of environment for fluid analysis. That is, the external force fi can be expressed by the following equation (10).

 f i = f g f s V, '(10)

Here, the external force i _gi is the external force due to the gravitational acceleration g, and in a two-dimensional case, is represented by the following equation (11). The three-dimensional case is expressed by the following equation (12). -'

 if ^ (0,

 (11)

g2 ノ 一 P'g

The external force fsvi is the external force due to the surface tension modeled by JU Brakbi 11 et al. In 1992 (CSF model). Therefore, it can be represented.

Here, _Κ (φ) is a curvature function representing the curvature of the interface, and is represented by the following equation (14).

 Specifically, the fluid behavior value calculation unit 8 executes the program stored in the ROM 102, RAMI 03, HD 105, FD 107, or the like shown in FIG. The function is realized by the IZF 109 shown in Fig. 1.

 The interface function calculation unit 9 calculates the interface function Φ in the analysis target range based on the calculated flow velocity calculated by the fluid behavior value calculation unit 8 using the digitizer method. Specifically, it is a process in which the digitizer method is applied to the advection equation. The calculated flow velocities u and V input from the fluid behavior value calculation unit 8 (in the case of two dimensions. In the case of three dimensions, the calculated flow velocity u , V, w) and digitizer processing is performed by the following equation (15). In this digitizer method, a function having a discontinuous distribution is obtained via a function F () using a tangent transformation instead of solving the actual discontinuous interface function φ.

¾) _{+ U} .¾) _{= 0} (15)

at ¹ 6κ:

 That is, solving equation (15) yields the tangent transformation equation of equation (16) below. Then, this equation (16) is converted into the following equation (17), and the interface function φ is calculated.

... (16) φ = ίοη ^-1 Ρ (φ) / {(ΐ-ε) π} -ι-1 / 2 · '■ (17)

In the above equation (17), ε is, for example, ε = 10 ⁵ . This is an adjustment value that suppresses the divergence of Eq. (17) to infinity. Specifically, the interface function calculating unit 9 executes the programs stored in, for example, the ROM 102, the RAMI 03, the HD 105, and the FD 107 shown in FIG. The function is realized by the I / F 109 shown in FIG. The interface function conversion unit 10 converts the interface function <ί »calculated by the interface function calculation unit 9 into a smoothed interface function ψ using the following equation (18), and Execute the smoothing process. Specifically, the interface function Φ calculated by the interface function calculator 9 is converted using a diffusion equation shown in the following equation (18).

Κ- = 0

 ds dx: dX i: ノ

 Here, s is a virtual time, and K is a virtual diffusion coefficient. The indicators for selecting s and Κ are as follows.

 (i) The diffusion equation is used to smooth the jagged shape by the interface function ψ calculated by the digitizer method.

 (ii) The virtual time s and the virtual diffusion coefficient K are selected so that the jagged shape due to the interface function φ becomes the same as the initial shape. The selection of the diffusion coefficient K is performed only once in the initial analysis.

 (iiii) The degree of the jaggedness depends on the division width, but a different value can be specified for the virtual diffusion coefficient K for each element, and it is applicable even when the element division is not homogeneous. Since the surface capture method generally uses a fixed mesh for time evolution, the initially selected virtual time s and virtual diffusion coefficient K are valid for subsequent time steps. .

In addition, as a specific expression method of the smoothed interface, the interpolation function used in the smoothing process (when solving the diffusion equation) is used. For example, if you use a first-order element to solve the diffusion equation, you can approximate the interface by first-order interpolation. I have. It should be noted that the interface function conversion unit 10 is executed by the CPU 101 executing a program stored in, for example, the ROM 102, the RAMI 03, the HD 105, the FD 107 shown in FIG. The function is realized by the IZF 109 shown in (1).

 In addition, the display control unit 6 outputs the analysis result of the fluid analysis unit 5 to the display 108 shown in FIG. Since this display control is generally used for fluid analysis by the VOF method, its description is omitted. Specifically, the display control unit 6 is executed by the CPU 101 executing a program stored in, for example, the ROM 102, the RAMI 03, the HD 105, and the FD 107 shown in FIG. The function is realized by the IZF 109 shown in Fig. 1.

