Turbulent flow simulation method, turbulent flow simulation system, turbulent flow simulation device, terminal device, design method, manufacturing method, and program

Abstract

Provided is a turbulent flow simulation method in which a computer uses a large-eddy simulation to analyze a flow field of a fluid, the method comprising: acquiring a simulation condition (S10); performing, on the basis of the acquired simulation condition, analysis of the flow field of the fluid by means of the large-eddy simulation (S20); and outputting an analysis result of the flow field of the fluid (S30). In the analysis of the flow field of the fluid, a turbulent flow model that includes an error term of a Navier-Stokes equation derived from a lattice Boltzmann equation as a correction term associated with coarse graining in the large-eddy simulation is used, the correction term being a body force calculated from eddy stress associated with the coarse graining.

Description

Turbulent flow simulation method, turbulent flow simulation system, turbulent flow simulation device, terminal device, design method, manufacturing method, and program

[0001] The present invention relates to a turbulent flow simulation method, a turbulent flow simulation system, a turbulent flow simulation device, a terminal device, a design method, a manufacturing method, and a program.

[0002] Conventionally, numerical analysis of turbulent flow fields has been performed in the design, development, etc. of fluidic equipment. Large eddy simulation (LES), for example, is known as a method for analyzing turbulent flow fields (see, for example, Patent Document 1).

[0003] Japanese Patent Application Laid-Open No. 2003-141181

[0004] Keiichi Yamamoto, "Novel Expansion Method for Deriving the Navier-Stokes Equation from the Lattice Boltzmann Equation," [online], January 13, 2022, Multiphase Science and Technology, [Retrieved October 31, 2023], Internet <URL: https: / / www. dl. begellhouse. com / es / journals / 5af8c23d50e0a883, 2e84b81900eabcea, 1af4c2084444923d. html>David J. Holdych, three others, “Truncation error analysis of lattice Boltzmann methods”, [online], January 20, 2004, Journal of the Society of Computational Physics, [searched October 31, 2023], Internet <https: / / www. sciencedirect. com / science / article / abs / pii / S0021999103004364>Y. Kuwata, et al., "Anomalous of the lattice Boltzmann methods in three-dimensional cylindrical flows," [online], October 8, 2014, Journal of Computational Physics, [Retrieved October 31, 2023], Internet <https: / / www.sciencedirect.com / science / article / abs / pii / S0021999114006767>

[0005] However, the technique of Patent Document 1 leaves room for improvement in simulation performance.

[0006] Therefore, the present invention provides a turbulent flow simulation method, a turbulent flow simulation device, and a program with improved simulation performance.

[0007] A turbulent flow simulation method according to one aspect of the present invention is a method for simulating turbulence in which a computer analyzes a fluid flow field using large eddy simulation, the method acquiring simulation conditions, performing an analysis of the fluid flow field using the large eddy simulation based on the acquired simulation conditions, and outputting an analysis result of the fluid flow field, wherein the analysis of the fluid flow field uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term associated with coarse graining in the large eddy simulation, and the correction term is a volume force calculated from the turbulent stress associated with the coarse graining.

[0008] A turbulent flow simulation system according to one aspect of the present invention is a simulation system comprising: a turbulent flow simulation device that analyzes a fluid flow field using large eddy simulation; and a terminal device capable of communicating with the turbulent flow simulation device, wherein the turbulent flow simulation device comprises: a first acquisition unit that acquires simulation conditions; a simulation unit that performs analysis of the fluid flow field using the large eddy simulation based on the acquired simulation conditions; and a first output unit that outputs analysis results of the fluid flow field, wherein the simulation unit uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term associated with coarse-graining in the large eddy simulation, and the correction term is a volume force calculated from turbulent stress associated with the coarse-graining, and the terminal device comprises: a second output unit that outputs the simulation conditions; a second acquisition unit that acquires the analysis results for the simulation conditions output by the second output unit; and a control unit that executes predetermined processing on the acquired analysis results.

[0009] A turbulent flow simulation device according to one aspect of the present invention is a turbulent flow simulation device in the above-described turbulent flow simulation system.

[0010] A terminal device according to one aspect of the present invention is a terminal device in the above-described turbulent flow simulation system.

[0011] A terminal device according to one aspect of the present invention includes a transmitting unit that transmits input simulation conditions to a server that analyzes a fluid flow field by large eddy simulation using a turbulence model that includes, based on the simulation conditions, an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term that is a volume force calculated from turbulence stress associated with coarse graining in the large eddy simulation, and a presenting unit that presents the analysis results of the fluid flow field received from the server.

[0012] A design method according to one aspect of the present invention is a design method for a fluid product that forms a flow path through which a fluid flows, which method acquires the analysis results output by the above-mentioned turbulent flow simulation method, and determines the structure of the fluid product based on the acquired analysis results.

[0013] A manufacturing method according to one aspect of the present invention is a method for manufacturing a fluid product that forms a flow path through which a fluid flows, and involves obtaining information indicating the structure of the fluid product determined by the above-mentioned design method, and manufacturing the fluid product based on the obtained information.

[0014] A program according to one aspect of the present invention is a program for causing a computer to execute a turbulent flow simulation method for analyzing a fluid flow field using large eddy simulation, the turbulent flow simulation method including: acquiring simulation conditions; analyzing the fluid flow field using the large eddy simulation based on the acquired simulation conditions; and outputting analysis results of the fluid flow field, wherein the analysis of the fluid flow field uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term associated with coarse graining in the large eddy simulation, and the correction term is a volume force calculated from the turbulent stress associated with the coarse graining.

[0015] According to one aspect of the present invention, it is possible to realize a turbulent flow simulation method and the like with improved simulation performance.

