Numerical simulation method, numerical simulation apparatus, and control program

Abstract

To provide a numerical simulation method configured to reduce the computational load associated with handling general geometries.SOLUTION: A numerical simulation method iteratively calculates a provisional velocity calculation step (S3), a pressure calculation step (S4), a velocity update step (S5), and a velocity correction step (S6) while advancing time steps. The provisional velocity calculation step (S3) includes calculating a provisional velocity of a non-Newtonian fluid at the n-th step. The pressure calculation step (S4) includes calculating a pressure of the non-Newtonian fluid at the (n+1)th step. The velocity update step (S5) includes updating the velocity of the non-Newtonian fluid and calculates an updated velocity at the (n+1)th step. The velocity correction step (S6) uses boundary conditions of a flow channel defined by an immersed boundary method to correct the velocity at the (n+1)th step to a correct velocity in consideration of the influence at the boundary at the (n+1)th step.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a method for numerically simulating a non-Newtonian fluid, a device for numerically simulating a non-Newtonian fluid, and a control program. [Background technology]

[0002] Conventionally, various methods have been proposed for numerical analysis of incompressible viscous fluids, such as the finite element method, the finite difference method, the finite volume method, and the boundary element method (see Non-Patent Document 1).

[0003] For example, Patent Document 1 discloses a method for performing computational fluid analysis of blood flow in a calculation target region using the SIMPLE (Semi Implicit Method for Pressure Linked Equation) method, which applies the finite volume method. In the analysis method of Patent Document 1, whether or not to take non-Newtonian fluid properties into consideration, that is, whether or not to make the viscosity of blood shear rate dependent, is determined in advance for each calculation target region, and then blood flow is analyzed. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2016 / 056642 [Non-patent literature]

[0005] [Non-Patent Document 1] Toshio Kobayashi et al., "Handbook of Computational Fluid Dynamics," Maruzen, March 2003, pp. 20-34 Summary of the Invention [Problem to be solved by the invention]

[0006] However, the analysis method of Patent Document 1 has a problem in that if the calculation target region has a complex shape, it takes a long time to generate a calculation grid, which increases the calculation load.

[0007] An object of one aspect of the present invention is to provide a numerical simulation method, a numerical simulation device, and a control block that reduce the calculation load when handling general shapes. [Means for solving the problem]

[0008] In order to solve the above-described problems, a numerical simulation method according to one aspect of the present invention is a numerical simulation method for a non-Newtonian fluid that is incompressible and has variable viscosity, the method including: a provisional velocity calculation step of calculating a provisional velocity of the non-Newtonian fluid at n steps (n is the number of time steps) flowing through a flow channel by discretizing the Navier-Stokes equations and using known variables; a pressure calculation step of calculating a pressure of the non-Newtonian fluid at n+1 steps by solving a Poisson equation for pressure from the provisional velocity at the n steps; a velocity update step of updating the velocity of the non-Newtonian fluid at the n+1 steps from the provisional velocity at the n steps and the pressure at the n+1 steps to calculate an updated velocity; and a velocity correction step of correcting the updated velocity at the n+1 steps to a correct velocity that takes into account the influence of the boundary at the n+1 steps, using boundary conditions of the flow channel set using the immersed boundary method, and performing calculations iteratively while progressing through the time steps.

[0009] In order to solve the above-mentioned problems, a numerical simulation device according to one aspect of the present invention is a numerical simulation device for a non-Newtonian fluid that is incompressible and has variable viscosity, and includes: an imaginary velocity calculation unit that discretizes the Navier-Stokes equations and calculates an imaginary velocity of the non-Newtonian fluid flowing through a flow path in n steps (n is the number of time steps) by using known variables; a pressure calculation unit that calculates the pressure of the non-Newtonian fluid from the imaginary velocity at the n step by solving a Poisson equation for pressure; a velocity update unit that updates the velocity of the non-Newtonian fluid to a velocity at the n+1 step from the pressure and the imaginary velocity at the n step to calculate an updated velocity; and a velocity correction unit that corrects the updated velocity at the n+1 step to a correct velocity that takes into account the influence of the boundary at the n+1 step, by using boundary conditions of the flow path that are set using the immersed boundary method. [Effects of the Invention]