Next, a processing procedure according to the present embodiment will be described with reference to flowcharts in FIGS. Here, fluid A is gas and fluid B is liquid. First, as shown in FIG. 4, when a fluid ID to be analyzed is selected via an input device (for example, the keyboard 110 or the mouse 111 shown in FIG. 1) (Step S401: Yes), Referring to the selected fluid ID from the data storage unit 2, the density PA, _β , viscosity coefficient μ _Β and surface tension coefficient σ _，, σ _{あ る} which are the fluid property values of the selected fluids A and B are selected. The analysis start velocities u _A , v _A , w _A , u _B , v _B , w _B and the analysis start pressures p _A , p _B which are the initial fluid behavior values of the obtained fluids Α, （are extracted (step S 402). ).

 After this data extraction, the angle of initiation interface function φ for one selected fluid is calculated. (Interface function ψ = 1), Analysis start interface function φ for the other fluid. (Interface function φ = 0) is set (step S403). Next, select the surface tension of the fluid あ る (S

404). Then, when an analysis start input is received from the input device (step S 4

05: Yess), and extracts a fixed mesh of the angular analysis target range stored in advance from the data storage unit 2 (step S406). Then, when the values of the virtual time s and the virtual diffusion coefficient K of the diffusion equation of Equation (18) are input (Step S407: Yes), the fluid analysis process is performed for each of the extracted fixed meshes. Execute (Step (Top S 408).

FIG. 5 and FIG. 6 are flowcharts showing the processing procedure of the fluid analysis processing. First, as shown in Fig. 5, the densities p _A and p _B and the viscosity coefficients / z _A and z _{B of the} fluids A and B from which the data were extracted, and the initial analysis start interface function φ. Is substituted into the advection equations of equations (6) and (7) (step S501). Then, the unknown density p and unknown viscosity coefficient μ at the interface between the fluids A and B are calculated by solving this advection equation (step S502).

Next, the calculated density ρ and the calculated viscosity coefficient, the analysis start flow velocity u _A , v _A , w _A , u _B , v _B , w _{B of} the fluid from which the data was extracted, and the angular analysis start pressures p _A , p _B And the surface tension coefficient σ _B selected in step S404 and the analysis start interface function φ. Are substituted into the Navier-S tokes equations of equations (8) and (9) (including equations (10) to (14)) (step S503). The unknown flow velocity u, V, w and the unknown pressure p at the interface between the fluids A and B after a predetermined time are calculated by solving the Navier-S tokes equation (step S504).

 The calculated flow velocities u, V, w are substituted into the above equation (15) (step S505), and the above equation (15) is developed into the above equation (16) (step S506). In the expanded equation (16), the analysis start interface function φ is given. (Interface function φ = 1 or interface function Φ = 0) is substituted to calculate a tangent conversion value F (φ) (step S507). Then, the above equation (16) is transformed into equation (17) (step S508), and the calculated value of F (φ) is substituted into the transformed equation (17) to calculate the interface function Φ. (Step S509).

 Next, the calculated interface function φ is substituted into the diffusion equation of the above equation (18), and this diffusion equation is solved, and the interface function 0 calculated in step S509 is replaced with the interface smoothing the interface. It is converted into a function Φ (step S510).

Next, the converted interface function φ, the densities p _A and p _B and the viscosity coefficients μ _{お よ び} and x _B of the fluids A and B are substituted into the advection equations of the above equations (6) and (7) ( Step S601). Then, solving this advection equation, unknown density p and unknown viscosity coefficient μ Is calculated (step S602).

Next, the calculated density _P and the calculated viscosity coefficient calculated in step S602, the calculated flow velocities u, v, w, and the calculated pressure p calculated in step S504, and the interface function converted in step S509 and phi, and the surface tension coefficient sigma _beta selected in step S 404, in the above equation (8) and Na vier- S tokes equations of formula (9) (formula (10) to (14) is also included) Substitution (step S603). Then, the Navier-Stokes equation is solved, and the calculated flow velocities u, V, w and the calculated pressure p at the interface between the fluids A and B after a predetermined time have elapsed are calculated (step S604).

Next, the calculated flow velocities u, v, w calculated in step S604 are substituted into the above equation (15) (step S605), and are developed into the above equation (16) (step S606). The tangent conversion value F (φ) is calculated by substituting the converted interface function Φ calculated in step S510 into the expanded equation (16) (step S607) _D

 Then, the above equation (16) is transformed into equation (17) (step S608), and the value of F (φ) calculated in step S607 is substituted into the transformed equation (17), and Calculate the interface function Φ (step S609). Then, the interface function φ calculated in step S609 is substituted into the diffusion equation of the above equation (18) to solve the diffusion equation, and the interface function calculated in step S609 is smoothed in the vicinity of the interface. (Step S610). Thereafter, steps S601 to S610 are repeatedly executed.