[0016] FIG. 1 is a block diagram showing the functional configuration of a simulation device according to an embodiment. FIG. 2 is a flowchart showing the operation of the simulation device according to an embodiment. FIG. 3 is a diagram showing the distribution of correction terms associated with coarse graining, calculated from an exact numerical solution according to a comparative example. FIG. 4 is a diagram showing the distribution of correction terms calculated using a Smagorinsky model according to a conventional example. FIG. 5 is a diagram showing the distribution of correction terms calculated using a model of the present invention. FIG. 6 is a flowchart showing a manufacturing method for manufacturing a fluid product according to an embodiment. FIG. 7 is a diagram showing the configuration of a simulation system according to an embodiment. FIG. 8 is a diagram showing a velocity model used to derive a turbulence model according to an embodiment. FIG. 9 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 10 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 11 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 12 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 13 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 14 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 15 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 16 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 17 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 18 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 19 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 20 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 21 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 22 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 23 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 24 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 25 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 26 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 27 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 28 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 29 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 30 is a diagram showing an example of a derivation of a turbulence model according to an embodiment. FIG. 31 is a diagram showing an example of a derivation of a turbulence model according to an embodiment.Fig. 32 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 33 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 34 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 35 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 36 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 37 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 38 is a diagram showing an example of derivation of a turbulence model according to an embodiment. Fig. 39 is a diagram showing an example of derivation of a turbulence model according to an embodiment.

[0017] (How the present invention was arrived at) Before describing the present invention, how the present invention was arrived at will be described.

[0018] A turbulence model (turbulent stress model) is a correction model associated with coarse graining for determining the values ​​of fluid velocity (u) and pressure (p) in coarse-grained space and time. In a turbulence model, space is divided into coarse meshes to reduce the amount of calculations, etc., but instead of calculating the space using the coarse mesh, the effects of small-scale turbulence that cannot be resolved by the mesh are expressed as correction terms. In other words, the turbulence model includes correction terms. Furthermore, small-scale turbulence refers to, for example, stress (turbulent stress) caused by small eddies (e.g., eddies also known as eddies) that cannot be captured within the mesh width.

[0019] The Smagorinsky model, which is also described in Patent Document 1, is often used as a turbulence model. The Smagorinsky model is a turbulence model that is standardly installed in general-purpose fluid software (analysis software). When time is t, spatial coordinates are x, vector suffixes are α, β, γ, and μ, density is ρ, velocity is u, kinematic viscosity is ν, spatial mesh width (computational mesh width) is Δ, pressure is p, and Smagorinsky parameter is C, the Smagorinsky model is expressed as the following Equation 1.

[0020]

[0021] The vector suffixes α, β, γ, and μ respectively represent components of the x, y, and z vectors. The following term (Equation 2) in Equation 1 is a correction term in the Smagorinsky model.

[0022]

[0023] As shown in Equation 2, the Smagorinsky model includes a Smagorinsky parameter C (also called the Smagorinsky constant), which is an empirical fitting parameter determined for each flow field. The correction term of the Smagorinsky model is defined only in the velocity field.

[0024] The Smagorinsky model described above has the following problems:

[0025] (Problem 1) Because the Smagorinsky model includes the Smagorinsky parameter C, it is necessary to set the Smagorinsky parameter C according to the flow field. Furthermore, the Smagorinsky parameter C may be a constant or a function of time and space, and even in the same flow field, for example, the optimal value of C may differ depending on the position of the fluid flowing inside a pipe (for example, the center or end of the pipe), making it difficult to use.

[0026] (Problem 2) When comparing the Smagorinsky model with a rigorous numerical solution that requires enormous computational costs, it is known that the local correlation coefficient between the two is low, and it is difficult to significantly coarse-grain the mesh with the Smagorinsky model.

[0027] (Issue 3) It is known that the Smagorinsky model does not provide a very high degree of global accuracy in reproducing the generation of turbulent stress due to coarse-graining caused by various large, medium, and small vortices, making it difficult to significantly coarse-grain the mesh.

[0028] As described above, various problems exist in the simulation of turbulent flows using the Smagorinsky model, which means that there is room for improvement in the simulation performance of the simulation of turbulent flows using the Smagorinsky model.

[0029] Therefore, the present inventors have conducted extensive research into turbulent flow simulation methods and the like to solve the above-mentioned problems, and have devised the turbulent flow simulation method and the like described below. While the details will be described later, the gist of the present invention is that the inventors discovered that the error term of the Navier-Stokes equations derived from the lattice Boltzmann equation can be used as a correction term associated with coarse-graining in large eddy simulation (LES) analysis, and have devised a turbulent flow simulation method and the like using a turbulence model including this error term. Note that improving any of the above (Problem 1) to (Problem 3) is an example of improving simulation performance. The correction term is a volume force calculated from turbulent stress associated with coarse-graining.

[0030] Hereinafter, the embodiments will be specifically described with reference to the drawings.

[0031] The embodiments described below are all comprehensive or specific examples. The numerical values, shapes, components, component placement and connection configurations, steps, and step order shown in the following embodiments are merely examples and are not intended to limit the present invention. Furthermore, among the components in the following embodiments, components not described in the independent claims are described as optional components.

[0032] Furthermore, each figure is a schematic diagram and is not necessarily an exact illustration. Therefore, for example, the scales of the figures do not necessarily match. Furthermore, in each figure, substantially the same components are given the same reference numerals, and redundant explanations are omitted or simplified.

[0033] Furthermore, in this specification, terms indicating relationships between elements such as coincidence, as well as numerical values ​​and numerical ranges, are not expressions that express only the strict meaning, but are expressions that also include a substantially equivalent range, for example, a difference of about several percent (or about 10%).

[0034] (Embodiment) Hereinafter, a simulation device according to the present embodiment will be described with reference to FIGS.

[0035] [1. Configuration of Simulation Apparatus] First, the configuration of a simulation apparatus according to this embodiment will be described with reference to Fig. 1. Fig. 1 is a block diagram showing the functional configuration of a simulation apparatus 10 according to this embodiment. The simulation apparatus 10 is an information processing apparatus that executes a turbulent flow simulation method that analyzes the flow field of a fluid using large eddy simulation (LES). The simulation apparatus 10 is an example of a turbulent flow simulation apparatus.

