Abstract:
A fluid-structure coupled numerical simulation method is provided. The method uses a finite volume method employing an orthogonal mesh and a computer and memory setting a solid area based on a solid rate inside a mesh and at a tangent position to each mesh, including the steps of: setting initial and boundary conditions of a moving film structure; setting a velocity boundary in the tangent direction of the film structure by computing a position and shape thereof; and computing a curvature thereof. The method further includes the step of computing a pressure balance based on a balance between a pressure obtained from a fluid computation and a repulsive force obtained from the tension and curvature of the film structure to implement processing of a mutually-coupled phenomenon. A shift amount of the film surface for each time of said computing steps is simulated using the same program.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS  
       [0001]     The present invention contains subject manner related to Japanese Patent Application JP 2005-311680 filed in the Japanese Patent Office on Oct. 26, 2005, the entire contents of which being incorporated herein by reference.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates to a fluid-structure coupled numerical simulation method and a program for a fluid-structure coupled numerical simulation storage device. Particularly, the present invention relates to the aforementioned method and program, in which when applying a fluid to a film structure, assuming that a film surface is a surface of a fixed area in a computational mesh, a fluid analysis is executed in the same solver with respect to the relationship between a repulsive force of the film surface of the film structure and a fluid pressure.  
         [0004]     2. Description of the Related Art  
         [0005]     In the past, when simulating physical action of a design model, for example, conducting a thermal conductivity analysis, fluid analysis, structural analysis, electromagnetic field analysis, electromagnetic wave analysis and the like by a computer to verify the design model, a coupled analysis in which two or more kinds of simulation are applied is performed on an object model, corresponding to the object model for analysis being complicated.  
         [0006]     In such coupled analysis, it is necessary to set a plurality of physical parameters for element groups if two or more physical models are provided, and so work of setting becomes complicated when one-dimensional list is used. Further, when boundary conditions are set, it is necessary to perform the setting while considering a setting condition for each of the element groups, that is, which boundary corresponds to which physical model, thereby bringing the complexity to the work. Japanese Patent Application Publication No. 2002-245097 discloses a coupled analysis method of easily setting conditions on element groups and boundaries regarding an object model, a method of setting the analysis conditions, a storage device and program in a coupled analysis system using two or more physical models.  
         [0007]      FIG. 1  shows the coupled analysis system disclosed in the above-mentioned patent reference configured to have a CPU (Central Processing Unit)  1 , display  2 , input device  3  such as a mouse and filing device (storage device)  4 . The CPU  1  implements CAD model preparation processing  10  by which a model to which a numerical simulation is implemented is prepared. The prepared model is divided into mesh (elements), and at this time, mesh preparation processing  11  that defines a group and boundary of each mesh is implemented. Groups are registered in a group list  6 , boundaries are registered in a boundary list  7 , and the corresponding relations between groups and boundaries are registered in a corresponding list  5 . As shown in  FIG. 1 , the corresponding list  5  is provided in the filing device  4 . List-registration processing  12  that stores group numbers and corresponding boundary numbers is performed, and analysis conditions with respect to the groups and boundaries of the meshes (elements) divided are set by element group analysis-condition-setting processing  13  and element boundary analysis-condition-setting processing  14 . For example, thermal conductivity is set to the element groups and a temperature and thermal conductivity are set to the boundaries in the thermal conductivity analysis. Further, a young&#39;s modulus or the like is set to the element groups and a weight condition or the like is set to the boundaries in the structural analysis. Both the analysis-condition-setting processings  13  and  14  are linked mutually.  
         [0008]     Subsequently, physical-model simulation/computation processing  15  and computed-result display processing  16  are implemented. Here, computation is implemented in the computation processing  15  using the model divided into mesh and analysis conditions, thereby obtaining a solution. A general-purpose thermal analysis program, structural analysis program and fluid analysis program are used in the computation processing  15 . The result display processing  16  is performed such that the computed result obtained by the computation processing is output to a screen of a display  2 . As described above, the CPU performs such steps  10  and  11  of setting physical models of the element groups constituting the object model, and step  12  of retrieving boundaries of the object model corresponding to the element groups that were set. Further, the CPU performs a step  13  of reflecting the physical models of the element groups to the retrieved boundaries on analysis-condition-setting screen for the boundaries of the object model, and a step  14  of setting analysis conditions of the boundaries on the analysis-conditions-setting screen for the boundaries reflected. By using a principle of a specific group and the boundary thereof having a common physical-model characteristic, correlation between the group and boundary is reflected on a boundary condition setting screen, and the physical model of the group is set to automatically retrieve the boundary corresponding to the group, and the analysis conditions of the boundary are set on the boundary condition-setting screen.  