As described above, the fluid analysis using only the VOF method results in an unrealistic fluid analysis, whereas the fluid analysis device 1 according to the present embodiment combines the VOF method with the digitizer method to generate a discontinuous function. By accurately calculating and smoothing by the diffusion equation, the interface reproduced by a function that is too discontinuous can be easily converted into a smooth (plausible) interface generated by actual phenomena. It can be evaluated by the method. In the fluid analysis apparatus 1 according to the above-described embodiment, the Navier-S tokes equation shown in Expressions (4) and (5) is applied as the governing equation of the fluid. As long as the governing equation is not limited to this equation, governing equations for other fluids can also be used. In this case, the data stored in the data storage unit 2 stores data applicable (substitutable) to the applied governing equation.

 Further, in the fluid analysis device 1 according to the above-described embodiment, as a smoothing method, the interface function is converted by a diffusion equation shown in Expression (18) to smooth the vicinity of the interface. However, the present invention is not limited to this diffusion equation. For example, it is also possible to apply a method of giving the effect of numerical diffusion (viscosity) to an interface function, such as the selective rubbing parameter method proposed by Kawahara et al. it can.

This selective rubbing parameter method is a method of converting the target interface function ¹¹ into an interface function Φ ^{η + 1} having an effect of several ^ ί direct diffusion by using the following equation (19). .

Iterate: For n = 1,2, ..., m do:

M ^{Lump ed in} this equation (19) is a concentrated matrix of the mass matrix M derived when the time derivative term is formulated by the finite element method, and is called a concentrated mass matrix. Here, n (n = l, 2,, m) is the number of iterations, and the interface function φ ¹ when n = l is the interface function calculated by the above equation (17). Interface function phi ^{eta + 1} calculated by the equation (1-9), when the next iteration is used as the interface function [psi ^eta, calculates a new interface function [Phi ^{eta + 1.} Then, the interface function <i> ^{m + 1} repeated at the m-th time becomes the interface function Φ converted from the interface function Φ ¹ to smooth the vicinity of the interface, and the above equation (6) and equation (7) ) Will be used for the advection equation.

Further, M ^{Mi xed} is called a following formula (20) as shown in, lumped mass matrix M ^{Lump ed} and mass matrix M is a matrix obtained by mixing a mixed mass matrix. _{M Mixed = eM} Lum _pe d ₊ — _{e) M} , o <e <l

 Here, e is called the Ramving parameter. e is a value that adjusts the degree of artificial viscosity when using Eq. (19), and is 0.0 Oe 1.0, and the property is that the more artificial the value of e approaches 1.0, the more artificial e Is that the natural viscosity is reduced. '

When this selective rubbing parameter method is used instead of the diffusion equation, in step S406 shown in FIG. 4, the number of repetitions m and the rumbling parameter e are input. Thus, in step S 407, to the interface function phi ^eta to be. Interest, can be m times repeating the calculation of equation (1 9), it is possible to perform a smoothing of the surface function phi.

 Since the selective rubbing parameter method only needs to obtain the above equation (19), the calculation for giving the effect of numerical diffusion is simple. This method can be applied when the mass matrix can be concentrated in the formulation of the finite element method. In addition, in the diffusion equation, a virtual time s and a diffusion coefficient K are accurately specified based on a mesh width.

 In the selective plumbing parameter method, since the number of iterations (an integer greater than or equal to 1) and the running parameter e "(0. 0 ≤ e <1.0), the input value can be a simple value, and the virtual It is easier to set the number directly than setting the effective time s and diffusion coefficient K.

 In the fluid analyzing apparatus 1 according to the above-described embodiment, the case where the selected fluid is a gas and a liquid has been described. The values may be stored in the data storage unit 2 in advance, and the surface tension coefficient used in the equation (13) may be selected according to the selected combination of fluids.

Next, using the analysis model shown in Fig. 45, the fluid analysis using only the VOF method, the fluid analysis combining the VOF method and the digitizer method, and the fluid analysis using the fluid analysis device 1 according to the present embodiment are described as follows. FIGS. 7 to 17 show comparative examples. This second FIGS. 7 to 17 are examples in which fluid angle analysis was performed every 0.5 seconds.

