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

Abstract

A simulation method of turbulent flow is a simulation method of turbulent flow in which a computer performs flow field analysis of a fluid using large eddy simulation, acquires simulation conditions (S10), performs the flow field analysis of the fluid by the large eddy simulation based on the acquired simulation conditions (S20), and outputs an analysis result of the flow field of the fluid (S30), and in the flow field analysis of the fluid, a turbulent flow model in which an error term of Navier-Stokes equations derived from lattice Boltzmann equations is included as a correction term accompanying coarsening in the large eddy simulation is used, and the correction term is a volume force calculated from turbulent stress accompanying the coarsening.

Description

Technical Field

[0001] This invention relates to methods for simulating turbulence, systems for simulating turbulence, devices for simulating turbulence, terminal devices, design methods, manufacturing methods, and procedures for turbulence simulation. Background Technology

[0002] In the past, numerical analysis of turbulent flow fields has been performed in the design and development of fluid equipment. As a method for analyzing turbulent flow fields, Large Eddy Simulation (LES) is known (for example, see Patent Document 1).

[0003] (Existing technical documents) (Patent Documents) Patent Document 1: Japanese Patent Application Publication No. 2003-141181 (Non-patent literature) Non-Patent Document 1: Keiichi Yamamoto, “NOVEL EXPANSION METHOD FOR DERIVINGTHE 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> Non-Patent Document 2: David J. Holdych, et al., "Truncation error analysis of lattice Boltzmann methods", [online], January 20, 2004, Journal of the Institute for Computational Physics, [retrieved October 31, 2023], Internet <https: / / www.sciencedirect.com / science / article / abs / pii / S0021999103004364> Non-patent literature 3: Y. Kuwata, et al., “Anomaly 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> Summary of the Invention

[0004] The problem that the invention aims to solve However, in the technology of Patent Document 1, there is room for improvement in simulation performance.

[0005] Therefore, the present invention provides a turbulence simulation method, a turbulence simulation device, and a program with improved simulation performance.

[0006] Methods for solving problems One aspect of the present invention relates to a turbulence simulation method in which a computer uses large eddy simulation (LES) to perform fluid flow field analysis. In this turbulence simulation method, simulation conditions are acquired, and based on these conditions, the fluid flow field analysis is performed using LES, outputting the analysis results. In the fluid flow field analysis, a turbulence model is used that includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying coarsening in the LES. These correction terms are body forces calculated based on the turbulent stresses accompanying the coarsening.

[0007] One aspect of the present invention relates to a turbulence simulation system comprising a turbulence simulation apparatus for analyzing the flow field of a fluid using large eddy simulation (LES), and a terminal device capable of communicating with the turbulence simulation apparatus. The turbulence simulation apparatus comprises: a first acquisition unit for acquiring simulation conditions; a simulation unit for performing flow field analysis of the fluid using LES based on the acquired simulation conditions; and a first output unit for outputting the analysis results of the flow field of the fluid. The simulation unit uses a turbulence model in the flow field analysis of the fluid, which includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying coarsening in the LES. The correction terms are volume forces calculated based on the turbulent stresses accompanying the coarsening. The terminal device comprises: a second output unit for outputting the simulation conditions; a second acquisition unit for acquiring the analysis results for the simulation conditions output by the second output unit; and a control unit for performing prescribed processing on the acquired analysis results.

[0008] One aspect of the present invention relates to a turbulence simulation device, which is the turbulence simulation device in the aforementioned turbulence simulation system.

[0009] One aspect of the present invention relates to a terminal device in the aforementioned turbulence simulation system.

[0010] One aspect of the present invention relates to a terminal device comprising: a transmitting unit for transmitting input simulation conditions to a server, the server performing a fluid flow field analysis based on the simulation conditions using a large eddy simulation (LES) model of turbulence, wherein the LES model includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms, the correction terms being volume forces calculated based on the turbulent stresses associated with coarsening in the LES model; and a prompting unit for prompting the analysis results of the fluid flow field received from the server.

[0011] One aspect of the present invention relates to a design method for forming a flow path for fluid to flow through, wherein the analysis results output by the above-mentioned turbulence simulation method are obtained, and the structure of the fluid product is determined based on the obtained analysis results.

[0012] One aspect of the present invention relates to a manufacturing method for forming a flow path through which a fluid flows, wherein information representing the structure of the fluid product determined by the above-described design method is obtained, and the fluid product is manufactured based on the obtained information.

[0013] One aspect of the present invention relates to a program for causing a computer to execute a turbulence simulation method, wherein the turbulence simulation method uses large eddy simulation (LES) to perform a fluid flow field analysis, the turbulence simulation method comprising: acquiring simulation conditions; performing a fluid flow field analysis by the LES based on the acquired simulation conditions; and outputting the analysis results of the fluid flow field. In the fluid flow field analysis, a turbulence model is used, which includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying coarsening in the LES, the correction terms being volume forces calculated based on the turbulent stresses accompanying the coarsening.

[0014] The effects of the invention According to one aspect of the present invention, a turbulence simulation method with improved simulation performance can be realized. Attached Figure Description

[0015] Figure 1 This is a block diagram illustrating the functional structure of the simulation device involved in the implementation method.

[0016] Figure 2 This is a flowchart illustrating the operation of the simulation device involved in the implementation method.

[0017] Figure 3 This is a graph showing the distribution of the coarsening correction terms derived from the rigorous numerical solutions involved in the comparative examples.

[0018] Figure 4 This is a graph showing the distribution of correction terms calculated using the Smagorinsky model involved in the prior art example.

[0019] Figure 5 This is a graph showing the distribution of the correction terms calculated using the model of this invention.

[0020] Figure 6 This is a flowchart illustrating a method for manufacturing a fluid product according to a manufacturing implementation method.

[0021] Figure 7 This is a diagram showing the structure of the simulation system involved in the implementation method.

[0022] Figure 8 This is a diagram representing the velocity model used to derive the turbulence model involved in the implementation method.

