A turbulence simulation method, system and device

Abstract

The present invention provides a turbulence simulation method, system and device, which relates to the technical field of turbulence simulation. The method mainly includes: based on the input data of the simulated turbulence, through the model, the numerical results of the sampling points are calculated as reference solutions; a PINNs network is constructed; based on the equation, the loss function term of the PINNs network is constructed; the PINNs network is trained; based on the input data, the prediction results of the sampling points are inferred through the PINNs network; the prediction results are visualized; and the error between the prediction results and the reference solution is evaluated. This solution can make the PINNs network more consistent with the laws of physics when performing calculations, thereby avoiding dependence on grid division; it can also capture the nonlinear characteristics of complex areas, and can improve the prediction accuracy of separation flow; even in a flow field with complex geometric shapes, the PINNs network can obtain high-precision calculation results through flexible sampling.

Description

Technical Field

[0001] The present invention relates to the technical field of turbulence simulation, and in particular to a turbulence simulation method, system and device. Background Art

[0002] Turbulence refers to a flow state of a fluid, which is characterized by many vortices of different scales in the flow field. Turbulence is a complex system with typical nonlinearity. Its motion is extremely irregular and unstable. The speed of each point varies randomly with time and space, so its structure is very complex.

[0003] The effective simulation of turbulence is beneficial for studying weather, ocean currents, pipe flow, stellar motion, and airfoil flow. It can also be applied to the design of aircraft and vehicles, blood circulation research, power station design, and pollution effect analysis.

[0004] At present, the industry mainly adopts The model simulates turbulence based on the Reynolds-averaged Navier-Stokes ( ) equation, introducing the eddy viscosity (Eddy Viscosity Model, referred to as ) to represent the influence of turbulence. Although this method can effectively simulate the average characteristics of turbulence, it still has problems when simulating some typical turbulence (such as backward step turbulence, forward step turbulence, natural convection turbulence, sudden expansion in pipe flow, nozzle flow, and flow around obstacles), including: In the model The equation (i.e., the single-equation turbulence model) is sensitive to meshing. When the mesh is coarse, the calculation accuracy of eddy viscosity will decrease, thus affecting the accuracy of flow characteristics. The equation usually assumes that the turbulent eddy viscosity is linearly related to the velocity gradient, but when dealing with flow separation and reattachment problems, it may lead to inaccurate predictions of the separation zone length, eddy structure and reattachment position; in the flow, the turbulent dissipation rate changes dramatically, The equation cannot accurately describe these changes, resulting in large deviations in the prediction of eddy viscosity. Summary of the invention

[0005] The object of the present invention is to provide a turbulence simulation method, system and device to solve at least one of the above-mentioned technical problems existing in the prior art.

[0006] In a first aspect, in order to solve the above technical problems, the present invention provides a turbulence simulation method, comprising the following steps: Step 1: Based on the input data of the simulated turbulence, a preset number of sampling points are randomly selected. The model is used to calculate the numerical results of the sampling points as reference solutions; the input data includes geometric regions, boundary conditions and turbulent eddy viscosity; Step 2: Build a PINNs network (Physical Information Neural Network, a machine learning method that combines physical laws with neural networks); Equation, constructing the loss function of the PINNs network; training the PINNs network; Step 3: Based on the input data, the prediction result of the sampling point is obtained by inference through the PINNs network; Step 4: Visualize the prediction result; and evaluate the error between the prediction result and the reference solution.

[0007] Through the above method, physical constraints can be embedded into the loss function of the PINNs network, so that the PINNs network is more in line with physical laws when performing operations, thereby avoiding dependence on grid division; it can also capture the nonlinear characteristics of complex areas and improve the prediction accuracy of separated flows; even in flow fields with complex geometric shapes, the PINNs network can obtain high-precision calculation results through flexible sampling.

[0008] In a feasible implementation manner, the numerical result in step 1 specifically includes: In two-dimensional conditions: the transverse coordinate of the flow field , vertical coordinate , lateral speed , longitudinal speed and pressure ; In three-dimensional conditions: transverse coordinates of the flow field , vertical coordinate , vertical coordinate , lateral speed , longitudinal speed , vertical speed and pressure .