 As shown in Fig. 7, in the combination of the VOF method and the digitizer method, the interface is rattled. However, in the fluid analysis according to the present embodiment, the discontinuous interface obtained by the digitizer method is too discontinuous. The function Φ is smoothed by the diffusion equation. Therefore, as shown in FIGS. 7 to 17, the fluid analysis according to the present embodiment can show the smoothness of the interface (caused by the influence of surface tension) in the actual phenomenon.

 In the VOF method, as shown in Fig. 7 to Fig. 17, the accuracy of the discontinuous distribution of the surface function Φ is poor, and as the calculation proceeds, two fluids, namely, air and water The interface force S is blurred, and the interface between the two fluids cannot be calculated accurately. In addition, in the combination of the VOF method and the digitizer method, since the value of the interface function φ is only 0 and 1, it is extremely discontinuous, and as shown in FIGS. 9 to 17, After 0.7 seconds, it can be seen that calculation is impossible.

 Next, examples of fluid analysis using the analysis model in FIG. 18 are shown in FIGS. 19 and 20. This simulation calculates the phenomenon that gas (bubbles) in a liquid rises toward the water surface. The shape of bubbles rising in a liquid varies depending on the physical properties of the liquid and gas and the balance of the bubble size.

 Experiments on bubbly flow were conducted by J.R.G.race et al. In 1973, and could be classified into several typical bubble shapes as three dimensionless physical property indicators consisting of physical properties of liquid and gas. It is shown. Fig. 19 shows the results of calculations using a physical property index that causes the bubbles to have a shape called Spherica1 (spherical shape) as the calculation conditions. On the other hand, Fig. 20 shows the results of calculations using physical property indices that result in bubbles having a shape called Skirtd (skirt shape). Both FIG. 19 and FIG. 20 reproduce the characteristic shape corresponding to the dimensionless physical property index, and can evaluate the reliability of the fluid analysis according to the present embodiment.

Next, examples of fluid analysis using the analysis model of FIG. 21 are shown in FIGS. This analysis model is based on the flow of high-temperature and high-pressure pure oxygen gas This is a model for analyzing the flow phenomena inside the converter where any metal is formed. As shown in the second 2 Fig-3 0 Figure respect density 3. 0 kg / m ³ of density of fast oxygen inflow and both fluids are significantly different (pure oxygen gas, the density of the metal is 7. 0 X Even under severe conditions (10 ³ kg / m ³ ), stable analysis results can be obtained, and accurate interface evaluation can be performed.

 As described above, in the converter, it is impossible to monitor the internal state because of the high temperature. However, according to the fluid analysis of the present embodiment, it is impossible to capture the behavior of the fluid inside the converter. it can. This can be used for converter design changes such as the size of the converter.

 Next, examples of fluid analysis using the analysis model in FIG. 31 are shown in FIGS. 32 to 39. FIG. 32 is a mesh diagram divided into fixed meshes. This analysis model is a model that analyzes the behavior of the fluid that ejects ink from the nozzles. As shown in Fig. 33 to Fig. 39, the state where ink is ejected from the nozzle and falls to the bottom surface is noticeable. As shown in this example, micron-order fluid analysis can be faithfully reproduced, and fluid behavior that cannot be captured by the naked eye can be captured. Although not shown, the fluid analysis device 1 according to the present embodiment also includes a river flood, a fluid behavior of waves at sea, a behavior of liquid in a container, and a tank truck during operation. It can be applied in various fields such as the behavior of liquid in a tank or when these are applied to computer graphics.

 As described above, the fluid analysis device 1 according to the present embodiment adopts the VOF method to handle complicated interfaces, and proposes the CI に method to calculate an accurate free surface. Digitizer method was incorporated into the finite element method (stabilized bubble function method). '

The CI Ρ method requires the use of an explicit method in the time direction formulation, and under very severe calculation conditions (especially at high inflow rates), numerical stability is limited ( CFL condition) The stabilized bubble function method can adopt an implicit method, which is very advantageous for numerical stability in the time direction. In addition, the finite element method Incorporating the tizer method, a smoothing method that can accurately represent the interface evaluation method by calculating using the finite element method is used. Can be performed.

 The fluid analysis method described in the present embodiment can be realized by executing a prepared program on a computer such as a personal computer or a workstation. This program is recorded on a computer-readable recording medium such as a hard disk, a flexible disk, a CD-ROM, an MO, and a DVD, and is executed by being read from the recording medium by the computer. The program may be a transmission medium that can be distributed via a network such as the Internet. Industrial applicability

 As described above, according to the fluid analysis method, the fluid analysis program and the fluid analysis device of the present invention, the behavior of a flow having an actual free surface problem can be accurately analyzed by a simple and general-purpose analysis method. It has the effect of being able to. Furthermore, there is an effect that the smoothness on the interface caused by the surface tension between fluids having different physical properties can be incorporated into the interface function.