[0010] According to one aspect of the present invention, the computational load for handling general shapes can be reduced. [Brief explanation of the drawings]

[0011] [Figure 1] 1 is a block diagram showing a configuration of a numerical simulation device according to an embodiment of the present invention. [Figure 2] FIG. 10 is a diagram comparing a computational grid used in a conventional computational method with a computational grid used in the computational method of this embodiment. [Figure 3] 1A and 1B are diagrams for explaining a method for representing a complex shape in the immersed boundary method; [Figure 4] FIG. 10 is a diagram illustrating a staggered grid. [Figure 5] 1 is a flowchart showing an example of the flow of a numerical simulation method according to the present embodiment. [Figure 6] FIG. 2 is a diagram illustrating an example of a calculation target of the numerical simulation device according to the present embodiment. [Figure 7] FIG. 10 is a diagram showing an example of a numerical simulation result obtained by the numerical simulation method of the present embodiment. [Figure 8] FIG. 1 is a diagram showing an example of a numerical simulation result obtained by a conventional calculation method. DETAILED DESCRIPTION OF THE INVENTION

[0012] [Embodiment] A numerical simulation method using a numerical simulation device 1 according to an embodiment of the present invention will be described below with reference to FIGS.

[0013] [Outline of calculation method] An outline of the calculation method used in the numerical simulation method executed by the numerical simulation device 1 shown in Fig. 1 will be described. In the numerical simulation method of this embodiment, the flow of a non-Newtonian fluid whose viscosity is incompressible and changes is analyzed by a calculation method that combines the fractional step method, which is an example of a MAC-based solution method, with the immersed boundary method. Note that, instead of the fractional step method, another MAC-based solution method or a SIMPLE-based solution method may be used.

[0014] A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., a fluid in which shear stress is not proportional to the velocity gradient of the flow. The numerical simulation method of this embodiment can be applied to, for example, the flow of a fluid flowing through a catalyst tank, the flow of a molten resin, and the analysis of a die coater or a stirring tank. Hereinafter, for convenience of explanation, a non-Newtonian fluid may be simply referred to as a fluid.

[0015] (Immersed Boundary Method) First, the immersed boundary method will be described with reference to Fig. 2 and Fig. 3. Fig. 2 is a diagram comparing a computational grid used in a conventional computational method with a computational grid used in the computational method of this embodiment.

[0016] Figure 2(a) shows a boundary fitted grid used in the finite volume method and other methods. A calculation method using a boundary fitted grid is a calculation method in which the shape of the object to be calculated is converted into a simple shape such as a rectangle, then solved and then returned to the original domain. When the shape of the object to be calculated is complex, it becomes difficult to convert it into a simple shape, and the form of the equation after conversion becomes complex, which poses the problem of making it difficult to create a calculation program.

[0017] Figure 2(b) shows an unstructured grid used in the finite element method, etc. Calculation methods using unstructured grids divide the shape of the object to be calculated into a mesh of polyhedrons and solve the fluid equations on each polyhedron. For this reason, if the shape of the object to be calculated is complex, it takes time to generate the mesh. In addition, it is necessary to store information such as adjacent contact points in memory, which increases memory capacity and creates the problem of complex calculation programs for meshes using polyhedrons.

[0018] Figure 2(c) shows the computational grid used in the immersed boundary method. In the immersed boundary method, the region to be calculated is divided into a large number of grid-like cells using a Cartesian grid, and the shape of the calculation target is simulated by applying appropriate external forces to the boundary between the solid object and the fluid. Unlike the computational grids used in the conventional calculation methods described above, the immersed boundary method does not require the generation of meshes, can use calculation programs for Cartesian grids, and does not require the storage of information such as adjacent contact points in memory.

[0019] Figure 3 is a diagram for explaining how complex shapes are represented in the immersed boundary method. Figure 3(a) shows the case where α = 0, where α is the solid occupancy rate in each cell, i.e., there are no solids in a single cell. Figure 3(b) shows the case where α = 0.4, i.e., the solid occupancy rate in a single cell is 40%. Figure 3(c) shows the case where α = 1, i.e., there are only solids in a single cell.