         [0009]     As described above, the technology described in Japanese Patent Application Publication No. 2002-245097 includes the function of displaying a two-dimensional list of the physical models (thermal conductivity, fluid, structural analysis, static electromagnetic field and electromagnetic field) and names of the boundaries. Therefore, referencing the corresponding list  5  in the filing device  4 , a situation in which the physical model of each element group is assigned is displayed on the boundary list and boundaries to which the conditions-setting in the boundaries list are needed are automatically checked. For example, a checked result is displayed with a circle or the like, and so the setting of the boundary condition of the physical model to which each boundary corresponds can be performed by clicking (or double clicking) an area of the boundary name checked. Accordingly, since the two-dimensional list is prepared as described above, the setting of physical parameters to the element groups becomes easy in an achievement analysis having a plurality of physical models. Further, situations of the physical parameters set to the element groups are determined, the boundary condition to which setting is needed is automatically checked, and can be set in the boundary list, thereby the setting of boundary conditions being facilitated. Furthermore, the element group list, boundary list and shapes of models can be output simultaneously, thus facilitating understanding of the setting conditions for analysis.  
         [0010]     Japanese Patent Application Publication No. 2000-271734 discloses a fluid-solidification analysis method to which computer simulation is applied. This method is to find an optimal method and optimal condition for producing a high quality product without casting defects such as a flow defect caused by the decrease in temperature in a molten metal flow, in the case where metal melt material is used as fluid to form cast or die-cast products.  
         [0011]     The state of molten metal solidified is modeled with a solid-phase rate which shows a rate of the solid phase existing in the liquid phase based on the temperature of each minute element. The molten metal is treated as Newtonian fluid in the state of the solid-phase rate of 0% at a temperature higher than the liquidous line temperature, is treated as non-Newtonian fluid in the solid-liquid co-existent area at a temperature higher than the solidus line temperature and lower than the liquidous line temperature, and is treated as the obstacle not fluid in the state of the solid-phase rate of 100% at a temperature lower than the solidus line temperature. Thus, an optimum flow-field analysis method is applied to each solidified state, enabling an analysis result with high accuracy for the process to be practically obtained in a short period of time.  
         [0012]      FIG. 2  shows a flow chart of the fluid-solidification analysis method to which the computer simulation described in the above-described patent reference is applied. In order to implement the fluid-solidification analysis of molten metal inside a mold, a shape model is prepared based on a molded product by injection molding and the mold used for the injection molding in step S 1 . An analysis shape model divided into minute elements is prepared using mesh in step S 2 . The analysis model is suitable for a difference method, finite element method, boundary element method, FAN method, control volume method and the like that are fluid-solidification analysis methods.  
         [0013]     In step S 3 , input condition data such as physical property data, boundary conditions, process conditions and the like necessary for the fluid-solidification analysis after preparing the analysis shape model are determined and input. Hereupon, the input condition data are set for simulating a process that produces a molded product by the numerical analysis with respect to the analysis shape model. Those are conditions necessary for the analysis, such as a inflow velocity of molten metal, inflow temperature and filling time, mold temperature, values of dynamic physical properties and thermal physical properties of the mold, values of dynamic physical properties and thermal physical properties of the molten material, boundary conditions (such as thermal boundary condition) and the like.  