[0023] Figure 9 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0024] Figure 10 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0025] Figure 11 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0026] Figure 12 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0027] Figure 13 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0028] Figure 14 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0029] Figure 15 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0030] Figure 16 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0031] Figure 17 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0032] Figure 18 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0033] Figure 19 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0034] Figure 20 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0035] Figure 21 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0036] Figure 22 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0037] Figure 23 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0038] Figure 24 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0039] Figure 25 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0040] Figure 26 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0041] Figure 27This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0042] Figure 28 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0043] Figure 29 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0044] Figure 30 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0045] Figure 31 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0046] Figure 32 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0047] Figure 33 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0048] Figure 34 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0049] Figure 35 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0050] Figure 36 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0051] Figure 37 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0052] Figure 38 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method.

[0053] Figure 39 This is a diagram illustrating a derived example of the turbulence model involved in the implementation method. Detailed Implementation

[0054] (How the present invention was obtained) Before describing the present invention, the process by which the present invention was obtained will be explained.

[0055] A turbulence model (turbulent stress model) is a coarsening-complementary correction model used to determine the values ​​of velocity (u) and pressure (p) of a fluid in coarsened space and time. In a turbulence model, space is partitioned with a coarse mesh to reduce computational cost, but the computational space is not performed through the coarse mesh. Instead, the effects of small-scale turbulence that the mesh cannot resolve are represented as correction terms. That is, the turbulence model includes correction terms. Furthermore, small-scale turbulence refers to stresses (turbulent stresses) generated, for example, by small eddies (also known as eddy eddies) that cannot be captured by the mesh width.

[0056] As a turbulence model, the Smagorinsky model, which is also described in Patent Document 1, is mostly used. The Smagorinsky model is a standard turbulence model included in general fluid analysis software. When time is set to t, spatial coordinates are set to x, vector suffixes are set to α, β, γ, μ, density is set to ρ, velocity is set to u, kinematic viscosity is set to ν, spatial grid width (computation grid width) is set to Δ, pressure is set to p, and Smagorinsky parameters are set to C, the Smagorinsky model is as shown in Equation 1 below.

[0057] [Mathematical Expression 1] (Equation 1) Furthermore, the vector suffixes α, β, γ, and μ represent the vector components of x, y, and z, respectively. Additionally, the following term in Equation 1 (Equation 2) is a correction term in the Smagorinsky model.

[0058] [Mathematical Expression 2] (Equation 2) As shown in Equation 2, the Smagorinsky model includes the Smagorinsky parameter C (also known as the Smagorinsky constant), which is an empirically fitted parameter determined for each flow field. Furthermore, the correction terms of the Smagorinsky model are defined only by the velocity field.

[0059] The following issues exist in the Smagorinsky model described above.

[0060] (Topic 1) Since the Smagorinsky model includes the Smagorinsky parameter C, it is necessary to set the Smagorinsky parameter C according to the flow field. In addition, the Smagorinsky parameter C can be a constant or a function of time and space. Even in the same flow field, the optimal value of C may be different due to the position of the fluid flowing in the pipe (e.g., the middle and the end of the pipe), which makes it difficult to use.

[0061] (Project 2) When comparing the Smagorinsky model with rigorous numerical solutions that require huge computational costs, it is known that the local correlation coefficients of the two are low. In the Smagorinsky model, it is difficult to coarsen the mesh significantly.

[0062] (Topic 3) It is known that in the Smagorinsky model, the global reproduction accuracy of turbulent stress caused by large, medium and small eddies and accompanied by coarsening is not very high, making it difficult to coarsen the mesh significantly.

[0063] As mentioned above, various challenges exist in turbulence simulations using the Smagorinsky model. Specifically, there is room for improvement in the simulation performance using the Smagorinsky model.

[0064] Therefore, the inventors of this application have conducted in-depth research on turbulence simulation methods for solving the aforementioned problems, and have conceived the turbulence simulation method described below. Details will be described later, but the key point is that the inventors of this application discovered that the error term of the Navier-Stokes equations derived from the lattice Boltzmann equations can be used as a correction term accompanying the coarsening in large eddy simulation analysis, and conceived a turbulence simulation method using a turbulence model incorporating this error term. Furthermore, improving any of the above-mentioned problems (1) to (3) is an example of improved simulation performance. Moreover, the correction term is a volume force calculated based on the turbulent stress accompanying the coarsening.

[0065] The embodiments will now be described in detail with reference to the accompanying drawings.

[0066] Furthermore, the embodiments described below are all general or specific examples. The numerical values, shapes, constituent elements, arrangement and connection patterns of constituent elements, steps, and order of steps shown in the following embodiments are merely examples and are not intended to limit the present invention. Moreover, in the constituent elements of the following embodiments, constituent elements not described in the independent technical solutions are described as arbitrary constituent elements.

[0067] Furthermore, all figures are schematic diagrams and not necessarily strict illustrations. Therefore, for example, the scale may not be consistent across different figures. In addition, substantially identical structures are given the same reference numerals across different figures, and repetitive descriptions are omitted or simplified.

[0068] Furthermore, in this specification, terms indicating relationships between elements such as consistency, as well as numerical values ​​and ranges, are not merely expressions with a strict meaning, but also include substantially equivalent ranges, such as expressions containing a difference of about a few percent (or about 10%).

[0069] (Implementation Method) The following is for reference Figures 1 to 39 The simulation device involved in this embodiment will be described.

[0070] [1. Structure of the simulation device] First, refer to Figure 1 The structure of the simulation device involved in this embodiment will be described. Figure 1 This is a block diagram illustrating the functional structure of the simulation device 10 according to this embodiment. The simulation device 10 is an information processing device that performs a turbulence simulation method for analyzing the flow field of a fluid using large eddy simulation. The simulation device 10 is an example of a turbulence simulation device.

[0071] The analog device 10 is implemented, for example, by a computer, which includes: a communication interface for communicating with other devices such as input devices and prompting devices; non-volatile memory for storing programs executed by each processing unit; volatile memory serving as a temporary storage area for executing programs; input / output ports for sending and receiving signals; and a processor for executing programs. The communication interface can be implemented by a connector with a communication line for wired communication, or by a wireless communication circuit for wireless communication. For example, the analog device 10 can also be implemented by a server.