[0020] As shown in Figure 3, the immersed boundary method uses the solid occupancy rate α of each cell to simulate the shape of the calculation target. That is, even if the calculation target, such as a flow path, has a complex shape, the shape of the calculation target can be simulated by treating the calculation target region as a collection of many cells with different solid occupancy rates α. This eliminates the need to generate complex triangular or quadrangular meshes to simulate the shape of the calculation target, as is the case with conventional calculation methods using unstructured grids, and reduces the computational load associated with handling general shapes. Here, general shapes include complex shapes such as reactors and flow paths.

[0021] (Fractional Step Method) Next, an overview of the fractional step method will be explained as an example of a MAC-based solution method. The fractional step method is a calculation method that is a modification of the MAC (Marker and Cell) method. Note that a MAC-based solution method other than the fractional step method or a SIMPLE-based solution method may also be used. Below, the derivation of the formulas used in the fractional step method will be explained.

[0022] First, the Navier-Stokes equations for an incompressible fluid can be expressed as the following equations (1) and (2). Note that, for the sake of convenience, it is assumed below that no external force acts, or that any external force acting can be ignored, but this calculation method can be applied even when an external force acts.

[0023]

number

[0024] Here, V represents the velocity vector of the fluid, and ▽ represents the gradient operator. Equation (1) is the mass conservation equation, which shows the conservation of mass of the fluid.

[0025]

number

[0026] Here, t is time, p is fluid pressure, ρ is fluid density, μ is fluid viscosity, and T is transpose. Equation (2) is the momentum conservation equation that shows the conservation of momentum of the fluid.

[0027] FIG. 4 is a diagram for explaining a staggered grid. In the MAC system solution method or the SIMPLE system solution method, the above-mentioned Navier-Stokes equations are discretized by using a staggered grid. In FIG. 4, u represents the fluid velocity in the x direction, v represents the fluid velocity in the y direction, and p represents the fluid pressure. As shown in FIG. 4, in the staggered grid, the definition point of the pressure p is different from the definition points of the velocity u in the x direction and the velocity v in the y direction.

[0028] By using a staggered grid, the mass conservation equation can be naturally expressed in one cell, and the nature of the Navier-Stokes equation, in which the pressure gradient in each direction determines the velocity in that direction, can also be naturally expressed. Specifically, when the mass conservation equation (1) above is approximated using the staggered grid shown in Figure 4, it is expressed as the following equation (3).

[0029]

number

[0030] The momentum conservation equation (2) can also be approximated using a staggered grid. For example, the defining point v i,j The value of u at is calculated by averaging four points around the defining point, as shown in equation (4) below.

[0031]

number

[0032] By using such an approximation method using a staggered grid and calculating the equations described below, the velocity and pressure of the fluid in each cell of the calculation domain can be obtained.

[0033] Next, we will explain how to calculate the fluid velocity and pressure when using the fractional step method to solve the MAC system. First, to calculate the fluid velocity, we remove the pressure term from equation (2) above and approximate the time differential term with a forward difference to derive equation (5) below.

[0034]

number

[0035] V in equation (5) * is called the virtual velocity because it is obtained by approximating the momentum conservation equation without the pressure term. From the above equation (5), the following equation (6) can be derived.

[0036]

number

[0037] Next, the virtual velocity V of the fluid in the n steps mentioned above * Using the above, the pressure of the fluid at the n+1 step is calculated from the Poisson equation shown in the following equation (7).

[0038]

number

[0039] By using the above equations (6) and (7), the updated velocity of the fluid at the n+1 step V ** is calculated by the following equation (8).

[0040]

number

[0041] In this embodiment, the immersed boundary method is further used to set the boundary conditions of the flow path through which the fluid flows, and the updated velocity V of the fluid at the n+1 step calculated by the above equation (8) is **is corrected to the correct velocity taking into account the influence of the boundary at the n+1 step based on the following equation (9).

[0042]

number

[0043] where V n+1 is the correct velocity considering the boundary effect at the n+1 step, α is the solid occupancy rate as mentioned above, V b represents the velocity of the solid.

[0044] In this way, in the fractional step method, the virtual velocity V is calculated from equation (6) using the fluid velocity at n steps. * and calculate the fluid pressure p at step n+1 from equation (7). n+1 Then, calculate the virtual velocity V * and pressure p n+1 Using Equation (8), the updated velocity of the fluid at step n+1, V ** Calculate.