[0036] The simulation device 10 is realized by a computer including, for example, a communication interface for communicating with other devices such as an input device and a presentation device, a non-volatile memory for storing programs executed by each processing unit, a volatile memory that is a temporary storage area for executing the programs, an input / output port for transmitting and receiving signals, and a processor for executing the programs. The communication interface may be realized by a connector to which a communication line is connected for wired communication, or by a wireless communication circuit for wireless communication. For example, the simulation device 10 may be realized by a server.

[0037] As shown in FIG. 1, the simulation device 10 includes an acquisition unit 11, a simulation unit 12, an output unit 13, and a storage unit 14.

[0038] The acquisition unit 11 acquires input information including simulation conditions for performing a simulation from an input device (for example, a terminal device 20 shown in FIG. 7 , which will be described later). The simulation conditions include information about a pipe through which a fluid flows, information about a mesh, information about the fluid, etc. The acquisition unit 11 is, for example, a communication interface that enables the simulation device 10 to communicate with other devices. The acquisition unit 11 is configured to include, for example, a communication circuit (communication module). The acquisition unit 11 is an example of a first acquisition unit. The input device is, for example, but is not limited to, a button, a keyboard, a microphone, a terminal device, etc.

[0039] The simulation unit 12 performs an analysis of the turbulent flow field by LES based on the simulation conditions acquired by the acquisition unit 11. In LES, the effects of vortices smaller than the filter scale are modeled, and vortices larger than the filter scale are directly calculated.

[0040] In analyzing the flow field of a fluid, the simulation unit 12 uses a turbulence model that includes, as a correction term, an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation. When time is t, spatial coordinates (position) are x, vector suffixes are α, β, γ, and μ, density is ρ, velocity is u, kinematic viscosity is ν, spatial mesh width (computational mesh width) is Δ, and pressure is p, an example of a turbulence model according to one aspect of the present invention is expressed as shown in Equation 3. The derivation of Equation 3 will be described later.

[0041]

[0042] The following term (Equation 4) in Equation 1 is a correction term in the turbulence model according to one aspect of the present invention. That is, Equation 4 is a term that expresses the turbulent stress associated with the coarse-graining of the mesh width Δ in the LES analysis.

[0043]

[0044] As shown in Equation 4, the correction term of the turbulence model according to one aspect of the present invention does not include a fitting parameter such as the Smagorinsky parameter C. This eliminates the need for the user to input fitting parameters, improving usability of the simulation device 10. Furthermore, the correction term is composed of only isotropic tensors.

[0045] Furthermore, as shown in Equation 4, the correction term includes pressure (p). Specifically, the correction term includes a harmonic function of pressure. Since pressure has a faster propagation speed than velocity and a turbulent field is thought to be formed when pressure (pressure waves) propagate before velocity, including pressure in the correction term makes it easier to reflect the global situation. In other words, including pressure in the correction term can improve the reproduction accuracy of the global turbulence model. Note that in the conventionally used Smagorinsky model, the correction term is defined only in terms of the velocity field, so it is thought to be difficult to improve the reproduction accuracy of the global situation.

[0046] The output unit 13 outputs the simulation results of the simulation unit 12 to a presentation device (for example, the terminal device 20 shown in FIG. 7 , which will be described later). The simulation results include the results of simulating a flow field using the above-mentioned equation 3. The output unit 13 is, for example, a communication interface that enables the simulation device 10 to communicate with other devices. The output unit 13 is configured to include, for example, a communication circuit (communication module). The presentation device is, for example, a liquid crystal display device, but is not limited to this. The output unit 13 is an example of a first output unit, and the simulation results are an example of analysis results.

[0047] The storage unit 14 is a storage device that stores various types of information used by the simulation unit 12 to execute a simulation. The storage unit 14 stores, for example, a turbulence model used in the simulation. In this embodiment, the storage unit 14 stores the above-mentioned Equation 3. The storage unit 14 is realized, for example, by a hard disk drive (HDD) or a semiconductor memory.

[0048] [2. Operation of the Simulation Apparatus] Next, the operation of the simulation apparatus 10 configured as described above will be described with reference to Fig. 2. Fig. 2 is a flowchart showing the operation (a method for simulating a turbulent flow) of the simulation apparatus 10 according to this embodiment. Fig. 2 shows a method for simulating a turbulent flow in which a computer analyzes the flow field of a fluid using large eddy simulation.

[0049] 2, the acquisition unit 11 acquires input information from an input device or the like (S10). The input information includes simulation conditions for executing a simulation using a turbulence model, but the simulation conditions do not include information related to fitting parameters.

[0050] Next, the simulation unit 12 performs a large eddy simulation using a turbulence model that includes, as a correction term, an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation (S20). In this embodiment, the simulation unit 12 reads out the turbulence model shown in Equation 3 from the storage unit 14, and performs a large eddy simulation using the read-out turbulence model.

[0051] Next, the output unit 13 outputs the simulation result by the simulation unit 12 to a presentation device or the like (S30). As a result, the output unit 13 can present the simulation result to the user. For example, the simulation result may be displayed to the user as an image. The simulation result may also be stored in the storage unit 14.

[0052] [3. Verification of Simulation Results] Next, the verification results (a priori test results) of the turbulence model of the simulation device 10 configured as described above will be described with reference to Figures 3 to 5. Figure 3 is a diagram (correct data) showing the distribution of correction terms (volume forces calculated from turbulent stresses) associated with coarse-graining, calculated from a rigorous numerical solution according to a comparative example. The distribution of correction terms shown in Figures 3 to 5 indicates the distribution of stresses at a certain moment in a certain cross section of a certain flow field. Furthermore, the coarse-graining magnification is the same in Figures 3 to 5.

[0053] The rigorous numerical solution is a solution obtained by solving the fundamental equations of fluid mechanics (Navier-Stokes equations) directly without modeling (direct numerical simulation (DNS)). FIG. 3 shows such a rigorous numerical solution viewed on a coarse grid with a coarse-graining factor of 125.