[0072] like Figure 1 As shown, the simulation device 10 includes an acquisition unit 11, an simulation unit 12, an output unit 13, and a storage unit 14.

[0073] The acquisition unit 11 obtains data from the input device (e.g., described later). Figure 7 The terminal device 20 shown acquires input information containing simulation conditions used for simulation. The simulation conditions include information about the pipe through which the fluid flows, information about the grid, information about the fluid, etc. The acquisition unit 11 is, for example, a communication interface used by the simulation device 10 to communicate with other devices. The acquisition unit 11 is configured, for example, to include a communication circuit (communication module). The acquisition unit 11 is an example of a first acquisition unit. Furthermore, input devices may include, for example, buttons, keyboards, microphones, terminal devices, etc., but are not limited to these.

[0074] The simulation unit 12 performs turbulent flow field analysis using large eddy simulation (LES) based on the simulation conditions acquired by the acquisition unit 11. In LES, the influence of eddies below the filter scale is modeled, while eddies larger than the filter scale are calculated directly.

[0075] In the flow field analysis of the fluid, the simulation unit 12 uses a turbulence model that incorporates error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms. When time is set to t, spatial coordinates (position) to x, vector suffixes to α, β, γ, μ, density to ρ, velocity to u, kinematic viscosity to ν, spatial grid width (computation grid width) to Δ, and pressure to p, an example of the turbulence model involved in one aspect of the present invention is shown in Equation 3. Furthermore, the derivation of Equation 3 will be described later.

[0076] [Mathematical Expression 3] (Equation 3) Furthermore, the following term (Equation 4) in Equation 1 is a correction term in the turbulence model involved in one aspect of the present invention. That is, Equation 4 is a term representing the turbulent stress caused by the coarsening of the mesh width Δ in the large eddy simulation analysis.

[0077] [Mathematical Expression 4] (Equation 4) As shown in Equation 4, the correction term of the turbulence model involved in one aspect of the present invention does not include fitting parameters such as the Smagorinsky parameter C. Therefore, since the user does not need to input fitting parameters, the ease of use is improved according to the simulation device 10. Furthermore, the correction term consists only of isotropic tensors.

[0078] Furthermore, as shown in Equation 4, the correction term includes pressure (p). Specifically, the correction term includes a harmonic function of pressure. Since pressure propagates faster than velocity, and it is assumed that the turbulent field is formed before velocity through the propagation of pressure (pressure wave), including pressure in the correction term makes it easier to reflect the situation globally. That is, including pressure in the correction term improves the global reproduction accuracy of the turbulence model. In addition, in the previously used Smagorinsky model, since the correction term is only defined by the velocity field, it is considered difficult to improve the global reproduction accuracy.

[0079] Output unit 13 outputs the simulation results of simulation unit 12 to a prompting device (e.g., described later). Figure 7 The terminal device 20 shown above, etc. The simulation results include the flow field simulation results using Equation 3 above. The output unit 13 is, for example, a communication interface used by the simulation device 10 to communicate with other devices. The output unit 13 is configured to include, for example, a communication circuit (communication module). In addition, the prompting device is, for example, a liquid crystal display device, etc., but is not limited to this. The output unit 13 is an example of the first output unit, and the simulation results are an example of the analysis results.

[0080] Storage unit 14 is a storage device that stores various information for simulation unit 12 to perform simulations. Storage unit 14 stores, for example, a turbulence model used for simulation. In this embodiment, storage unit 14 stores the above-described formula 3. Storage unit 14 is implemented, for example, by a hard disk drive (HDD) or a semiconductor memory.

[0081] [2. Operation of the simulation device] Next, refer to Figure 2 To explain the operation of the simulation device 10 constructed in the above manner. Figure 2 This is a flowchart illustrating the operation (turbulence simulation method) of the simulation device 10 involved in this embodiment. Figure 2 This refers to a simulation method for analyzing the flow field of fluids using large eddy simulation by a computer.

[0082] like Figure 2 As shown, the acquisition unit 11 acquires input information from the input device or the like (S10). The input information includes simulation conditions for performing a simulation using a turbulence model, but these simulation conditions do not include information about the fitting parameters.

[0083] Next, the simulation unit 12 performs a large eddy simulation (S20) using a turbulence model that includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms. In this embodiment, the simulation unit 12 reads the turbulence model shown in Equation 3 from the storage unit 14 and uses the read turbulence model to perform a large eddy simulation.

[0084] Next, the output unit 13 outputs the simulation results from the simulation unit 12 to a prompting device or the like (S30). Thus, the output unit 13 can prompt the user with the simulation results. For example, the simulation results can be displayed to the user as an image. Furthermore, the simulation results can also be stored in the storage unit 14.

[0085] [3. Verification of simulation results] Next, refer to Figures 3-5 The verification results (a priori test results) of the turbulence model of the simulation device 10 constructed in the above manner will be explained. Figure 3 This is a graph showing the distribution of the coarsening correction terms (body forces calculated from turbulent stress) derived from the rigorous numerical solutions involved in the comparative examples (correct data). Figures 3-5 The distribution of the correction terms shown represents the stress distribution at a specific cross-section of a flow field at a specific instant. Furthermore, Figures 3-5 The coarsening ratios are the same.

[0086] Furthermore, a rigorous numerical solution refers to the solution obtained by directly solving (direct numerical simulation: DNS) the fundamental equations of fluid dynamics (Navier-Stokes equations) without modeling them. Figure 3 The results of this rigorous numerical solution were observed under a coarse mesh with a coarsening factor of 125.

[0087] Figure 3 In other words, it represents the correct data on the volume force distribution that must be modified for each mesh during coarsening, according to the Navier-Stokes equations. This correct data is obtained from rigorous calculations and therefore includes the effects of small eddies that the mesh cannot capture.

[0088] In addition, rigorous numerical solutions were obtained using numerical solutions from a publicly available database (URL: http: / / turbulence.pha.jhu.edu / Forced_isotropic_turbulence.aspx).