[0045] Then, taking into account the boundary effect at the n+1 step, the updated velocity of the fluid at the n+1 step, V ** The correct velocity V at step n+1 n+1 This procedure is repeated over time starting from the initial conditions, and the velocity and pressure of the fluid at each time are calculated sequentially.

[0046] [Configuration of the numerical simulation device] Next, the configuration of a numerical simulation device 1 according to this embodiment will be described with reference to Fig. 1. Fig. 1 is a block diagram showing the configuration of the numerical simulation device 1. As shown in Fig. 1, the numerical simulation device 1 includes a control unit 10 and a storage unit 20. An input device 2 and a display device 3 are connected to the numerical simulation device 1.

[0047] The input device 2 is a device for operating the numerical simulation device 1. The input device 2 may be any device that can accept input operations for operating the numerical simulation device 1 and transmit operation data indicating the content of the accepted input operation to the numerical simulation device 1, and may be, for example, a mouse, a keyboard, or the like.

[0048] The display device 3 is a device that displays an image using display data output by the numerical simulation device 1. The display device 3 may be any device that can display an image, and may be a liquid crystal display device, an organic EL (Electro Luminescence) display device, or the like. The display device 3 displays an operation screen for operating the numerical simulation device 1, numerical simulation results, and the like.

[0049] The control unit 10 comprehensively controls the operation of the numerical simulation device 1. The control unit 10 performs the above control by reading out a program stored in the storage unit 20 into, for example, a RAM (Random Access Memory) and executing it.

[0050] The storage unit 20 stores data, programs, etc. necessary for the operation of the numerical simulation device 1. The storage unit 20 also stores intermediate results calculated during the numerical simulation process, final results of the simulation, etc.

[0051] The control unit 10 has a simulation calculation unit 30, a simulation control unit 40, and a display control unit 50. The simulation calculation unit 30 has a tentative velocity calculation unit 31, a pressure calculation unit 32, a velocity update unit 33, and a velocity correction unit 34, which will be described later.

[0052] The tentative velocity calculation unit 31 calculates the tentative velocity V of the fluid at n steps by substituting known variables into the above equation (6). * Calculate.

[0053] The pressure calculation unit 32 applies the imaginary velocity V of the fluid at n steps calculated by the imaginary velocity calculation unit 31 to the Poisson equation for pressure shown in the above equation (7). * By substituting, the fluid pressure p n+1 Calculate.

[0054] The velocity update unit 33 calculates the virtual velocity V at n steps based on the above equation (8). * and update the update rate V at n+1 steps. ** Calculate.

[0055] The velocity correction unit 34 calculates the updated velocity V at the n+1 step using the boundary conditions of the flow path set using the immersed boundary method. ** The correct velocity V considering the boundary effect at the n+1 step n+1 Correct it to:

[0056] Specifically, the speed correction unit 34 adds the updated speed V ** , the solid occupancy rate of the cell α, the solid velocity V b By substituting, the correct velocity V at step n+1 is obtained. n+1 Calculate.

[0057] The simulation control unit 40 controls the simulation calculation unit 30 to perform calculations for each time point in each cell of the calculation domain as described above, thereby executing a numerical simulation of the fluid to be calculated, and transmits the execution results to the display control unit 50. The simulation control unit 40 may store the execution results of the numerical simulation in the storage unit 20.

[0058] More specifically, when the simulation calculation unit 30 finishes calculation for one cell, the simulation control unit 40 updates the cell to be calculated and performs calculation for the updated cell. The simulation control unit 40 causes the simulation calculation unit 30 to repeatedly execute calculation until calculation for all cells is finished.

[0059] Then, the simulation control unit 40 updates the number of time steps n, causes the simulation calculation unit 30 to execute calculations for all cells, and sets the maximum number of time steps n max The calculation is repeated while updating the time step number n until

[0060] The display control unit 50 displays the results of the numerical simulation executed by the simulation control unit 40 on the display device 3. The display control unit 50 also reads display data to be displayed from the storage unit 20 and displays it on the display device 3. That is, the display control unit 50 displays the results of the numerical simulation performed by the numerical simulation device 1 on the display device 3, and reads operation screen data for operating the numerical simulation device 1 from the storage unit 20 and displays it on the display device 3.