[0054] Figure 3 can also be said to show the correct data for the distribution of body forces, which indicates what corrections must be added to the Navier-Stokes equations for each grid when coarse-graining is used. The correct data is obtained from the results of rigorous calculations, and therefore includes the effects of small vortices that cannot be captured by the mesh.

[0055] The exact numerical solutions used are those in a publicly available database (URL: http: / / turbulence.pha.jhu.edu / Forced_isotropic_turbulence.aspx).

[0056] Fig. 4 is a diagram showing the distribution of the correction term (volume force calculated from turbulent stress) calculated by the Smagorinsky model (turbulence model shown in Equation 1) according to the conventional example. Fig. 5 is a diagram showing the distribution of the correction term (volume force calculated from turbulent stress) calculated by the model of the present invention (turbulence model shown in Equation 3).

[0057] As shown in Figures 3 to 5, the distribution shown in Figure 5 is closer to the distribution shown in Figure 3 than the distribution shown in Figure 4. According to the turbulence model according to one embodiment of the present invention, the improved accuracy of the distribution of the correction term can be confirmed even by visual inspection. Furthermore, the correlation coefficient between the distribution shown in Figure 3 and the distribution shown in Figure 4 is 0.2, while the correlation coefficient between the distribution shown in Figure 3 and the distribution shown in Figure 5 is 0.48. The correlation coefficient indicates the degree of agreement with the correct data.

[0058] As described above, the turbulence model according to one aspect of the present invention can significantly improve the correlation coefficient with the correct data compared to the Smagorinsky model. This means that the correction term of the turbulence model according to one aspect of the present invention can more accurately calculate the stress (turbulent stress) caused by small vortices (also called eddies) that cannot be captured within the mesh width. As a result, the simulation device 10 can improve simulation performance in terms of the accuracy of the simulation results.

[0059] In the Smagorinsky model, the model format is limited to eddy viscosity differential calculations, and the degree of freedom in expressing complex turbulent phenomena is low, which is thought to be why the correlation coefficient is low as described above. On the other hand, the turbulence model according to one embodiment of the present invention is not limited to eddy viscosity differential calculations, and therefore the degree of freedom is higher than that of the Smagorinsky model, which is thought to be why the correlation coefficient is higher than that of the Smagorinsky model as described above.

[0060] The above correlation coefficients are values ​​when the number of bases (see FIG. 8 ), which will be described later, is 27. It is believed that the correlation coefficients can be further improved by using a turbulence model derived with a larger number of bases.

[0061] [4. Manufacturing Method] Next, a method for manufacturing a fluid product using the simulation method described above will be described with reference to Fig. 6. Fig. 6 is a flowchart showing a manufacturing method for manufacturing a fluid product according to this embodiment. The fluid product is a product that forms a flow path through which a fluid flows, and examples thereof include, but are not limited to, pipes through which a fluid flows. The fluid product may also be used in, for example, a cleaning device, a cooling device, etc.

[0062] As shown in FIG. 6, the manufacturing method includes performing a design step (S110) and then performing a manufacturing step (S120).

[0063] In the design step, the structure of the fluid product is designed using the analysis results of the fluid flow field obtained by the simulation method described above. The structure includes the shape, size, etc. of the fluid product. For example, the structure of the fluid product that can realize a desired flow field is determined using the analysis results.

[0064] Next, in the manufacturing step, the fluid product designed in the design step is actually manufactured, and processing, assembly, etc. are performed to form the fluid product.

[0065] Each step in the manufacturing method may be implemented as a separate step (method). For example, step S110 may be implemented as a design method for a fluid product that forms a flow path through which a fluid flows. Step S120 may be implemented as a manufacturing method that acquires information indicating the structure of the fluid product determined by the design method and manufactures the fluid product based on the acquired information.

[0066] 5. Configuration of Simulation System Next, a simulation system including the simulation device 10 according to this embodiment will be described with reference to Fig. 7. Fig. 7 is a diagram showing the configuration of the simulation system 1 according to this embodiment.

[0067] 7 , the simulation system 1 includes the simulation device 10 described above and a terminal device 20 communicably connected to the simulation device 10. The simulation device 10 and the terminal device 20 may be located in the same facility, or may be located apart (for example, in different facilities). Furthermore, when the simulation device 10 and the terminal device 20 are located apart, the simulation device 10 and the terminal device 20 may be located in the same country or region, or may be located in different countries or regions.

[0068] The terminal device 20 is, for example, a device installed with application software for executing a turbulent flow simulation that analyzes the flow field of a fluid, and outputs accepted simulation conditions to the simulation device 10 and obtains analysis results for the simulation conditions from the simulation device 10. The terminal device 20 has a function of, for example, remotely causing the simulation device 10 to execute an analysis of the flow field of a fluid.

[0069] The terminal device 20 includes a communication unit 21, a reception unit 22, a control unit 23, a display unit 24, and a storage unit 25. The terminal device 20 may be a stationary device such as a PC (Personal Computer), or may be a portable device such as a tablet terminal.

[0070] The communication unit 21 is a communication interface for the terminal device 20 to communicate with the simulation device 10. The communication unit 21 is configured to include, for example, a communication circuit (communication module). The communication unit 21 functions as a second output unit and a transmission unit that outputs (transmits) simulation conditions to the simulation device 10. The communication unit 21 also functions as a second acquisition unit that acquires (receives) analysis results for the simulation conditions output by the communication unit 21.

[0071] The simulation conditions may include information indicating the use of a turbulence model according to this embodiment (i.e., a turbulence model that includes an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation as a correction term associated with coarse-graining in large eddy simulation). Furthermore, communication between the terminal device 20 and the simulation device 10 may be wired communication or wireless communication.

[0072] The reception unit 22 receives operations from the user. For example, the reception unit 22 receives input of simulation conditions from the user. The reception unit 22 may also receive a selection to perform a simulation using the turbulence model according to this embodiment. The reception unit 22 is realized by, for example, a button, a keyboard, a touch panel, or the like, but may also be a device that receives input such as voice.