[0089] Figure 4 It is a graph showing the distribution of the correction terms (body forces calculated from turbulent stress) calculated using the Smagorinsky model (turbulence model shown in Equation 1) involved in the prior art example. Figure 5 This is a graph showing the distribution of correction terms (body forces calculated from turbulent stress) calculated using the model of the present invention (the turbulence model shown in Equation 3).

[0090] like Figures 3-5 As shown, Figure 5 The distribution ratio shown Figure 4 The distribution shown is closer to Figure 3 The distribution shown. According to one aspect of the turbulence model of the invention, the improved accuracy of the correction term distribution can be confirmed even at a visual level. Furthermore, Figure 3 The distribution shown is Figure 4 The correlation coefficient between the distributions shown is 0.2, while Figure 3 The distribution shown is Figure 5 The correlation coefficient between the distributions shown is 0.48. The correlation coefficient indicates the degree of agreement with the correct data.

[0091] As described above, the turbulence model according to one aspect of the present invention significantly improves the correlation coefficient with accurate data compared to the Smagorinsky model. This means that the correction terms of the turbulence model according to one aspect of the present invention can more accurately calculate the stress (turbulent stress) generated by small eddies (also called eddies) that cannot be captured by the grid width. Thus, from the viewpoint of the accuracy of the simulation results, the simulation performance can be improved according to the simulation apparatus 10.

[0092] Furthermore, in the Smagorinsky model, the form of the model is limited to differential operations of eddy viscosity, resulting in a low degree of freedom for representing complex turbulent phenomena. Therefore, the correlation coefficient is considered to be low as described above. However, the turbulence model involved in one aspect of the present invention, since its form is not limited to differential operations of eddy viscosity, has a higher degree of freedom than the Smagorinsky model, and the correlation coefficient is considered to be higher than that of the Smagorinsky model as described above.

[0093] Furthermore, the correlation coefficients mentioned above are based on a basis of 27 (see below). Figure 8 The value at which the correlation coefficient is calculated is given. Using a turbulence model derived by increasing the number of substrates, it is assumed that the correlation coefficient will further improve.

[0094] [4. Manufacturing method] Next, refer to Figure 6 The manufacturing method of fluid products using the above simulation method will be described. Figure 6 This is a flowchart illustrating a method for manufacturing the fluid product according to this embodiment. The fluid product is a product having a flow path through which fluid flows; examples include, for instance, piping through which fluid flows, but it is not limited to these. The fluid product can be used, for example, in cleaning devices, cooling devices, etc.

[0095] like Figure 6 As shown, the manufacturing method includes the execution of the design steps (S110) and the execution of subsequent manufacturing steps (S120).

[0096] In the design phase, the analysis results of the fluid flow field obtained through the simulation methods described above are used to design the structure of the fluid product. The structure includes the shape and dimensions of the fluid product. For example, the analysis results are used to determine the structure of the fluid product that can achieve the desired flow field.

[0097] Next, in the manufacturing step, the fluid product designed in the design step is actually manufactured. In the manufacturing step, processing and assembly are performed to form the fluid product.

[0098] Furthermore, each step in the manufacturing method can also be implemented as a separate step (method). For example, step S110 can be implemented as a design method for forming a fluid product with a flow path through which fluid flows. Furthermore, step S120 can be implemented as a manufacturing method for acquiring information representing the structure of the fluid product determined by the design method and manufacturing the fluid product based on the acquired information.

[0099] [5. The Structure of the Simulation System] Next, refer to Figure 7 The simulation system equipped with the simulation device 10 according to this embodiment will be described. Figure 7 This is a diagram showing the configuration of the simulation system 1 according to this embodiment.

[0100] like Figure 7 As shown, the simulation system 1 includes the simulation device 10 described above, and a terminal device 20 capable of communicating with the simulation device 10. The simulation device 10 and the terminal device 20 can be configured in one facility or separately (e.g., in different facilities). Furthermore, when the simulation device 10 and the terminal device 20 are configured separately, they can be configured in the same country or region or in different countries or regions.

[0101] Terminal device 20, for example, is a device that has installed application software for performing turbulence simulations to analyze the flow field of a fluid. It outputs received simulation conditions to simulation device 10 and obtains analysis results from simulation device 10 for those simulation conditions. Terminal device 20, for example, has the function of enabling simulation device 10 to perform fluid flow field analysis remotely.

[0102] The terminal device 20 includes a communication unit 21, a receiving unit 22, a control unit 23, a display unit 24, and a storage unit 25. The terminal device 20 can be a fixed device such as a PC (Personal Computer) or a portable device such as a tablet terminal.

[0103] The communication unit 21 is a communication interface for communication between the terminal device 20 and the analog device 10. The communication unit 21 is configured, for example, to include a communication circuit (communication module). The communication unit 21 functions as a second output unit and a transmission unit that outputs (transmits) analog conditions to the analog device 10. Furthermore, the communication unit 21 functions as a second acquisition unit that acquires (receives) the analysis results of the analog conditions output by the communication unit 21.

[0104] Furthermore, the simulation conditions may include information indicating the use of the turbulence model involved in this embodiment (i.e., a turbulence model that includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying coarsening in large eddy simulations). Additionally, communication between the terminal device 20 and the simulation device 10 can be wired or wireless.

[0105] The receiving unit 22 receives operations from the user. For example, the receiving unit 22 receives input of simulation conditions from the user. Furthermore, the receiving unit 22 may also receive a selection to use the turbulence model involved in this embodiment for simulation. The receiving unit 22 may be implemented, for example, via a button, keyboard, touch panel, etc., but may also be a device for receiving input such as voice.

[0106] The control unit 23 is a control device for each component of the control terminal device 20. After acquiring the analysis results from the analog device 10 via the communication unit 21, the control unit 23 performs predetermined processing on the acquired analysis results. The predetermined processing may be processing that causes the display unit 24 to display the analysis results, processing that causes the storage unit 25 to store the analysis results, or other processing related to the analysis results.