         [0014]     In the next step S 4 , a process in which the molten metal is filled inside the mold is simulated using a numerical analysis method on the basis of the given input condition data. When implementing the analysis, the solidified state of molten metal in each minute element is modeled using the solid-phase rate that shows a rate of solid phase existing in the liquid phase from the temperature of each minute element, and a state of the molten metal is determined. Specifically, as shown in step S 5 , the state of the molten metal, which is the complete liquid-phase state, solid-liquid co-existing state or complete solid-phase state, is determined from the temperature of the molten metal. The complete liquid-phase state is the range at a temperature higher than the liquidous line temperature and the solid-phase rate is 0%. The solid-liquid co-existent state is the range at a temperature higher than solidus line temperature and lower than liquidous line temperature. The complete solid-phase state is the range at the temperature lower than solidus line temperature and the solid-phase rate is 100%.  
         [0015]     After the state is determined, an optimal flow-field analysis method is applied to each solidified state based on the state determined, and the simulation is implemented using the numerical analysis method to conduct a flow analysis. The flow analysis employing the numerical analysis method is implemented at predetermined time intervals in accordance with the input condition data and the solid-phase rate. Here, the predetermined time interval is an interval in the range of about 0.001 to 0.01 sec. When implementing the flow analysis to the state in which the molten metal in each minute element is in the solid-phase rate of 0% at the temperature higher than the liquidous line temperature, the flow analysis is implemented regarding the molten metal as Newtonian fluid. Further, in the state in which the molten metal in each minute element is in the solid-liquid coexistent range at the temperature higher than the solidus line temperature and lower than the liquidous line temperature, the flow analysis is implemented regarding the molten metal as non-Newtonian fluid. Furthermore, in the state in which the molten metal in each minute element is in the solid-phase rate of 100% at the temperature lower than the solidus line temperature, the molten metal is treated as the obstacle instead of fluid and the flow analysis is not implemented.  
         [0016]     After the fluid analysis, in order for the filling state of molten metal in the mold being changed by the result of the fluid analysis to be reflected in temperature distribution, temperature analysis is implemented in step S 6  regarding temperature changed situations of the molten metal and mold using the numerical analysis method at predetermined time intervals of about 0.01 to 0.02 sec. After the temperature analysis, whether to continue the analysis is judged from the given input condition data, and in the case of “NO”, operation goes back to the step S 4 , and in the case of “YES”, operation proceeds to step S 8  to end. Further, positions such as flow defect portions where defects may occur are predicted in step S 8  based on the analysis result obtained in step S 7  indicating molten metal unfilled portions.  
         [0017]     If the occurrence of defects are predicted in step S 8 , as shown in step S 9 , at least one of the conditions of the analysis shape model and input condition data is changed and each of process from the step S 1  to step S 8  is repeated until it is recognized that the occurrence of defects is not predicted. Then, the processing ends when the occurrence of defects is not predicted in the step S 8 .  
         [0018]     As described above, Japanese Patent Application Publication No. 2002-245097 discloses the technology to simplify settings of boundary conditions that become complicated when the structural analysis and fluid analysis are implemented, and Japanese Patent Application Publication No. 2000-271734 discloses the technology to implement the fluid-solidification analysis of molten metal in a mold. Problems in the above-described computational solving method have not sufficiently been solved with a simplified method, and there remains complexity in the computation and modeling when implementing the fluid-structure coupled simulation or the like.  
         [0019]     For example, there are provided methods of simulating a fluid-structure coupled processing phenomenon in a process of liquid being applied on a film. In such phenomenon a position or shape of a surface of the film is changed by the behavior of liquid discharged and the liquid flows on this surface, and so the phenomenon progresses while both the behaviors of the film and liquid being closely related to each other. There is proposed, for example, a method in which two solvers for a fluid and structure are provided and computation progresses while exchanging information on pressure distribution and a structure position between the two solbers. Further, there is provided another method in which a coupled Jacobian matrix is prepared using a finite element method, fluid equation or structure equation and the like, and the matrix solution is obtained. Although these methods are accurate, computational load is high and a convergence computation becomes unstable in the case where film is greatly transformed or the film touches another structure.  
       SUMMARY OF THE INVENTION  
       [0020]     In view of the above, it is desirable to provide a fluid-structure coupled numerical simulation method in which a fluid-analysis and a structure-analysis can be implemented in one solver. In this method, a film surface is assumed to be the surface of a solid area in a computational mesh, when simulating a fluid-structure coupled phenomenon in the process of a liquid being applied on the film, in which a position and shape of the film surface are changed by the behavior of the liquid discharged and further the liquid flows on this surface.  