Claims

The scope of the claims

1. a first unknown property value calculation step of calculating a first unknown property value near the interface between the fluids based on the known property values of the respective fluids forming the interface using an advection equation;

 A first unknown fluid behavior value representing a behavior near the interface between the fluids is calculated based on the first unknown property value calculated in the first unknown property value calculation step using a governing equation of the fluid. A first unknown fluid behavior value calculation step,

 An interface function calculating step of calculating an interface function near the interface between the fluids based on the first unknown fluid behavior calculated in the first unknown fluid behavior value calculating step using a digitizer method;

 An interface function conversion step of converting the interface function calculated in the interface function calculation step using a smoothing method;

 A fluid analysis method comprising:

2. Using the advection equation, a second property near the interface between the fluids based on the known physical property values of the fluids forming the interface and the interface function converted by the interface function conversion step. A second unknown property value calculating step of calculating an unknown property value; a second unknown property value calculated by the second unknown property value calculating step using the governing equation of the fluid; and A second unknown fluid that calculates a second unknown fluid behavior value representing a behavior near the interface between the fluids based on the first unknown fluid behavior value calculated in the unknown fluid behavior value calculation step and 2. The fluid analysis method according to claim 1, further comprising: a behavior value calculating step.

3. a first unknown property value calculating step of calculating a first unknown property value near the interface between the fluids based on the known property values of the respective fluids forming the interface using an advection equation; A first unknown physical property value calculated in the first unknown physical property value calculation step using a governing equation of a fluid, a surface tension coefficient of one of the fluids, and a curvature function representing a curvature of the interface. A first unknown fluid behavior value calculating step of calculating a first unknown fluid behavior value representing a behavior in the vicinity of the interface between the fluids based on the first unknown fluid behavior value using a digitizer method. An interface function calculating step of calculating an interface function near the interface between the fluids based on the first unknown fluid behavior value calculated in the calculating step;

 An interface function conversion step of converting the interface function calculated in the interface function calculation step using a smoothing method;

 A fluid analysis method comprising:

4. Using the advection equation, a second physical property near the interface between the fluids based on the known physical property values of the fluids forming the interface and the interface function converted by the interface function conversion step. A second unknown property value calculating step of calculating an unknown property value; a second unknown property value calculated by the second unknown property value calculating step using the governing equation of the fluid; and A first unknown fluid behavior value calculated in the unknown fluid behavior value calculation step, a surface tension coefficient of one of the fluids, a curvature at an interface between the fluids obtained from the converted interface function, A second unknown fluid behavior value calculation step of calculating a second unknown fluid behavior value representing a behavior near the interface between the fluids based on a curvature function representing a curvature of the interface, and Special Fluid analysis method according to claim 3 to.

5. A fluid analysis program for causing a computer to execute the fluid analysis method according to any one of claims 1 to 4.

6. Data storage means for storing a known physical property value representing a property of the fluid for each fluid; Data extraction means for selecting two fluids to be analyzed and extracting known physical property values of the selected fluid from the data storage means;

 A fluid behavior value calculating means for calculating a fluid behavior value representing a behavior in the vicinity of the interface between the fluids based on a physical property value in the vicinity of the interface of the fluid using a governing equation of the fluid;

 Interface function calculating means for calculating an interface function near the interface between the fluids based on the fluid behavior value calculated by the fluid behavior value calculating means, using a digitizer method;

 An interface function conversion unit that converts the interface function calculated by the interface function calculation unit using a smoothing method;

 Using an advection equation, based on the physical property values of the fluid extracted by the data extracting means and the interface functions converted by the interface function converting means, calculating physical property values near the interface between the fluids Value calculation means;

 A fluid analysis device comprising:

7. The data storage means further stores a surface tension coefficient for each of the fluids,

 The data extraction unit further extracts, from the data storage unit, a surface tension coefficient of one of the fluids selected by the fluid selection unit,

 The fluid behavior value calculating means is further extracted from the data extracting means using the governing equation of the fluid! /, The surface tension coefficient of one of the fluids, the interface function converted by the interface function conversion means, and the curvature at the interface between the fluids obtained from the converted interface function. 7. The fluid analyzer according to claim 6, wherein a fluid behavior value representing a behavior near an interface between the fluids is calculated.