[0009] In a feasible implementation manner, the step 2 specifically includes (taking a two-dimensional working condition as an example, the specific formula for a three-dimensional working condition can be derived similarly): Step 21: In the PINNs network, the hidden layer is set according to the preset number of layers, and the number of neurons in each layer is set according to the preset number; the format of the input coordinate vector of the PINNs network is , the format of the output solution vector is , Represents the energy of the fluid; Step 22: The loss function calculation formula for constructing the PINNs network is: ; in, represents the total loss, represents the amount of physical loss, represents the amount of boundary loss; Step 23: Build The calculation formula is: ; in, represents the lateral momentum conservation loss term, represents the longitudinal momentum conservation loss term, represents the mass conservation loss term, express Restriction term; These four parameters are determined by the output solution vector of the PINNs network Substitute the corresponding loss term calculation formula to solve it, Indicates time; Step 24: Build The calculation formula is: ; in, represents the total number of boundary sampling points, Indicates The coordinate vector of the boundary sampling points, Indicates that the PINNs network is in The predicted solution of the boundary sampling points is Indicates The data of the boundary sampling points; Step 25: Based on the loss function constructed in step 22, the PINNs network is trained; the optimal solution is obtained by minimizing the loss function; and the final PINNs network is determined by the Adam optimizer.

[0010] In one possible implementation, The specific calculation formula is as follows: ; in, Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates pressure right The first derivative of ; represents the initial fluid density; represents the initial viscosity coefficient; represents the current viscosity coefficient, and ; express parameter; Indicates the current viscosity coefficient right The first derivative of ; Indicates the current viscosity coefficient right The first derivative of ; Indicates longitudinal speed right The first derivative of .

[0011] In one possible implementation, The specific calculation formula is as follows: ; in, Indicates longitudinal speed right The second derivative of Indicates longitudinal speed right The first derivative of ; Indicates longitudinal speed right The second derivative of Indicates pressure right The first derivative of .

[0012] In one possible implementation, The specific calculation formula is as follows: .

[0013] In one possible implementation, The specific calculation formula is as follows: .

[0014] In one possible implementation, The calculation formula is: ; in, Indicates the total number of boundary sampling points; Indicates The coordinate vector of the boundary sampling points; Indicates that the PINNs network is in The predicted solution for each boundary sampling point; Indicates The data of the boundary sampling points.

[0015] In a feasible implementation, the visualization processing in step 4 specifically includes visualizing the prediction result through a contour map; each line of the contour map represents the equal value (or the same value) of the prediction result in the geometric area, and the size of the value is represented by a color map.

[0016] In the second aspect, based on the same inventive concept, the present application also provides a turbulence simulation system, including a data receiving module, a data processing module and a result generating module; The data receiving module is used to receive input data of the simulated turbulence; the input data includes geometric regions, boundary conditions and turbulent eddy viscosity; The data processing module includes Model unit, PINNs network unit and reasoning unit; Said Model unit, storage with A model, based on the input data, calculates numerical results of sampling points as reference solutions; The PINNs network unit stores a pre-trained PINNs network, and obtains the prediction result of the sampling point based on the input data by inference; the PINNs network is based on Equation, construct the loss function of the PINNs network; The result generation module is used to visualize the prediction result and evaluate the error between the prediction result and the reference solution.

[0017] On the third aspect, based on the same inventive concept, the present application also provides a turbulence simulation device, including a processor, a memory and a bus, wherein the memory stores instructions and data that can be read by the processor, and the processor is used to call the instructions and data in the memory to execute the turbulence simulation method as described above, and the bus connects the functional components for transmitting information.

[0018] By adopting the above technical solution, the present invention has the following beneficial effects: The present invention provides a turbulence simulation method, system and device, which embed physical constraints into the loss function of the PINNs network, so that the PINNs network is more in line with physical laws when performing operations, thereby avoiding dependence on grid division; it can also capture the nonlinear characteristics of complex areas and improve the prediction accuracy of separated flows; even in flow fields with complex geometric shapes, the PINNs network can obtain high-precision calculation results through flexible sampling. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 An example diagram of a region of a backward step turbulent flow field provided by an embodiment of the present invention; Figure 2 A flow chart of a turbulence simulation method provided by an embodiment of the present invention; Figure 3 for Figure 2 Flowchart of step 2 in ; Figure 4 A visualization processing diagram provided for an embodiment of the present invention: Figure a represents a reference solution for lateral velocity, Figure b represents a predicted result for lateral velocity, Figure c represents an error between the reference solution for lateral velocity and the predicted result, Figure d represents a reference solution for longitudinal velocity, Figure e represents a predicted result for longitudinal velocity, Figure f represents an error between the reference solution for longitudinal velocity and the predicted result, Figure g represents a reference solution for pressure, Figure h represents a predicted result for pressure, and Figure i represents an error between the reference solution for pressure and the predicted result; Figure 5 A schematic diagram of a natural convection case along a vertical wall provided by an embodiment of the present invention; Figure 6 A diagram of a turbulence simulation system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0023] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0024] The present invention is further explained below in conjunction with specific implementation modes.