         [0021]     It is further desirable to provide a fluid-structure coupled numerical simulation method in which a fluid-analysis and a structure-analysis are implemented in one solver. In this method, a film surface is assumed to be the surface of a solid area in a computational mesh, when simulating a fluid-structure coupled phenomenon in the process of a liquid being applied on the film, in which a position and shape of the film surface are changed by the behavior of the liquid discharged and further the liquid flows on this surface. Further, this method is capable of simulating a shift amount of the film surface of a film-structure in each computational time step from a balance between a pressure obtained from a fluid computation and a repulsion force obtained from a tension and curvature of the film structure by assuming that the film-structure has no rigidity for bend.  
         [0022]     It is further desirable to provide a program for a fluid-structure coupled numerical simulation storage device in which a fluid-analysis and a structure-analysis are implemented in one solver. In this program, a film surface is assumed to be the surface of a solid area in a computational mesh, when simulating a fluid-structure coupled phenomenon in the process of a liquid being applied on the film, in which a position and shape of the film surface are changed by the behavior of the liquid discharged and further the liquid flows on this surface. Further, this program is capable of simulating a shift amount of the film surface of a film-structure in each computational time step from a balance between a pressure obtained from a fluid computation and a repulsion force obtained from a tension and curvature of the film structure by assuming that the film-structure has no rigidity for bend.  
         [0023]     According to an embodiment of the present invention, there is provided a fluid-structure coupled numerical simulation method using a finite volume method employing an orthogonal mesh and a computer and memory setting a solid area based on a solid rate inside a computational mesh and at a tangent position to each mesh. The fluid-structure coupled numerical simulation method includes the steps of: setting initial and boundary conditions of a shape, shift computed area, tension, feeding velocity and the like of a moving film structure; setting a velocity boundary in the tangent direction of the film structure by computing a position and shape of the film structure; and computing a curvature of the film structure. Further, the method includes the step of computing a pressure balance based on the balance between a pressure obtained from a fluid computation and a repulsive force obtained from the tension of the film structure and curvature thereof computed in the curvature computing step to implement processing of a mutually-coupled phenomenon between the film structure assumed to have no rigidity for bend moving in a predetermined direction and a fluid flowing on a surface of the film structure. In this method, a shift amount of a film surface for each time of the computing steps is simulated using the same program.  
         [0024]     According to another embodiment of the present invention, there is provided a program for a fluid-structure coupled numerical simulation storage device, using a finite volume method employing an orthogonal mesh and a computer and memory setting a solid area based on a solid rate inside a computational mesh and at a tangent position to each mesh. The program includes the steps of: setting initial and boundary conditions of a shape, shift computated area, tension, feeding velocity and the like of a moving film structure; setting a velocity boundary in the tangent direction of the film structure by computing a position and shape of the film structure; and computing a curvature of the film structure. Further, the program includes the steps of computing a pressure balance based on a balance between a pressure obtained from a fluid computation and a repulsive force obtained from the tension of the film structure and the curvature thereof computed in the curvature computing step to implement processing of a mutually-coupled phenomenon between the film structure assumed to have no rigidity for bend moving in a predetermined direction and a fluid flowing on a surface of the film structure. In this program, a shift amount of a film surface for each time of the computing steps is simulated using the same program.  