[0107] Display unit 24 is a display device for displaying information to the user. For example, display unit 24 displays the analysis results of simulation device 10. Furthermore, when receiving input of simulation conditions, display unit 24 can display information indicating that the simulation was performed using the turbulence model involved in this embodiment, or information indicating that a turbulence model has been selected. Furthermore, when displaying analysis results, display unit 24 can display information indicating that the analysis results were performed using the turbulence model involved in this embodiment. Display unit 24 is implemented, for example, using a liquid crystal display (LCD). Display unit 24 is an example of a prompting unit. Furthermore, the prompting unit can also prompt the analysis results via voice or the like.

[0108] The storage unit 25 stores information related to the simulation in the simulation device 10. The storage unit 25 may, for example, store the application software described above. Furthermore, the storage unit 25 may also store analysis results obtained from the simulation device 10. These analysis results may, for example, be stored corresponding to the simulation conditions. The storage unit 25 may be implemented, for example, using an HDD or a semiconductor memory.

[0109] In addition, the terminal device 20 may also be a device with application software installed for designing fluid products.

[0110] Furthermore, in the simulation system 1, the simulation device 10 and the terminal device 20 can each be implemented as separate devices.

[0111] [6. Derivation of the turbulence model] Next, refer to Figures 8 to 39The derivation of the turbulence model used in simulation device 10 is explained. Figure 8 This is a diagram showing the velocity model used to derive the turbulence model involved in this embodiment.

[0112] First, one aspect of this invention involves a turbulence model based on molecular fluid dynamics, which treats fluid motion as molecular motion. Specifically, the turbulence model is derived using the lattice Boltzmann equations. The lattice Boltzmann equations are equations describing molecular behavior (flow field). Because the lattice Boltzmann equations can also be viewed as discretized Boltzmann equations, they are considered to have a wider applicability than the Navier-Stokes equations.

[0113] Furthermore, the lattice Boltzmann method is a computational approach that confines countless random molecular motions to a finite velocity basis and describes fluid motion through an analogy to the Boltzmann equations. The lattice Boltzmann equations approximate the fluid as a collection of multiple virtual particles with a finite number of velocities (lattice gas model), successively calculating the collisions and translations of each particle using the particle velocity distribution function, and then calculating the macroscopic flow field from the sum of their moments.

[0114] In this embodiment, such as Figure 8 As shown, a three-dimensional 27-velocity (D3Q27) model is used as the velocity model. In this case, the particle's motion is restricted to 27 directions by this lattice. That is, a model with 27 basis points is used. However, the number of basis points is not limited to 27; it can be less than 27 or more than 27. Commonly used number of basis points include 9, 15, 19, 39, 40, 41, 48, 49, 72, etc., but other numbers are also possible.

[0115] When the time is set to t, the position to x, the particle velocity (e.g., average velocity) to c, the time step to δt, and the direction to i, the lattice Boltzmann equation is expressed by the following equation 5.

[0116] [Mathematical Expression 5] (Equation 5) Furthermore, fi(x, t) represents the distribution function of a particle with a velocity in the i-direction at time t and position x.

[0117] Even with the same flow, the lattice Boltzmann equation exhibits different patterns depending on the observation timescale. Therefore, this timescale is used as a variable to perform a Taylor expansion of the lattice Boltzmann equation (refer to the expansion theory described in Non-Patent Document 1). Furthermore, known expansion theories for the lattice Boltzmann equation include the Chapmann-Enskog theory and Sone's asymptotic S-expansion, but these theories cannot estimate the error term and therefore cannot be used in this derivation.

[0118] Expanding Equation 5 based on the expansion theory described in Non-Patent Document 1, we obtain Equation 6. Furthermore, we set time as t, position as x, velocity as u, vector suffixes as α, β, γ, μ, and p as pressure. Here, terms up to the square of the grid width Δ are used.

[0119] [Mathematical Expression 6] (Equation 6) Furthermore, ρ and μ are represented by Equations 7 and 8 below.

[0120] [Mathematical Expression 7] (Equation 7) Furthermore, fi is set as the velocity distribution function in the i-direction.

[0121] [Mathematical Expression 8] (Equation 8) In addition, setting δt as the time step, Set as the relaxation parameter. Additionally, c ｓ Defined by the following equation 9.

[0122] [Mathematical Expression 9] (Equation 9) In addition, c is the velocity of the particle.

[0123] This method is more of a physical expansion method than a mathematical one.

[0124] Here, as mentioned above, when deriving the Navier-Stokes equations from the lattice Boltzmann equations, error terms based on the grid width Δ are generated (e.g., error terms of the 4th, 6th, etc., power of the grid width Δ). In the case of Equation 3, the terms shown in Equation 4 are error terms.

[0125] Previously, this error term was considered a truncation error. However, the inventors of this application believe that if the expansion theory has physical meaning like Non-Patent Document 1, then the error term (Equation 4) obtained from the lattice Boltzmann equation, which has a wide applicability, should also have physical meaning. Specifically, the inventors of this application believe that this error term has a greater impact at low grid resolution, that is, it describes the effect of fine flows that the grid cannot resolve. In other words, the inventors of this application believe that the error term shown in Equation 4 is the turbulent stress itself (i.e., the correction term for turbulent stress).

[0126] The inventors of this application calculated the expansion theory shown in Non-Patent Document 1 to a higher order. For example, by calculating the expansion theory to order 4 (the fourth order of Δt (time width)), the above Equation 3 was derived. Furthermore, the calculation is not limited to order 4 and can be of any order. Moreover, in cases where the expansion is beyond order 4, the modification terms in Equation 3 may differ from those in Equation 4.

[0127] Furthermore, as shown in the above derivation method, since the turbulence model is derived from the lattice Boltzmann equation, the formulation shown in Equation 3, which includes pressure p but does not include fitting parameters, has been successfully realized.

[0128] Furthermore, in the error terms of higher-order expansions, terms that violate the spatial isotropy of the tensor are removed as inherent errors, and the remaining parts are used as correction terms (e.g., Equation 4). Terms that violate spatial isotropy are terms of non-isotropic tensors. That is, correction terms consist only of isotropic tensors.