[0025] It should also be noted that the following specific embodiments or specific implementations are a series of optimized settings listed in the present invention to further explain the specific content of the invention, and these settings can be used in combination or in association with each other.

[0026] Embodiment 1: The proposed method is applied to a specific case of backward step turbulence, where the specific geometric region is as follows Figure 1 As shown: The white area (horizontal coordinate range -4 ~ 0, vertical coordinate range 0 ~ 1) is the step area, recorded as: ; The blue area is the turbulent flow area, which consists of two parts on the right and left, namely the first part (horizontal coordinate range 0~4, vertical coordinate range 0~8) and the second part (horizontal coordinate range -4~0, vertical coordinate range 1~8), which are combined as: ; Then preset the boundary conditions and turbulent eddy viscosity.

[0027] like Figure 2 As shown, a turbulence simulation method provided in this embodiment, under two-dimensional working conditions, specifically includes the following steps: Step 1: Based on the input data of the simulated turbulence, a preset number of sampling points (e.g., 132098) are randomly selected. Model, calculate the numerical results of the sampling points As a reference solution, the lateral velocity , longitudinal speed and pressure ; The input data includes geometric regions, boundary conditions and turbulent eddy viscosity. Step 2: Build PINNs network; based on Equation, construct the loss function of the PINNs network; train the PINNs network.

[0028] Furthermore, if Figure 3 As shown, the step 2 specifically includes: Step 21. In the PINNs network, the number of hidden layers is set to 4, and the number of neurons in each layer is set to 120, so that a balance can be achieved in terms of computational effect and efficiency. The format of the input coordinate vector of the PINNs network is , the format of the output solution vector is ; Represents the energy of the fluid; Step 22: The loss function calculation formula for constructing the PINNs network is: ; in, represents the total loss, represents the amount of physical loss, represents the amount of boundary loss; Step 23: Build The calculation formula is: ; in, represents the lateral momentum conservation loss term, represents the longitudinal momentum conservation loss term, represents the mass conservation loss term, express Restrictions; These four parameters are determined by the output solution vector of the PINNs network. Substitute the corresponding loss term calculation formula to solve it, Indicates time; Preferably, The specific calculation formula is as follows: ; in, Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates pressure right The first derivative of ; represents the initial fluid density; represents the initial viscosity coefficient; represents the current viscosity coefficient, and ; express parameter; Indicates the current viscosity coefficient right The first derivative of ; Indicates the current viscosity coefficient right The first derivative of ; Indicates longitudinal speed right The first derivative of ; The specific calculation formula is as follows: ; in, Indicates longitudinal speed right The second derivative of Indicates longitudinal speed right The first derivative of ; Indicates longitudinal speed right The second derivative of Indicates pressure right The first derivative of ; The specific calculation formula is as follows: ; The specific calculation formula is as follows: ; Step 24: Build The calculation formula is: ; in, Indicates the total number of boundary sampling points, which is set to 3000 to provide a sufficient number of samples; Indicates The coordinate vector of the boundary sampling points; Indicates that the PINNs network is in The predicted solution for each boundary sampling point; Indicates The data of the boundary sampling points; Step 25: Based on the loss function constructed in step 22, the PINNs network is trained, specifically including: selecting a preset number (e.g., 60,000, which can provide a sufficient number of samples) of internal sampling points; training the internal sampling points in batches (e.g., 10 batches, each batch has 60 internal sampling points) by minimizing the loss function to obtain the optimal solution; first set , the learning rate of the Adam optimizer is 1e-3, and the training is performed for a preset number of rounds (for example, 10,000 rounds, which can take into account both training efficiency and effect); then set , the learning rate of the Adam optimizer is 2e-4, and the training is performed for a preset number of rounds (for example, 10,000 rounds); the model parameters of the final PINNs network are determined; in this way, the eddy viscosity calculation can be adaptively adjusted by gradually optimizing the parameters, so that the turbulence simulation characteristics are closer to the actual flow state, thereby compensating for the distortion problem caused by the simplified calculation of eddy viscosity in the background technology.

[0029] Step 3: Based on the input data, a preset number of sampling points (e.g., 132098, which can provide sufficient sampling volume) are selected, and four components are inferred through the PINNs network: The prediction results are saved.