         [0025]     According to the embodiments, when a film coating process is considered, stable coating conditions based on a film tension, a fixed roller position, a film feeding velocity, a coating-liquid discharging velocity, a viscosity of coating liquid and a shape of discharge nozzle and the like can be examined on the simulation using a simple procedure. Therefore, a fluid-structure coupled numerical simulation method and a program for a fluid-structure coupled numerical simulation storage device are obtained, with which computation can be implemented with small load, stability and high velocity when implementing the fluid-structure coupled numerical simulation for targeting the behavior of fluid with which a film structure is coated. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0026]      FIG. 1  is a configuration diagram showing a coupled analysis system of related art;  
         [0027]      FIG. 2  is a flow chart of a fluid-solidification analysis method of related art;  
         [0028]      FIG. 3  is a schematic view of a running path of a coating device, showing a fluid-structure coupled numerical simulation method according to an embodiment of the present invention;  
         [0029]      FIG. 4  is a view showing a computational model of the coating device shown in  FIG. 3 ;  
         [0030]      FIG. 5  is a system diagram showing a computer and memories that implement the fluid-structure coupled numerical simulation according to an embodiment of the present invention;  
         [0031]      FIG. 6  is a flow chart showing a fluid-structure coupled numerical simulation method according to an embodiment of the present invention;  
         [0032]      FIGS. 7A and 7B  are explanatory views showing divided mesh, in which  FIG. 7A  shows the divided mesh at the start of computation in a fluid-structure coupled numerical simulation method according to an embodiment of the present invention, and  FIG. 7B  shows the divided mesh when considering a curvature of a film structure in a fluid-structure coupled numerical simulation method according to an embodiment of the present invention;  
         [0033]      FIG. 8  is a display screen of a coupled boundary surface at the start, showing a computed result of a fluid-structure coupled numerical simulation method according to an embodiment of the present invention; and  
         [0034]      FIG. 9  is a display screen of a coupled boundary surface after a predetermined time has passed, showing a computed result of a fluid-structure coupled numerical simulation method according to an embodiment of the present invention. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0035]     A fluid-structure coupled numerical simulation method and a program for a fluid-structure coupled numerical simulation storage device according to embodiments of the preset invention are explained in the followings with reference to FIGS.  3  to  9 .  FIG. 3  is a schematic view of a running path of a coating device, showing a fluid-structure coupled numerical simulation method according to an embodiment of the present invention.  FIG. 4  is a view showing a computational model of the coating device shown in  FIG. 3 .  FIG. 5  is a system diagram showing a computer and memories that implement the fluid-structure coupled numerical simulation according to an embodiment of the present invention.  FIG. 6  is a flow chart showing a fluid-structure coupled numerical simulation method according to an embodiment of the present invention.  FIG. 7A  shows an explanatory view showing divided mesh at the start of computation of a fluid-structure coupled numerical simulation method according to an embodiment of the present invention.  FIG. 7B  shows an explanatory view showing divided mesh when considering a curvature of a film structure in a fluid-structure coupled numerical simulation method according to an embodiment of the present invention.  FIG. 8  shows a display screen of a coupled boundary surface at the start of film moving, showing a computed result.  FIG. 9  is a display screen of a coupled boundary surface after a predetermined time has passed, showing a computed result.  
         [0036]     Hereinafter, a fluid-structure coupled numerical simulation method according to an embodiment of the present invention is explained with reference to FIGS.  3  to  9 . This embodiment is applied to a coating system in which a surface of a film structure is coated with a fluid or the like. A coating device  17  shown in  FIG. 3  is a device assumed in this simulation example. A fluid  21  is discharged from an outlet  20  of a nozzle  19  onto a belt-shaped flexible film  18  being fed, and the film  18  is coated with the fluid  21 . The film  18  is set to have a predetermined tension between two feeding rollers  22 ,  23  provided between a feeding reel and a winding reel not shown in the figure.  
         [0037]      FIG. 4  shows the initial state of a physical simulation model of the coating device  17  shown in  FIG. 3 . An area  24  under a line segment connecting the point A to point D in  FIG. 4  is defined as a moving object area, where a solid-area surface position inside a computational mesh assumed to be a solid-surface is gradually changed in each computational mesh prepared using a known mesh-preparation processing. A film surface of the film  18  is expressed by interpolating the solid-area surface positions. Further, a boundary condition is set so that the fluid  21  is discharged from the outlet  20  of the nozzle  19 . Other than those, tension T by which the film  18  is pulled to the feeding reel side and to the winding reel side and a film feeding velocity V are input as computational conditions.  
         [0038]     An initial shape of the film  18  of this coating device  17  has a concave curvature at the point B and point C at both right/left ends of the nozzle  19  in  FIG. 4 , and so force pushing the film  18  upward in the direction of the nozzle  19  is worked, which presumably affects the shape of the film  18  to enter the nozzle  19 . In this regard, if a computer (hereinafter called a CPU) is used to determine whether to make the film  18  and the nozzle  19  in contact or not, this problem is solved, however, typically the load becomes high when the decision of contact/non-contact is implemented during the numerical computation and also simulation may become unstable. Further, in this embodiment, since the film  18  obviously moves in the negative direction of Z axis (minus z-axis direction), a moving range in the computational process is limited by assuming that the film surface of the film  18  does not move in the positive direction of z axis (plus z-axis direction) from the initial state, thereby reducing the computational load in the CPU.  