[0073] The control unit 23 is a control device that controls each component of the terminal device 20. When the control unit 23 acquires the analysis result from the simulation device 10 via the communication unit 21, the control unit 23 executes a predetermined process on the acquired analysis result. The predetermined process may be a process of displaying the analysis result on the display unit 24, a process of storing the analysis result in the storage unit 25, or other process on the analysis result.

[0074] The display unit 24 is a display device that displays information to the user. The display unit 24 displays, for example, the analysis results of the simulation device 10. Furthermore, when accepting input of simulation conditions, the display unit 24 may display information indicating that a simulation will be performed using the turbulence model according to this embodiment or information that prompts the user to select a turbulence model. Furthermore, when displaying the analysis results, the display unit 24 may display information indicating that the analysis results were obtained using the turbulence model according to this embodiment. The display unit 24 is realized, for example, by a liquid crystal display or the like. The display unit 24 is an example of a presentation unit. The presentation unit may present the analysis results by voice or the like.

[0075] The storage unit 25 stores information related to the simulation in the simulation device 10. The storage unit 25 may store, for example, the above-mentioned application software. The storage unit 25 may also store analysis results acquired from the simulation device 10. The analysis results may be stored in association with, for example, simulation conditions. The storage unit 25 is realized, for example, by an HDD or a semiconductor memory.

[0076] The terminal device 20 may also be a device on which application software for designing fluid products is installed.

[0077] In addition, the simulation device 10 and the terminal device 20 in the simulation system 1 may each be realized as a separate device.

[0078] 6. Derivation of Turbulence Model Next, the derivation of the turbulence model used in the simulation device 10 will be described with reference to Fig. 8 to Fig. 39. Fig. 8 is a diagram showing a velocity model used in the derivation of the turbulence model according to this embodiment.

[0079] First, a turbulence model according to one embodiment of the present invention is constructed based on molecular fluid dynamics, which considers fluid motion as molecular motion. Specifically, the turbulence model is derived using the lattice Boltzmann equation. The lattice Boltzmann equation is an equation that describes the behavior of molecules (flow field). Since the lattice Boltzmann equation can also be regarded as a discretized Boltzmann equation, it is considered to be an equation with a broader range of application than the Navier-Stokes equation.

[0080] The lattice Boltzmann method is a computational technique that describes fluid motion by analogy with the Boltzmann equation, restricting the motion of countless random molecules to a finite velocity basis. The lattice Boltzmann equation approximates a fluid as an aggregate of many virtual particles with finite velocities (a lattice gas model), sequentially calculates the collisions and translations of each particle using the particle velocity distribution function, and calculates the macroscopic flow field from the sum of these moments.

[0081] In this embodiment, as shown in FIG. 8 , a three-dimensional 27-velocity (D3Q27) model is used as the velocity model. In this case, the movement of particles is limited to 27 directions by this lattice. That is, a model with 27 basis points (27 pieces) is used. Note that the basis point is not limited to 27, and may be less than 27 or more than 27. For example, the basis point number is often 9, 15, 19, 39, 40, 41, 48, 49, 72, etc., but other numbers may also be used.

[0082] When the time is t, the position is x, the particle velocity (for example, the average velocity) is c, the time step is δt, and the direction is i, the lattice Boltzmann equation is expressed by the following Equation 5.

[0083]

[0084] Here, fi(x, t) represents the distribution function of a particle having a velocity in the i direction at time t and position x.

[0085] Since the appearance of such a lattice Boltzmann equation varies depending on the time scale observed, even for the same flow, this scale is taken as a variable and the lattice Boltzmann equation is subjected to a Taylor expansion (see the expansion theory described in Non-Patent Document 1). Note that, although the Chapmann-Enskog theory and Sone's asymptotic S-expansion are known as expansion theories for the lattice Boltzmann equation, these expansion theories cannot estimate the error term and therefore cannot be used in the present derivation.

[0086] When Equation 5 is expanded based on the expansion theory described in Non-Patent Document 1, the following Equation 6 is obtained. Note that time is represented by t, position by x, velocity by u, vector suffixes by α, β, γ, μ, and pressure by p. Here, up to the square of the mesh width Δ is used.

[0087]

[0088] Note that ρ and μ are expressed by the following equations 7 and 8.

[0089]

[0090] Here, fi is the distribution function of the velocity in the i-direction.

[0091]

[0092] Here, δt is the time step and φ is the relaxation parameter. ｓ is defined by the following equation 9.

[0093]

[0094] where c is the particle velocity.

[0095] Such an approach is more of a physical development than a mathematical one.

[0096] Here, when deriving the Navier-Stokes equations from the lattice Boltzmann equation as described above, an error term based on the mesh width Δ (for example, an error term of the fourth or sixth power of the mesh width Δ) occurs. In the case of Equation 3, the term shown in Equation 4 is the error term.

[0097] Conventionally, this error term has been considered to be a truncation error. However, the present inventors believed that if the expansion theory is physically meaningful as in Non-Patent Document 1, then the error term (Equation 4) obtained from the lattice Boltzmann equation, which has a wide range of applicability, should also have physical meaning. Specifically, the present inventors believed that this error term has a large effect when the mesh resolution is low, that is, that it describes the influence of fine flows that cannot be resolved by the mesh. In other words, the present inventors believed that the error term shown in Equation 4 is the turbulent stress itself (i.e., a correction term for turbulent stress).

[0098] The inventors of the present application calculated the expansion theory shown in Non-Patent Document 1 up to a higher order, for example, up to the fourth order (fourth order of Δt (time width)), thereby deriving the above Equation 3. Note that the calculation is not limited to the fourth order, and any order may be used. Note that when expanding up to an order other than the fourth order, the correction term in Equation 3 may change from Equation 4.

[0099] As shown in the above derivation method, the turbulence model is derived from the lattice Boltzmann equation, and therefore a formulation that includes pressure p and does not include fitting parameters, as shown in Equation 3, has been successfully achieved.

[0100] In addition, the error term of the higher-order expanded formula, which destroys the spatial isotropy of the tensor, is deleted as an inherent error and used as a correction term (for example, formula 4). The term that destroys spatial isotropy is a term of an anisotropic tensor. In other words, the correction term is composed only of isotropic tensors.