[0129] Furthermore, the method for deriving turbulence models from the lattice Boltzmann equations is not limited to the expansion theory of Non-Patent Document 1; for example, the expansion theory of Non-Patent Document 2 can also be used. The expansion theory of Non-Patent Document 2 is mathematical and differs from the physical viewpoint expansion theory of Non-Patent Document 1 in its approach and assumptions, but including error terms, its calculation results are completely consistent with those of Non-Patent Document 1.

[0130] Furthermore, as shown in Non-Patent Document 3, the error terms represented by Equation 4 are generally treated as inherent errors. That is, the inventor's concept that "the error terms represented by Equation 4 represent correction terms accompanying coarsening" is itself a novel concept not found in the prior art.

[0131] In addition, refer to Figures 9 to 39 The derivation of the turbulence model (Equation 3) involved in this embodiment will be explained. Figures 9 to 39 This is a diagram illustrating a derived example of the turbulence model (turbulence stress) involved in this embodiment.

[0132] Figure 9 This represents the expansion of both sides of the lattice Boltzmann equation.

[0133] Figure 10 This represents the recurrence relation derived from the uniqueness of the Taylor expansion.

[0134] Figure 11 This indicates an expression that uses lower-order terms to describe higher-order terms.

[0135] Figure 12 This represents the expression describing terms up to the fourth order using the equilibrium distribution function.

[0136] Figure 13 This represents the expression describing terms up to the 5th order using the equilibrium distribution function.

[0137] Figure 14 and Figure 15 This represents the expression that describes the lattice Boltzmann equation using the equilibrium distribution function.

[0138] Figure 16 This represents the expression for the equilibrium distribution function.

[0139] Figure 17 This represents the expression for substituting the equilibrium distribution function into the lattice Boltzmann equation and performing calculations.

[0140] Figure 18 Indicates to Figure 17 The right side of the character has been modified.

[0141] Figure 19 Indicates to Figure 18 The right side of the character has been modified.

[0142] Figure 20 Indicates to Figure 19 The right side of the character has been modified.

[0143] Figure 21 This is represented using Kronecker notation. Figure 20 The formula for tensors up to order 4 on the right.

[0144] Figure 22 Indicates to Figure 21 The right side of the character has been modified.

[0145] Figure 23 This indicates the use of Euler's law to... Figure 22 The right side of the character has been modified.

[0146] Figure 24 Indicates to Figure 23 The right side of the character has been modified.

[0147] Figure 25 Indicates to Figure 24 The right side of the character has been modified.

[0148] Figure 26 It means Figure 25The expression for calculating the 6th-order tensor in the 6th term on the right-hand side, specifically, represents the... Figure 32 Substitute the result into the expression of the 6th tensor of the 6th term on the right.

[0149] Figure 27 Indicates will Figure 26 Substitute the right side Figure 25 The expression for the 6th term of the right-hand side is shown.

[0150] Figure 28 Indicates to Figure 27 The right side of the character has been modified.

[0151] Figure 29 Indicates to Figure 28 The right side of the character has been modified.

[0152] Figure 30 (a) indicates that Figure 37 Substitute the result Figure 29 The final term on the right side of the expression.

[0153] Figure 30 (b) is from Figure 30 In equation (a), remove the two terms derived from the non-isotropic tensor and arrange the terms horizontally in a row. Figure 30 The first and second terms on the left side of (b) can be obtained from the Navier-Stokes equations, thus completing the derivation.

[0154] Figure 31 Yes Figure 30 The transformed form of (b) corresponds to equation 3 above. Furthermore, in Figure 31 In the diagram, two terms derived from the non-isotropic tensor are also illustrated for reference.

[0155] Figures 32-36 Indicates that it is used for exporting. Figure 31 The calculation of the relationship shown.

[0156] Figure 38 and Figure 39 Indicates that it is used for exporting. Figure 37 The calculation of the relationship shown.

[0157] [7. Effects, etc.] The invention derived from the disclosure in this specification and the effects obtained by the invention will be described below.

[0158] (Invention 1) A turbulence simulation method for analyzing the flow field of a fluid using large eddy simulation by a computer, wherein simulation conditions are obtained (S10), and flow field analysis of the fluid is performed by the large eddy simulation based on the obtained simulation conditions (S20), and the analysis results of the flow field of the fluid are output (S30). In the flow field analysis of the fluid, the error term of the Navier-Stokes equation derived from the lattice Boltzmann equation is used as a correction term for coarsening in the large eddy simulation and is included in the turbulence model. The correction term is the volume force calculated based on the turbulent stress accompanying the coarsening.

[0159] Accordingly, by using a turbulence model that incorporates error terms, which can be considered as expressions of turbulent stress itself, as correction terms, turbulent stress can be calculated more accurately, thereby improving the accuracy of the analysis results in the turbulence model. That is, simulation performance is improved in terms of the increased accuracy of the analysis results (simulation results). Furthermore, this can, for example, improve upon the aforementioned (Project 2).

[0160] (Invention 2) A turbulence simulation method based on Invention 1, wherein the correction term includes a harmonic function of pressure.

[0161] Therefore, since the pressure, which has a greater propagation speed and is more likely to reflect the global situation, is included in the turbulence model, the global reproduction accuracy of turbulent stress occurrence can be improved compared to the Smagorinsky model, which only includes the velocity field. This helps to make the mesh coarser, i.e., improve the computational speed. In other words, simulation performance is improved in terms of improving computational speed. Furthermore, for example, this can improve the above (Project 3).

[0162] (Invention 3) A turbulence simulation method based on Invention 1 or 2, wherein the correction term consists only of isotropic tensors.

[0163] Therefore, since the anisotropic tensor, which is an inherent error, is not included in the correction term, the accuracy of the analysis results is improved. That is, the simulation performance is improved in terms of the improved accuracy of the analysis results.

[0164] (Invention 4) A turbulence simulation method based on any one of Inventions 1 to 3, wherein the error term does not include fitting parameters.

[0165] Accordingly, the ease of use of the simulation method is improved because there is no need to set fitting parameters. Furthermore, this can, for example, improve upon the aforementioned (Project 1).