         [0039]      FIG. 5  is a system diagram showing a relation between the CPU and memories for explaining a fluid-structure coupled numerical simulation method according to an embodiment of the present invention, when the surface of a film structure is coated with a fluid.  FIG. 5  shows: a host CPU  25  for computational processing of the simulation according to an embodiment of the present invention; an input device  26  such as a mouse, keyboard and the like; a display  27  that displays computational situations and results; memories  28 ,  29  such as ROM and RAM; and a coating device  17  constituting a fluid-structure body shown in  FIG. 3  and to which the coupled numerical simulation is implemented. The host CPU  25  controls the coating device  17 , input device  26 , display  27  and memories  28 ,  29  via a bus  30 .  
         [0040]      FIG. 6  shows computational procedures of the host CPU  25  when simulating the coating device shown in  FIGS. 3 and 4 . In  FIG. 6 , at step ST 1 , initial settings and boundary condition settings and the like are implemented. Regarding the film  18 , a film moving computational area of the moving object area  24  shown in  FIG. 4 , a tension T of the film  18  and a feeding velocity of the film  18  and the like are set.  
         [0041]     The mesh division is implemented by the infinite volume method using a known orthogonal mesh, and a solid rate for each mesh and a position of each mesh in the tangent direction that show a flow state of fluid are set at the next step ST 2 . The settings regarding a position, shape, velocity-boundary in the tangent direction of the film  18  are implemented at step ST 3 .  FIG. 7A  shows the state of mesh division at the portion corresponding to the nozzle  19  before the film  18  moving, and shows each computational mesh (computational cell)  31  where each element shown with broken line is computed.  
         [0042]     A curvature of the film  18  is computed at step ST 4 . In this regard, the film  18  in this embodiment is assumed to have no rigidity for bend, and a shift amount of the film surface in each computational time step is computed based on a balance between a repulsive force obtained from a tension and curvature computation of the film  18  and a pressure obtained from a fluid computation in step ST 5  mentioned later on. In this regard, assuming that a film surface of the film  18  is represented by a surface of a solid-setting area, a position, shape and shift amount of the film surface of the film  18  are computed by gradually increasing/decreasing the solid-setting area in each computational mesh in accordance with the shift amount of the film  18 .  
         [0043]     Further, when the film  18  moves in the direction of a normal line of the film surface or moves in one direction dominantly, a balance of force only in that componential direction may be computed to reduce the computational load. Further, in order to stabilize the computation, a position of the moving film  18  may be limited not to exceed the initial position set at the step ST 1 .  
         [0044]     The computation of the fluid  21  is implemented and the pressure balance is computed at step ST 5 . At the time of the fluid computation in the step ST 5 , considering the state of feeding the film  18  other than a velocity in the moving direction of the film  18  as the velocity-boundary conditions on the film surface of the film  18 , a tangent velocity equivalent to the feeding velocity may be computed in the computational step for each mesh. On implementing the computation of the fluid  21 , a fluid pressure in the computational cell  31  of each mesh is computed, thus obtaining a moving velocity in the direction of the normal line of the film surface and a position of the film surface in the next time step from a motion equation {mδu z /δt=−P cell A}. Here, “m” denotes the mass of film, “u z ” denotes a moving velocity in the z-axis direction of the film  18 , “P cell ” denotes a fluid pressure in each mesh and “A” denotes the area of a computational cell.  