[0061] [Flow of numerical simulation method using numerical simulation equipment] Next, the flow of the numerical simulation performed by the numerical simulation device 1 will be described with reference to Fig. 5. In this embodiment, the numerical simulation device 1 performs a numerical simulation on a non-Newtonian fluid whose viscosity (viscosity) changes in an incompressible manner.

[0062] Fig. 5 is a flowchart showing an example of the flow of the numerical simulation method according to this embodiment. In the flowchart shown in Fig. 5, the numerical simulation device 1 reads calculation data from the storage unit 20 (S1).

[0063] The user is to input in advance the calculation data to be calculated in the numerical simulation into the storage unit 20 of the numerical simulation device 1 via the input device 2. The calculation data includes data on the size of the flow path through which the fluid flows, the solid occupancy rate α, the number of cells, the time step width Δt, the number of time steps n, the Reynolds number Re, the initial conditions, the boundary conditions, the order of calculation commands, and physical property values ​​such as the density ρ and viscosity μ of the fluid.

[0064] The fluid flow in the flow channel is preferably a laminar flow with a Reynolds number Re of less than 2300. This numerical simulation method is suitable for non-Newtonian fluid flows in the laminar flow region, and can improve the accuracy of calculation results in the laminar flow region.

[0065] After S1, the simulation calculation unit 30 acquires initial conditions from the storage unit 20 (S2). The initial conditions include an initial velocity u0 of the fluid, etc. In S1, the user may input the initial conditions to the simulation calculation unit 30 via the input device 2.

[0066] After S2, the imaginary velocity calculation unit 31 of the simulation calculation unit 30 calculates the imaginary velocity V of the fluid at n steps by substituting known variables into the above equation (6). * is calculated (S3: tentative velocity calculation step).

[0067] Specifically, the tentative velocity calculation unit 31 adds the velocity V of the fluid at n steps as a known variable to the above equation (6). n By substituting the values ​​of the time step size Δt, the fluid density ρ, the fluid viscosity μ, the fluid shear rate, etc., the virtual velocity V at n steps can be calculated. * Calculate.

[0068] In this tentative velocity calculation step S3, the tentative velocity V is calculated by dividing the time into a plurality of sub-steps with short time intervals. * It is preferable to calculate the viscosity of the fluid by taking into account the velocity of the fluid at the wall and by using the harmonic mean.

[0069] After S3, the pressure calculation unit 32 of the simulation calculation unit 30 calculates the virtual velocity V * From this, by solving the Poisson equation for pressure, the fluid pressure p n+1 is calculated (S4: pressure calculation step).

[0070] In S4, the pressure calculation unit 32 calculates the time step width Δt, the density ρ of the fluid, and the virtual velocity V * and solving the Poisson equation for pressure to calculate the pressure at the n+1 step.

[0071] After S4, the velocity update unit 33 of the simulation calculation unit 30 calculates the virtual velocity V at n steps in the above equation (8). * , time step size Δt, density ρ, pressure p at n+1 step n+1 By substituting, the updated velocity of the fluid at step n+1, V ** is calculated (S5: speed update step).

[0072] After S5, the velocity correction unit 34 of the simulation calculation unit 30 calculates the updated velocity V of the fluid at the n+1 step in the above equation (9). ** , the solid occupancy fraction of the cell α, and the solid velocity V b By substituting, the updated velocity of the fluid at step n+1, V ** The correct velocity V considering the boundary effect at the n+1 step n+1 (S6: speed correction step).

[0073] After S6, the simulation calculation unit 30 advances the number of time steps n by one step (S7), and the number of time steps n reaches the maximum number of time steps n max It is determined whether it is smaller than (S8).

[0074] The number of time steps n is the maximum number of time steps n max If n is smaller than the maximum number of time steps n (S8: YES), the simulation calculation unit 30 repeats S3 to S7. max The calculations of S3 to S6 are repeated until

[0075] The simulation control unit 40 then calculates the time step number n when the time step number n reaches the maximum time step number n maxIf the time reaches (S8: NO), that is, if the calculation is completed up to the end time of the numerical simulation, the numerical simulation by the simulation calculation unit 30 is ended, and the calculation result is output (S9).