[0166] (Invention 5) A turbulence simulation method based on any one of Inventions 1 to 4, wherein when the spatial coordinates are set as x, the vector suffixes are set as α, β, γ, μ, the density is set as ρ, the velocity is set as u, the kinematic viscosity is set as ν, the spatial grid width is set as Δ, and the pressure is set as p, the correction term is represented by the following Equation 1. [Mathematical Expression 1] (Equation 1).

[0167] Accordingly, the accuracy of the simulation results is further improved by using the 4th order (4th order of Δt (time width)) correction term calculated by the expansion theory of non-patent literature 1, etc.

[0168] (Invention 6) A turbulence simulation system 1 includes a turbulence simulation device 10 for analyzing fluid flow field using large eddy simulation (LES), and a terminal device 20 capable of communicating with the turbulence simulation device 10. The turbulence simulation device 10 includes: an acquisition unit 11 for acquiring simulation conditions; a simulation unit 12 for performing flow field analysis of the fluid using LES based on the acquired simulation conditions; and an output unit 13 for outputting the analysis results of the fluid flow field. The simulation unit 12 uses LES from lattice Boltzmann... The error terms of the Navier-Stokes equations derived from the equations are included in the turbulence model as correction terms accompanying the coarsening in the large eddy simulation. These correction terms are volume forces calculated based on the turbulent stresses accompanying the coarsening. The terminal device 20 includes: a second output unit (e.g., a communication unit 21) that outputs the simulation conditions; a second acquisition unit (e.g., a communication unit 21) that acquires analysis results for the simulation conditions output by the second output unit; and a control unit 23 that performs prescribed processing on the acquired analysis results. It is a turbulence simulation device 10.

[0169] (Invention 7) is a turbulence simulation device 10 in the simulation system of Invention 6.

[0170] (Invention 8) is the terminal device 20 in the simulation system of Invention 6.

[0171] Therefore, the same effect as the above-mentioned turbulence simulation method can be obtained.

[0172] (Invention 9) A terminal device 20 includes: a transmitting unit (e.g., a communication unit 21) for transmitting input simulation conditions to a server (e.g., a simulation device 10), which performs a fluid flow field analysis based on the simulation conditions using a large eddy simulation of a turbulence model, wherein the turbulence model includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms, the correction terms being volume forces calculated based on the turbulent stresses associated with coarsening in the large eddy simulation; and a prompting unit (e.g., a display unit 24) for prompting the analysis results of the fluid flow field received from the server.

[0173] Therefore, the same effect as the turbulence simulation method described above can be achieved.

[0174] (Invention 10) A design method for a fluid product that forms a flow path through which a fluid flows, wherein the analysis results output by a turbulence simulation method of any one of Inventions 1 to 5 are obtained, and the structure of the fluid product is determined based on the obtained analysis results (S110).

[0175] Therefore, the analysis results of the turbulence model can be reflected in the structure of fluid products.

[0176] (Invention 11) A method for manufacturing a fluid product that forms a flow path through which a fluid flows, wherein information representing the structure of the fluid product determined by the design method described in Invention 10 is obtained, and the fluid product is manufactured based on the obtained information (S120).

[0177] Therefore, it is possible to manufacture fluid products with structures that correspond to the analysis results of turbulence models.

[0178] (Invention 12) A program for enabling a computer to perform a turbulence simulation method for analyzing the flow field of a fluid using large eddy simulation, the turbulence simulation method comprising: acquiring simulation conditions; performing a flow field analysis of the fluid using the large eddy simulation based on the acquired simulation conditions; and outputting the analysis results of the flow field of the fluid, wherein in the analysis of the flow field, an error term of the Navier-Stokes equations derived from the lattice Boltzmann equations is included in the turbulence model as a correction term accompanying coarsening in the large eddy simulation, the correction term being a volume force calculated based on the turbulent stress accompanying the coarsening.

[0179] Therefore, the same effect as the turbulence simulation method described above can be achieved.

[0180] Alternatively, it can be a program used to enable a computer to perform the turbulence simulation method of any one of inventions 1 to 5.

[0181] Alternatively, it can be a program used to enable a computer to execute the design method of invention 10.

[0182] Furthermore, these general or specific methods can be implemented using non-transitory recording media such as systems, methods, integrated circuits, computer programs, or computer-readable CD-ROMs, or any combination of systems, methods, integrated circuits, computer programs, or recording media. The program can be pre-stored on the recording medium or provided to the recording medium via wide area communication networks, including the Internet.

[0183] (Other implementation methods) The above description illustrates one or more methods for simulating turbulence based on various embodiments, but the present invention is not limited to these embodiments. Various modifications to these embodiments and combinations of constituent elements from different embodiments that can be conceived by those skilled in the art without departing from the spirit of the invention are all included in the present invention.

[0184] For example, in the above embodiment, the case where the number of substrates is 27 is illustrated, but the number of substrates is not limited to 27 and can be any value (for example, the value illustrated in the above embodiment). Furthermore, even if the number of substrates is not 27, the same effect as shown above can be obtained.

[0185] Furthermore, in the above embodiments, an example is shown where the expansion theory shown in Non-Patent Document 1 is calculated to order 4 for Δt (time width), but the calculation is not limited to order 4 for Δt, and can be of any order. Similarly, regarding Δ (mesh width), an example is shown where it is calculated to order 2, but the calculation is not limited to order 2 for Δ, and can be of any order.

[0186] Furthermore, in the above embodiments, each component can be constructed by dedicated hardware or implemented by executing software programs suitable for each component. Each component can also be implemented by a program execution unit such as a CPU or processor reading and executing software programs recorded on a recording medium such as a hard disk or semiconductor memory.

[0187] Furthermore, the execution order of the steps in the flowchart is illustrative for the purpose of explaining the present invention, and may also be in a different order than described above. Additionally, some of the above steps may be executed simultaneously (in parallel) with other steps, or some of the above steps may not be executed.

[0188] Furthermore, the division of functional blocks in the block diagram is one example. Multiple functional blocks can be implemented as a single functional block, or a single functional block can be divided into multiple functional blocks, or some functions can be moved to other functional blocks. In addition, the functions of multiple functional blocks with similar functions can also be processed in parallel or in time-division multiplexed by a single hardware or software.