[0101] The method of deriving a turbulence model from the lattice Boltzmann equation is not limited to the expansion theory of Non-Patent Document 1, and for example, the expansion theory of Non-Patent Document 2 may also be used. The expansion theory of Non-Patent Document 2 is mathematical, and differs in its path and assumptions from the expansion theory from a physical perspective of Non-Patent Document 1, but it completely matches the calculation results of Non-Patent Document 1, including the error terms.

[0102] As shown in Non-Patent Document 3, the error term shown in Equation 4 etc. is generally treated as a fundamental error. In other words, the idea of ​​the inventors of the present application that the error term shown in Equation 4 etc. represents a correction term associated with coarse-graining is itself a novel idea that has not been seen before.

[0103] The derivation of the turbulence model (Equation 3) according to this embodiment will be described with reference to Figures 9 to 39. Figures 9 to 39 are diagrams showing examples of derivation of the turbulence model (turbulent stress) according to this embodiment.

[0104] FIG. 9 shows an expression obtained by expanding both sides of the lattice Boltzmann equation.

[0105] FIG. 10 shows the recurrence formula derived from the uniqueness of the Taylor expansion.

[0106] FIG. 11 shows an equation in which a higher order is written in a lower order.

[0107] FIG. 12 shows an equation describing up to the fourth order using equilibrium distribution functions.

[0108] FIG. 13 shows an equation describing up to the fifth order using the equilibrium distribution function.

[0109] 14 and 15 show the lattice Boltzmann equation described by the equilibrium distribution function.

[0110] FIG. 16 shows the equation written down for the equilibrium distribution function.

[0111] FIG. 17 shows the equation used to perform the calculation by substituting the equilibrium distribution function into the lattice Boltzmann equation.

[0112] FIG. 18 shows an equation obtained by transforming the right side of FIG.

[0113] FIG. 19 shows an equation obtained by transforming the right side of FIG.

[0114] FIG. 20 shows an equation obtained by transforming the right side of FIG.

[0115] FIG. 21 shows an equation in which the right side of FIG. 20 is written in Kronecker notation for tensors up to the fourth order.

[0116] FIG. 22 shows an equation obtained by transforming the right side of FIG.

[0117] FIG. 23 shows an equation obtained by transforming the right side of FIG. 22 using Euler's law.

[0118] FIG. 24 shows an equation obtained by transforming the right side of FIG.

[0119] FIG. 25 shows an equation obtained by transforming the right side of FIG.

[0120] FIG. 26 is an equation showing the calculation of the sixth-order tensor of the sixth term on the right-hand side shown in FIG. 25, and specifically shows an equation obtained by substituting the result of FIG. 32 into the sixth-order tensor of the sixth term on the right-hand side.

[0121] FIG. 27 shows an equation obtained by substituting the right-hand side of FIG. 26 into the sixth-order tensor of the sixth term on the right-hand side shown in FIG.

[0122] FIG. 28 shows an equation obtained by transforming the right side of FIG.

[0123] FIG. 29 shows an equation obtained by transforming the right side of FIG.

[0124] FIG. 30(a) shows an equation obtained by substituting the result of FIG. 37 into the last term on the right side of FIG.

[0125] Figure 30(b) is an equation obtained by deleting the two terms derived from the anisotropic tensor from Figure 30(a) and arranging the terms in a horizontal row. The first and second terms on the left side of Figure 30(b) can be obtained from the Navier-Stokes equation, so the derivation is now complete.

[0126] Fig. 31 is a modified version of (b) in Fig. 30, and corresponds to the above-mentioned equation 3. Note that Fig. 31 also shows two terms derived from an anisotropic tensor for reference.

[0127] 32 to 36 show the calculations used to derive the relationship shown in FIG.

[0128] 38 and 39 show the calculations used to derive the relationship shown in FIG.

[0129] [7. Effects, etc.] The invention derived from the disclosure of this specification and the effects, etc. obtained by the invention will be described below.

[0130] (Invention 1) A method for simulating turbulence in which a computer analyzes a fluid flow field using large eddy simulation, the method comprising: acquiring simulation conditions (S10); performing an analysis of the fluid flow field using the large eddy simulation based on the acquired simulation conditions (S20); and outputting an analysis result of the fluid flow field (S30); the analysis of the fluid flow field uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term associated with coarse-graining in the large eddy simulation; the correction term is a volume force calculated from the turbulent stress associated with the coarse-graining.

[0131] This allows the use of a turbulence model that includes, as a correction term, an error term that is considered to be a term that represents the turbulent stress itself, thereby enabling more accurate calculation of the turbulent stress and improving the accuracy of the analysis results in the turbulence model. In other words, the simulation performance is improved in that the accuracy of the analysis results (simulation results) is improved. This can also improve, for example, the above-mentioned (Problem 2).

[0132] (Invention 2) The method for simulating turbulence according to Invention 1, wherein the correction term includes a harmonic function of pressure.

[0133] This allows the turbulence model to include pressure, which has a faster propagation speed and is more likely to reflect global conditions, thereby improving the accuracy of global reproduction of turbulent stress generation compared to turbulence models that only include velocity fields, such as the Smagorinsky model. This contributes to making the mesh coarser, which in turn improves calculation speed. In other words, the simulation performance improves in terms of improving calculation speed. This can also improve, for example, the above-mentioned (Problem 3).

[0134] (Invention 3) The turbulent flow simulation method of Invention 1 or 2, wherein the correction term is composed of only isotropic tensors.

[0135] This improves the accuracy of the analysis results because the anisotropic tensor, which is an inherent error, is not included in the correction term. In other words, the simulation performance improves in terms of the improved accuracy of the analysis results.

[0136] (Invention 4) The turbulent flow simulation method according to any one of Inventions 1 to 3, wherein the error term does not include a fitting parameter.

[0137] This eliminates the need to set fitting parameters, improving the ease of use of the simulation method, and may also alleviate, for example, the above-mentioned (Problem 1).