[0076] In S9, the simulation control unit 40 transmits the calculation results of the numerical simulation of the fluid performed by the simulation calculation unit 30 to the display control unit 50. The display control unit 50 causes the display device 3 to display the output results of the numerical simulation performed by the simulation control unit 40. The display device 3 visualizes and displays, for example, changes in the speed, pressure, viscosity, etc. of the fluid flowing through the flow path.

[0077] According to the numerical simulation method using the numerical simulation device 1 described above, the flow of a non-Newtonian fluid whose viscosity (viscosity) changes in incompressibility can be analyzed with high speed and accuracy. In particular, the flow of a non-Newtonian fluid flowing through a flow path with a complex shape can be analyzed faster than conventional methods. This allows, for example, the flow of a fluid flowing through a catalyst tank, the flow of a molten resin, a die coater, or a mixing tank to be analyzed with high speed and accuracy, and can be used for design.

[0078] [Example] Next, an example of the calculation results of the numerical simulation method using the above-described numerical simulation device 1 will be described with reference to FIGS.

[0079] [Calculation conditions] Fig. 6 is a diagram showing an example of a calculation target of the numerical simulation device 1. The flow path to be calculated shown in Fig. 6 is a two-dimensional area of ​​1 m x 1 m. Multiple circular solids are arranged within this two-dimensional area. Therefore, the flow path through which the fluid flows has a complex shape.

[0080] The inflow condition is that a non-Newtonian fluid with variable viscosity flows uniformly from the left to the right in Fig. 6 at an initial velocity of u0 = 0.05 [m / s]. As the non-Newtonian fluid, for example, a Carreau fluid is used.

[0081] The spatial increment is 1 / 150 [m]. In other words, the calculation area is divided into 150 x 150 = 22,500 [cells] and the calculation is performed. The time increment Δt is 0.001 [s]. The maximum time step number n max was set to 1000.

[0082] The Carreau model was used as the non-Newtonian viscosity model. In the Carreau model, the relationship between the viscosity of a fluid and the shear rate is shown in the following equation (10). Note that, in addition to the Carreau model, other non-Newtonian viscosity models such as the power law model, the Bingham model, and the Cross model may also be used.

[0083]

number

[0084] In this calculation, λ=2.5, m=0.5, μ0=0.0131, μ ∞ =0.00131, density ρ=10 [kg / m 3 〕

[0085] [Calculation result] Fig. 7 shows an example of the results of calculating the calculation object shown in Fig. 6 by inputting the above-mentioned calculation conditions into the numerical simulation device 1 via the input device 2 and using the numerical simulation method shown in Fig. 5. Fig. 8 is a diagram showing an example of the results of a numerical simulation using a conventional calculation method.

[0086] As shown in FIG. 7, the numerical simulation method using the numerical simulation device 1 of this embodiment was able to reproduce the calculation results using conventional fluid analysis software (Ansys Fluent) shown in FIG.

[0087] Furthermore, while the calculation time required by the conventional calculation method was 90 minutes, the calculation time by the numerical simulation method of this embodiment was 30 minutes. In other words, the numerical simulation method of this embodiment was able to obtain calculation results similar to those of the conventional calculation method at a calculation speed three times faster than that of the conventional calculation method.

[0088] Specifically, with the conventional calculation method, it took 40 minutes to create a CAD model, 30 minutes to generate a mesh, and 20 minutes to set the conditions and perform calculations. As shown in Figure 3(b), the conventional calculation method involves dividing the shape of the object to be calculated into a polyhedral mesh and solving the fluid equations on each polyhedron. For this reason, if the shape of the object to be calculated is complex, it takes a long time to generate the mesh.

[0089] In contrast, our calculation method, which incorporates the immersed boundary method into the fractional step method, an example of a MAC-based solution method, can represent the shape of the object to be calculated using an orthogonal grid, which simplifies mesh generation and shortens calculation time compared to conventional calculation methods.