[0189] Furthermore, the simulation device described in the above embodiments can be implemented as a single device or by multiple devices. When the simulation device is implemented by multiple devices, the various components of the simulation device can be arbitrarily allocated to the multiple devices. When the simulation device is implemented by multiple devices, the communication method between these multiple devices is not particularly limited; it can be wireless communication or wired communication. Furthermore, wireless communication and wired communication can also be used in combination between the devices.

[0190] Furthermore, the constituent elements described in the above embodiments can be implemented as software or typically as LSIs of integrated circuits. These can be fabricated as individual chips or partially or entirely within a single chip. Although referred to here as LSI, depending on the level of integration, they are sometimes also called ICs, system LSIs, super LSIs, or ultra-large-scale LSIs. Moreover, the method of integrated circuitization is not limited to LSIs; it can also be implemented using dedicated circuits (general-purpose circuits that execute dedicated programs) or general-purpose processors. Programmable FPGAs (Field Programmable Gate Arrays) or reconfigurable processors that allow for the connection or configuration of reconfigurable LSI internal circuit cells can also be fabricated using LSIs. Furthermore, if advancements in semiconductor technology or other derived technologies lead to integrated circuitization technologies that replace LSIs, these technologies can certainly be used for the integration of constituent elements.

[0191] A system LSI is a multifunctional LSI that integrates multiple processing units onto a single chip. Specifically, it is a computer system comprising a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), and other components. The ROM stores the computer program. The microprocessor operates according to the computer program, and the system LSI performs its functions accordingly.

[0192] Furthermore, another aspect of the present invention can be that a computer executes... Figure 2 The computer program for each characteristic step included in the turbulence simulation method shown.

[0193] Furthermore, for example, the program can be a program for causing a computer to execute. Additionally, one aspect of the invention can be a non-transitory, computer-readable recording medium on which such a program is recorded. For example, such a program can be recorded on a recording medium for distribution or circulation. For example, by installing the distributed program into a device having another processor and having that processor execute the program, the device can perform the aforementioned processes.

[0194] Industrial availability This invention is useful for simulation devices and the like that used for turbulence simulation.

[0195] Explanation of reference numerals in the attached figures 1: Simulation System 10: Simulation device (turbulence simulation device) 11: Acquisition Department (First Acquisition Department) 12: Simulation Department 13: Output section (first output section) 14, 25: Storage Department 20: Terminal device 21: Communication Department (Second Acquisition Department, Second Output Department, Transmission Department) 22: Receiving Department 23: Control Department 24: Display section (prompt section).

Claims

1. A method for simulating turbulence, using large eddy simulation (LES) with a computer to analyze the fluid flow field. In the aforementioned turbulence simulation method, Obtain simulation conditions. Based on the obtained simulation conditions, the flow field analysis of the fluid is performed using the large eddy simulation. Output the analysis results of the flow field of the fluid. In the flow field analysis of the fluid, a turbulence model is used that incorporates the error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying the coarsening in the large eddy simulation. The correction term is the volume force calculated based on the turbulent stress accompanying the coarsening.

2. The turbulence simulation method as described in claim 1, The correction term includes a harmonic function for the pressure.

3. The turbulence simulation method as described in claim 1 or 2, The correction term consists only of isotropic tensors.

4. The turbulence simulation method as described in claim 1 or 2, The error term does not include the fitting parameters.

5. The turbulence simulation method as described in claim 1 or 2, When the spatial coordinates are set to x, the vector suffixes are set to α, β, γ, μ, the density is set to ρ, the velocity is set to u, the kinematic viscosity is set to ν, the spatial grid width is set to Δ, and the pressure is set to p, the correction term is represented by the following equation 1. [Mathematical Expression 1] (Equation 1).

6. A turbulence simulation system, comprising a turbulence simulation apparatus for analyzing the flow field of a fluid using large eddy simulation, and a terminal device capable of communicating with the turbulence simulation apparatus. The turbulence simulation device includes: The first acquisition unit acquires the simulation conditions; The simulation unit performs flow field analysis of the fluid using the large eddy simulation based on the acquired simulation conditions. as well as The first output unit outputs the analysis results of the fluid's flow field. The simulation unit uses a turbulence model in the flow field analysis of the fluid. This turbulence model includes the error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying the coarsening in the large eddy simulation. The correction term is the body force calculated based on the turbulent stress accompanying the coarsening. The terminal device includes: The second output unit outputs the simulation conditions; The second acquisition unit acquires the analysis results for the simulation conditions output by the second output unit; as well as The control unit performs prescribed processing on the acquired analysis results.

7. A turbulence simulation device, which is the device in the turbulence simulation system of claim 6.

8. A terminal device, which is a device in the turbulence simulation system of claim 6.

9. A terminal device comprising: A sending unit is used to send the input simulation conditions to a server, which performs a fluid flow field analysis based on the simulation conditions using a large eddy simulation (LES) model of turbulence. This turbulence model includes error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms, which are body forces calculated based on the turbulent stresses associated with coarsening in the LES model. The prompting section is used to display the analysis results of the flow field of the fluid received from the server.

10. A design method for a fluid product that forms a flow path through which fluid flows. Obtain the analysis results output using the turbulence simulation method described in claim 1 or 2. Based on the obtained analysis results, the structure of the fluid product is determined.

11. A manufacturing method for forming a flow path through which a fluid product is manufactured. Obtain information representing the structure of the fluid product determined by the design method of claim 10. Based on the acquired information, the fluid product is manufactured.

12. A program for enabling a computer to perform a turbulence simulation method, wherein the turbulence simulation method uses large eddy simulation to perform flow field analysis of the fluid. The turbulence simulation method includes: Obtain simulation conditions. Based on the obtained simulation conditions, the flow field analysis of the fluid is performed using the large eddy simulation. Output the analysis results of the flow field of the fluid. In the flow field analysis of the fluid, a turbulence model is used that incorporates the error terms of the Navier-Stokes equations derived from the lattice Boltzmann equations as correction terms accompanying the coarsening in the large eddy simulation. The correction term is the volume force calculated based on the turbulent stress accompanying the coarsening.

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