[0138] (Invention 5) This is a turbulent flow simulation method according to any one of Inventions 1 to 4, wherein the correction term is expressed by the following equation 1, where x is the spatial coordinate, α, β, γ, and μ are vector suffixes, ρ is density, u is velocity, ν is dynamic viscosity, Δ is spatial mesh width, and p is pressure.

[0139]

[0140] This uses correction terms calculated up to the fourth order (fourth order of Δt (time width)) using expansion theories such as those in Non-Patent Document 1, thereby further improving the accuracy of the simulation results.

[0141] (Invention 6) A turbulent flow simulation system 1 includes a turbulent flow simulation device 10 that analyzes a fluid flow field using large eddy simulation, and a terminal device 20 that can communicate with the turbulent flow simulation device 10, the system including an acquisition unit 11 that acquires simulation conditions, a simulation unit 12 that executes analysis of the fluid flow field using the large eddy simulation based on the acquired simulation conditions, and an output unit 13 that outputs the analysis results of the fluid flow field, and the simulation unit 12 performs a lattice analysis in the analysis of the fluid flow field. The turbulence simulation device 10 uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the Boltzmann equation as a correction term associated with coarse-graining in the large eddy simulation, and the correction term is a volume force calculated from the turbulence stress associated with the coarse-graining. The terminal device 20 is equipped with a second output unit (e.g., a communication unit 21) that outputs the simulation conditions, a second acquisition unit (e.g., the communication unit 21) that acquires analysis results for the simulation conditions output by the second output unit, and a control unit 23 that executes predetermined processing on the acquired analysis results.

[0142] (Invention 7) A turbulent flow simulation device 10 in the simulation system of Invention 6.

[0143] (Invention 8) The terminal device 20 in the simulation system of Invention 6.

[0144] These provide the same effects as the above-mentioned turbulent flow simulation method.

[0145] (Invention 9) A terminal device 20 includes a transmitting unit (e.g., a communication unit 21) that transmits input simulation conditions to a server (e.g., a simulation device 10) that analyzes a fluid flow field by large eddy simulation using a turbulence model that includes, based on the simulation conditions, an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a volume force calculated from turbulence stress associated with coarse graining in the large eddy simulation, and a presentation unit (e.g., a display unit 24) that presents the analysis results of the fluid flow field received from the server.

[0146] This provides the same effect as the above-mentioned turbulent flow simulation method.

[0147] (Invention 10) A design method for a fluid product that forms a flow path through which a fluid flows, the design method comprising: acquiring the analysis results output by the turbulent flow simulation method of any one of Inventions 1 to 5; and determining the structure of the fluid product based on the acquired analysis results (S110).

[0148] This allows the analysis results of the turbulence model to be reflected in the structure of the fluid product.

[0149] (Invention 11) A method for manufacturing a fluid product that forms a flow path through which a fluid flows, the method comprising: acquiring information indicating the structure of the fluid product determined by the design method described in Invention 10; and manufacturing the fluid product based on the acquired information (S120).

[0150] This makes it possible to manufacture a fluid product having a structure according to the analysis results of the turbulence model.

[0151] (Invention 12) A program for causing a computer to execute a turbulent flow simulation method for analyzing a fluid flow field using large eddy simulation, the turbulent flow simulation method including: acquiring simulation conditions; analyzing the fluid flow field using the large eddy simulation based on the acquired simulation conditions; and outputting analysis results of the fluid flow field; the analysis of the fluid flow field uses a turbulence model that includes an error term of the Navier-Stokes equations derived from the lattice Boltzmann equation as a correction term associated with coarse graining in the large eddy simulation; and the correction term is a volume force calculated from the turbulent stress associated with the coarse graining.

[0152] This provides the same effect as the above-mentioned turbulent flow simulation method.

[0153] The present invention may also be a program for causing a computer to execute any one of the turbulent flow simulation methods according to Inventions 1 to 5.

[0154] The design method of the present invention 10 may also be a program for causing a computer to execute the method.

[0155] These general or specific aspects may be realized as a system, a method, an integrated circuit, a computer program, or a non-transitory recording medium such as a computer-readable CD-ROM, or as any combination of the system, method, integrated circuit, computer program, or recording medium. The program may be pre-stored in the recording medium, or may be supplied to the recording medium via a wide area communication network including the Internet.

[0156] While the turbulent flow simulation method according to one or more aspects has been described above based on the embodiments, the present invention is not limited to these embodiments. As long as it does not deviate from the spirit of the present invention, various modifications conceivable by a person skilled in the art to the present embodiments and embodiments constructed by combining components of different embodiments may also be included in the present invention.

[0157] For example, although the embodiment above illustrates a case where the number of bases is 27, the number of bases is not limited to 27 and may be any number (for example, the number exemplified in the embodiment above). Furthermore, even if the number of bases is other than 27, the same effects as those described above can be achieved.

[0158] In the above embodiment, the expansion theory shown in Non-Patent Document 1 is calculated up to the fourth order for Δt (time width), but the calculation is not limited to the fourth order of Δt and may be performed up to any order. Similarly, the expansion theory shown in Non-Patent Document 1 is calculated up to the second order for Δ (mesh width), but the calculation is not limited to the second order of Δ and may be performed up to any order.

[0159] In the above embodiments, each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for each component. Each component may be realized by a program execution unit such as a CPU or processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.

[0160] The order in which the steps in the flowchart are executed is merely an example for specifically explaining the present invention, and other orders may be used. Some of the steps may be executed simultaneously (in parallel) with other steps, or some of the steps may not be executed.

[0161] The division of functional blocks in the block diagram is an example, and multiple functional blocks may be realized as a single functional block, one functional block may be divided into multiple blocks, or some functions may be moved to another functional block.Furthermore, the functions of multiple functional blocks having similar functions may be processed in parallel or in time-sharing by a single piece of hardware or software.