[0090] In the above-described embodiment, the calculation target is a two-dimensional region, but the present invention is not limited to this, and the numerical simulation method using the numerical simulation device 1 of this embodiment can also be applied to a three-dimensional region. Also, instead of the fractional step method, other MAC-based solution methods or SIMPLE-based solution methods may be used.

[0091] [Software implementation example] The functions of the numerical simulation device 1 (hereinafter referred to as the "device") are realized by a control program for causing a computer to function as the device, and by a control program for causing a computer to function as each control block of the device (in particular, the provisional velocity calculation unit 31, the pressure calculation unit 32, the velocity update unit 33, and the velocity correction unit 34).

[0092] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the control program. The control device and storage device execute the control program, thereby realizing each function described in the above embodiment.

[0093] The control program may be non-transitory and may be recorded on one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the control program may be supplied to the device via any wired or wireless transmission medium.

[0094] Furthermore, some or all of the functions of the control blocks can be realized by logic circuits. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of the control blocks can also be realized by, for example, a quantum computer.

[0095] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention. [Explanation of symbols]

[0096] 1. Numerical simulation equipment 2 Input devices 3 Display device 10 Control Unit 20 Memory section 30 Simulation calculation section 31 Provisional speed calculation unit 32 Pressure calculation unit 33 Speed ​​update section 34 Speed ​​correction section

Claims

1. A numerical simulation method for non-Newtonian fluids with incompressible, variable viscosity, comprising: a step of calculating an implied velocity of the non-Newtonian fluid flowing through a flow path in n steps (n is the number of time steps) by discretizing the Navier-Stokes equations and using known variables; a pressure calculation step of calculating a pressure of the non-Newtonian fluid at the n+1 step by solving a Poisson equation for pressure from the virtual velocity at the n step; a velocity updating step of updating the velocity of the non-Newtonian fluid at the n+1 step from the tentative velocity at the n step and the pressure at the n+1 step to calculate an updated velocity; a velocity correction step of correcting the updated velocity at the n+1 step to a correct velocity that takes into account the influence of the boundary at the n+1 step, using a boundary condition of the flow path set using the immersed boundary method; Including, A numerical simulation method in which the tentative velocity calculation step, the pressure calculation step, the velocity update step, and the velocity correction step are iteratively calculated while advancing the time step.

2. In the tentative velocity calculation step, the tentative velocity is calculated based on the following formula (1): [Equation 1] In the pressure calculation step, the pressure is calculated by solving the Poisson equation shown in the following formula (2) where p is the pressure: [Equation 2] In the speed updating step, the updated speed is calculated based on the following formula (3): [Equation 3] In the speed correction step, the correct speed is calculated taking into account the influence of the boundary based on the following equation (4): [Equation 4] where α is the solid occupancy ratio, which is the ratio of the solid to the flow path, and V ｂ The numerical simulation method according to claim 1 , wherein: represents the velocity of the solid.

3. 3. The numerical simulation method according to claim 2, wherein the non-Newtonian viscosity model is selected from the group including at least a power law model, a Carreau model, a Bingham model, and a Cross model.

4. The numerical simulation method according to claim 1 , wherein the flow of the non-Newtonian fluid in the flow channel is a laminar flow.

5. A numerical simulation device for a non-Newtonian fluid whose viscosity changes in an incompressible manner, an implied velocity calculation unit that discretizes the Navier-Stokes equations and calculates the implied velocity of the non-Newtonian fluid flowing through the flow path in n steps (n is the number of time steps) using known variables; a pressure calculation unit that calculates the pressure of the non-Newtonian fluid by solving a Poisson equation related to pressure from the virtual velocity at the n steps; a velocity update unit that updates the velocity of the non-Newtonian fluid to a velocity at n+1 steps based on the pressure and the virtual velocity at the nth step to calculate an updated velocity; a velocity correction unit that corrects the updated velocity at the n+1 step to a correct velocity that takes into account the influence of the boundary at the n+1 step, using a boundary condition of the flow path that is set using the immersed boundary method; A numerical simulation device equipped with

6. A control program for causing a computer to function as the numerical simulation apparatus according to claim 5, a control program for causing a computer to function as the tentative velocity calculation unit, the pressure calculation unit, the velocity update unit, and the velocity correction unit;

Images