[0030] Step 4: Visualize the prediction results, including contour maps, where each line of the contour map represents the equivalent value (or the same value) of the prediction results in the geometric area, and use color mapping to represent the magnitude of the values. The warmer the color, the larger the value, and the colder the color, the smaller the value, so as to achieve the effect of intuitively displaying the value change; evaluate the error between the prediction result and the reference solution; Visualization effects such as Figure 4 As shown, figure a represents the reference solution of lateral velocity, figure b represents the predicted result of lateral velocity, figure c represents the error between the reference solution and the predicted result of lateral velocity (i.e., the absolute value of the difference between the reference solution and the predicted result), figure d represents the reference solution of longitudinal velocity, figure e represents the predicted result of longitudinal velocity, figure f represents the error between the reference solution and the predicted result of longitudinal velocity, figure g represents the reference solution of pressure, figure h represents the predicted result of pressure, and figure i represents the error between the reference solution and the predicted result of pressure; Comparing the predicted result graph with the reference solution graph, it can be seen that the turbulence curves are very close; from the error graph, it can be seen that the error between the predicted result and the reference solution is mainly displayed in blue, indicating that the error value is very small, proving that the improved PINNs network can accurately simulate turbulence.

[0031] Through the above method, physical constraints can be embedded into the loss function of the PINNs network, so that the PINNs network is more in line with physical laws when performing operations, thereby avoiding dependence on grid division; it can also capture the nonlinear characteristics of complex areas and improve the prediction accuracy of separated flows; even in flow fields with complex geometric shapes, the PINNs network can obtain high-precision calculation results through flexible sampling.

[0032] Embodiment 2: For the natural convection case along the vertical wall in the natural convection turbulence problem, turbulence simulation is performed through this application solution: Case legend and main parameters, such as Figure 5 As shown, the height of the vertical wall is set to H.

[0033] By using the method in the first embodiment, effective turbulence simulation can also be performed.

[0034] In other embodiments, the method of this scheme can also be applied to scenes such as forward step flow (i.e., Forward-facing Step Flow, commonly seen in computer hardware cooling, aircraft and automobile appearance design cases), sudden expansion in pipe flow (i.e., Sudden Expansion in Pipes, commonly seen in pipeline design, water delivery systems, oil and gas pipelines, etc.), nozzle flow (i.e., Flow Through a Nozzle, commonly seen in jet propulsion, turbines, gas or liquid delivery system design cases, etc.), and flow around obstacles (i.e., Flow Around Obstacles, commonly seen in aerospace, ship design, building wind load calculation, etc.) to perform intuitive and accurate turbulence simulation.

[0035] Embodiment three: like Figure 6 As shown, this embodiment provides a turbulence simulation system, including a data receiving module, a data processing module and a result generating module; The data receiving module is used to receive input data of the simulated turbulence; the input data includes geometric regions, boundary conditions and turbulent eddy viscosity; The data processing module includes Model unit, PINNs network unit and reasoning unit; Said Model unit, storage with A model, based on the input data, calculates numerical results of sampling points as reference solutions; The PINNs network unit stores a pre-trained PINNs network, and obtains the prediction result of the sampling point based on the input data by inference; the PINNs network is based on Equation, construct the loss function of the PINNs network; The result generation module is used to visualize the prediction result and evaluate the error between the prediction result and the reference solution.

[0036] Embodiment 4: This embodiment provides a turbulence simulation device, including a processor, a memory and a bus, wherein the memory stores instructions and data that can be read by the processor, the processor is used to call the instructions and data in the memory to execute the turbulence simulation method as described above, and the bus connects the functional components for transmitting information.

[0037] In another embodiment, the present solution can be implemented by an integrated device, which may include corresponding modules for performing each or several steps in the above-mentioned embodiments. The module may be one or more hardware modules specially configured to perform the corresponding steps, or implemented by a processor configured to perform the corresponding steps, or stored in a computer-readable medium for implementation by a processor, or implemented by some combination.

[0038] The processor performs the various methods and processes described above. For example, the method implementation in the present solution can be implemented as a software program, which is tangibly contained in a machine-readable medium, such as a memory. In some embodiments, part or all of the software program can be loaded and / or installed via a memory and / or a communication interface. When the software program is loaded into the memory and executed by the processor, one or more steps in the method described above can be executed. Alternatively, in other embodiments, the processor can be configured to perform one of the above methods by any other appropriate means (for example, by means of firmware).

[0039] The device can be implemented using a bus architecture. The bus architecture can include any number of interconnecting buses and bridges, depending on the specific application and overall design constraints of the hardware. The bus connects various circuits including one or more processors, memories, and / or hardware modules together. The bus can also connect various other circuits such as peripherals, voltage regulators, power management circuits, external antennas, etc.