         [0045]     Next, after moving a position of the film surface of the film  18 , the film surface after movement and transformation is obtained by interpolation as shown in  FIG. 7B . In this state, a velocity equivalent to the feeding velocity of the film is set in the direction of the normal line at the boundary of the surface of the film  18 , again the fluid computation is implemented to compute a pressure, and then a film position in the subsequent mesh is computed. It should be noted that a repulsive force of P′=2γK is generated in accordance with tension γ and curvature K of the film  18  in the transformed state of the film  18 . Therefore, after computing the curvature of the film  18  in the computational cell  31  of each mesh, only a balance of repulsive force of a component in the z-direction shown in  FIG. 7B  is considered for simplification among the force that works in the direction of the normal line of the film  18  in this embodiment. In practice, an inclined but vertical component z′ shown with broken line in the z-axis direction is selected, and the repulsive force (P′=2γK) in each area of the computational cell  31  is added as shown in step ST 6  to the aforementioned motion equation, implementing computation using the following equation 1;  
         [0000]     [Equation 1]
 
 mδu   z   /δt=−P   cell   A+ 2 γK   cell   A·n   z   (1) 
 
         [0046]     where the “n z ” is a unit vector in the direction of z-axis.  
         [0047]     After the step ST 6 , then after (t+Δt) has elapsed, operation goes back to the step ST 3  through the step ST 7 , then the computational processing in each computational cell  31  is repeated from the step ST 3  to the step ST 7 .  
         [0048]     A liquid having free surface, gas, compressible fluid, and non-Newtonian fluid in which the transform in a pressure state at an arbitrary point is not proportional to a temporal change rate can be set as a fluid in the aforementioned computation. Further, in order to consider the state where the film surface of the film  18  is pressed by some kind of mechanism or structure, other than the repulsive force by the tension and curvature of the film  18 , a pressure on the bottom surface of the film  18  may be designated in advance to be added for computation.  
         [0049]      FIGS. 8 and 9  show examples of screen that displays the relation between the nozzle  19  and the film surface of the film  18  after computational results for each computational cell  31  described above are processed.  FIG. 8  shows the initial state of t=1, and  FIG. 9  shows the state of t=2. The state of curvature of the film  18 , flow of the fluid  21  and thickness of coating in each computational cell  31  of the fluid and the like can be seen directly. From the results thereof, using the above-mentioned computational method shown with equation 1, it is confirmed that the computation can be implemented stably in one simplified solver by focusing on the balance between a fluid pressure and a repulsive force obtained from tension and curvature of the film and by assuming that the film surface is the surface of solid area inside the computational mesh. The stable computation can be implemented even in the case where the film  18  is in contact with other structures and even in the case where the transform of the film  18  is considerable. Also, from the results thereof, information on the shape of film, shape of liquid surface, thickness of coating, pressure distribution, flow vector and the like can be obtained. It should be appreciated that an optimal coating condition can be examined at the time of simulation, while changing the tension of the film  18 , positions (fixed points) of feeding rollers  22 ,  23 , feeding velocity of the film  18 , discharge velocity of the fluid  21  that is a coating liquid, viscosity of the fluid  21 , the shape of the discharge nozzle  19  and the like.  
         [0050]     Though the initial position of the film  18  in this embodiment is shown with the line segment from point A to point D as shown in  FIG. 4 , the line segment can also be defined as a curve. When there is provided a mechanism or the like by which the film is pushed upward in the direction of the nozzle  19  at a setting area of the film  18 , that effect can be taken into consideration by adding the pressure of that amount to the right side of the equation 1. In this embodiment, assuming that the film  18  does not move in the positive z-axis direction from the initial position, restriction is imposed to obtain high speed computation. However, that restriction can be cancelled or the range of restriction can be narrowed and, for example, a state in which the film  18  is wound into the nozzle  19  can also be computed.  
         [0051]     Further, a Newtonian fluid, non-Newtonian fluid in which a viscosity coefficient and a pressure change at an arbitrary point are not proportional to a temporal change rate and a compressible gas can also be set as the fluid  21  to be computed. For simplification, the computation is implemented in this embodiment by focusing only on the z-axis direction among the moving directions of the film  18 , however, the computation may be implemented by focusing on the normal line direction of the film surface. By changing such computational settings, an embodiment of the present invention can be applied to the discharge nozzle  19  with complicated shape. Further, not limited to simulation of a liquid-coating process, this computational method can also be applied to simulation analysis of a floating state of a tape caused by an air filter and to the simulation analysis of the tape path in the vicinity of a magnetic head, for example.  
         [0052]     It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alterations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalents thereof.