[0162] Furthermore, the simulation apparatus according to the above-described embodiments may be realized as a single apparatus or may be realized by multiple apparatuses. When the simulation apparatus is realized by multiple apparatuses, the components of the simulation apparatus may be distributed among the multiple apparatuses in any manner. When the simulation apparatus is realized by multiple apparatuses, the communication method between the multiple apparatuses is not particularly limited, and may be wireless communication or wired communication. Furthermore, wireless communication and wired communication may be combined between the apparatuses.

[0163] Furthermore, each component described in the above embodiments may be implemented as software or, typically, as an LSI, which is an integrated circuit. These components may be individually integrated into a single chip, or some or all of them may be integrated into a single chip. Here, the term "LSI" is used, but depending on the level of integration, it may also be referred to as an IC, system LSI, super LSI, or ultra LSI. Furthermore, the integrated circuit implementation method is not limited to LSI, and may be implemented using a dedicated circuit (a general-purpose circuit that executes a dedicated program) or a general-purpose processor. After LSI fabrication, a field programmable gate array (FPGA) that can be programmed or a reconfigurable processor that can reconfigure the connections or settings of circuit cells within the LSI may also be used. Furthermore, if an integrated circuit technology that replaces LSI emerges due to advances in semiconductor technology or a derivative technology, that technology may naturally be used to integrate the components.

[0164] A system LSI is an ultra-multifunctional LSI manufactured by integrating multiple processing units on a single chip. Specifically, it is a computer system that includes a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), etc. Computer programs are stored in the ROM. The system LSI achieves its functions when the microprocessor operates in accordance with the computer program.

[0165] Another aspect of the present invention may be a computer program that causes a computer to execute each of the characteristic steps included in the turbulent flow simulation method shown in FIG.

[0166] Furthermore, for example, the program may be a program to be executed by a computer. Another aspect of the present invention may be a computer-readable non-transitory recording medium on which such a program is recorded. For example, such a program may be recorded on a recording medium and distributed or circulated. For example, the distributed program may be installed in a device having another processor, and the program may be executed by the processor, thereby causing the device to perform each of the above processes.

[0167] The present invention is useful for a simulation device or the like that performs a simulation of a turbulent flow.

[0168] REFERENCE SIGNS LIST 1 Simulation system 10 Simulation device (turbulent flow simulation device) 11 Acquisition unit (first acquisition unit) 12 Simulation unit 13 Output unit (first output unit) 14, 25 Storage unit 20 Terminal device 21 Communication unit (second acquisition unit, second output unit, transmission unit) 22 Reception unit 23 Control unit 24 Display unit (presentation unit)

Claims

1. A method for simulating turbulent flow in which a computer analyzes a flow field of a fluid using large eddy simulation, the method comprising: obtaining simulation conditions; based on the obtained simulation conditions, performing analysis of the flow field of the fluid by the large eddy simulation; outputting an analysis result of the flow field of the fluid; in the analysis of the flow field of the fluid, using a turbulence model that includes an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation as a correction term associated with coarsening in the large eddy simulation, wherein the correction term is a body force calculated from a turbulent stress associated with the coarsening. A method for simulating turbulent flow.

2. The method for simulating turbulent flow according to claim 1, wherein the correction term includes a harmonic function of pressure.

3. The method for simulating turbulent flow according to claim 1 or 2, wherein the correction term is composed of only an isotropic tensor.

4. The method for simulating turbulent flow according to claim 1 or 2, wherein the error term does not include a fitting parameter.

5. When the spatial coordinate is x, the vector suffixes are α, β, γ, μ, the density is ρ, the velocity is u, the kinematic viscosity is ν, the spatial mesh width is Δ, and the pressure is p, the correction term is represented by the following formula 1 The method for simulating turbulent flow according to claim 1 or 2.

6. A turbulent flow simulation system comprising a turbulent flow simulation apparatus for analyzing a fluid flow field using large eddy simulation and a terminal device communicable with the turbulent flow simulation apparatus, wherein the turbulent flow simulation apparatus includes a first acquisition unit that acquires simulation conditions, a simulation unit that executes analysis of the fluid flow field by the large eddy simulation based on the acquired simulation conditions, and a first output unit that outputs the analysis result of the fluid flow field. The simulation unit uses a turbulence model that includes, in the analysis of the fluid flow field, an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation as a correction term associated with coarsening in the large eddy simulation. The correction term is a body force calculated from the turbulent stress associated with the coarsening. The terminal device includes a second output unit that outputs the simulation conditions, a second acquisition unit that acquires the analysis result for the simulation conditions output by the second output unit, and a control unit that executes a predetermined process on the acquired analysis result. A turbulent flow simulation system.

7. The turbulent flow simulation apparatus in the turbulent flow simulation system according to claim 6.

8. The terminal device in the turbulent flow simulation system according to claim 6.

9. A terminal device comprising a transmission unit that transmits input simulation conditions to a server that performs analysis of a fluid flow field by large eddy simulation using a turbulence model that includes, as a correction term, an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation based on the simulation conditions and is a body force calculated from turbulent stress associated with coarsening in the large eddy simulation, and a presentation unit that presents the analysis result of the fluid flow field received from the server.

10. A design method of a fluid product that forms a flow path through which a fluid flows, the method comprising: obtaining the analysis result output by the turbulent flow simulation method according to claim 1 or 2; and determining the structure of the fluid product based on the obtained analysis result.

11. A manufacturing method of a fluid product that forms a flow path through which a fluid flows, the method comprising: obtaining information indicating the structure of the fluid product determined by the design method according to claim 10; and manufacturing the fluid product based on the obtained information.

12. A program for causing a computer to execute a turbulent flow simulation method for analyzing a flow field of a fluid using large eddy simulation, the turbulent flow simulation method comprising: obtaining simulation conditions; based on the obtained simulation conditions, performing analysis of the flow field of the fluid by the large eddy simulation; and outputting an analysis result of the flow field of the fluid, wherein in the analysis of the flow field of the fluid, a turbulence model is used that includes an error term of the Navier-Stokes equation derived from the lattice Boltzmann equation as a correction term associated with coarsening in the large eddy simulation, and the correction term is a body force calculated from the turbulent stress associated with the coarsening.

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