[0040] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Component (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A turbulence simulation method, characterized in that: include: Step 1: Based on the input data of the simulated turbulence, a preset number of sampling points are randomly selected. The model is used to calculate the numerical results of the sampling points as reference solutions; the input data includes geometric regions, boundary conditions and turbulent eddy viscosity; Step 2: Construct PINNs network; based on Equation, constructing the loss function of the PINNs network; training the PINNs network; Step 3: Based on the input data, the prediction result of the sampling point is obtained by inference through the PINNs network; Step 4: Visualize the prediction result; and evaluate the error between the prediction result and the reference solution.

2. The method according to claim 1, characterized in that The numerical results in step 1 specifically include: In two-dimensional conditions: the transverse coordinate of the flow field , vertical coordinate , lateral speed , longitudinal speed and pressure ; In three-dimensional conditions: transverse coordinates of the flow field , vertical coordinate , vertical coordinate , lateral speed , longitudinal speed , vertical speed and pressure .

3. The method according to claim 2, characterized in that In a two-dimensional working condition, the step 2 specifically includes: Step 21: In the PINNs network, the hidden layer is set according to the preset number of layers, and the number of neurons in each layer is set according to the preset number; the format of the input coordinate vector of the PINNs network is , the format of the output solution vector is , Represents the energy of the fluid; Step 22: constructing the loss function calculation formula of the PINNs network includes: ； in, represents the total loss, represents the amount of physical loss, represents the amount of boundary loss; Step 23: Build The calculation formula includes: ； in, represents the lateral momentum conservation loss term, represents the longitudinal momentum conservation loss term, represents the mass conservation loss term, express Restriction term; These four parameters are determined by the output solution vector of the PINNs network Substitute the corresponding loss term calculation formula to solve it, Indicates time; Step 24: Build The calculation formula includes: ； in, represents the total number of boundary sampling points, Indicates The coordinate vector of the boundary sampling points, Indicates that the PINNs network is in The predicted solution of the boundary sampling points is Indicates The data of the boundary sampling points; Step 25: Based on the loss function constructed in step 22, the PINNs network is trained; the optimal solution is obtained by minimizing the loss function; and the final PINNs network is determined by the Adam optimizer.

4. The method according to claim 3, characterized in that In step 21, the number of hidden layers is set to 4, and the number of neurons in each layer is set to 120.

5. The method according to claim 3, characterized in that: The specific calculation formula includes: ； in, Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates the lateral speed right The first derivative of ; Indicates the lateral speed right The second derivative of Indicates pressure right The first derivative of ; represents the initial fluid density; represents the initial viscosity coefficient; represents the current viscosity coefficient, and ; express parameter; Indicates the current viscosity coefficient right The first derivative of ; Indicates the current viscosity coefficient right The first derivative of ; Indicates longitudinal speed right The first derivative of ; The specific calculation formula includes: ； in, Indicates longitudinal speed right The second derivative of Indicates longitudinal speed right The first derivative of ; Indicates longitudinal speed right The second derivative of Indicates pressure right The first derivative of ; The specific calculation formula includes: ； The specific calculation formula includes: 。 6. The method according to claim 5, characterized in that The step 25 specifically includes: Select a preset number of internal sampling points; train the internal sampling points in batches by minimizing the loss function to obtain the optimal solution; first set , the learning rate of the Adam optimizer is 1e-3, and the training rounds are preset; then set , the learning rate of the Adam optimizer is 2e-4, and the preset rounds of training are performed; the model parameters of the final PINNs network are determined.

7. The method according to claim 6, characterized in that The number of internal sampling points is 60,000; the number of training batches is 10, and the number of internal sampling points in each batch is 60.

8. The method according to claim 1, characterized in that The visualization processing in step 4 specifically includes a contour map; each line of the contour map represents the equivalent value of the prediction result in the geometric area, and the size of the value is represented by color mapping.

9. A turbulence simulation system, characterized in that: It includes a data receiving module, a data processing module and a result generating module; The data receiving module is used to receive input data of the simulated turbulence; the input data includes geometric regions, boundary conditions and turbulent eddy viscosity; The data processing module includes Model unit, PINNs network unit and reasoning unit; Said Model unit, storage with A model, based on the input data, calculates numerical results of sampling points as reference solutions; The PINNs network unit stores a pre-trained PINNs network, and obtains the prediction result of the sampling point based on the input data by inference; the PINNs network is based on Equation, construct the loss function of the PINNs network; The result generation module is used to visualize the prediction result and evaluate the error between the prediction result and the reference solution.

10. A turbulence simulation device, characterized in that: It includes a processor, a memory and a bus, wherein the memory stores instructions and data read by the processor, the processor is used to call the instructions and data in the memory to execute any method as claimed in claim 1-8, and the bus connects the functional components for transmitting information.

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