Method and system for constructing prediction model of fluid mechanics flow field velocity

Abstract

The invention discloses a method for constructing a prediction model of fluid mechanics flow field velocity. The method comprises the following steps: acquiring a large number of coronary artery CTA images of coronary heart disease patients, and respectively constructing 3D blood vessel geometric models; setting different inlet flow rates and physiological pressure boundary conditions in different 3D blood vessel geometric models, and performing CFD simulation to obtain simulation results; inputting the obtained contrast agent particle concentration 3D point cloud in the flow field, the actual flow field speed and the coronary artery model 3D point cloud into a PDMNN neural network for learning; and encoding the advection diffusion equation to a loss function, and driving the PDMNN neural network to calculate convergence by using the relationship between the contrast agent concentration and the fluid velocity to obtain a prediction model of the fluid mechanics flow field velocity. Through the prediction model constructed by the method, the prediction effect can be more accurately and quickly realized, and meanwhile, the method can face different geometric models and different boundary conditions.

Description

Technical Field

[0001] The present application relates to the field of artificial intelligence technology, and in particular to a method and system for constructing a prediction model for fluid mechanics flow field velocity. Background Art

[0002] The accurate calculation of blood flow velocity in flow fields plays a vital role in biomedical engineering and clinical diagnosis. It is not only crucial for understanding the pathogenesis of cardiovascular diseases, such as atherosclerosis and thrombosis, but also has significant significance for clinical applications such as evaluating surgical effects, guiding interventional treatments, and designing cardiovascular devices. In addition, the calculation results of blood flow velocity can provide a scientific basis for disease prevention, diagnosis, and treatment, thereby improving patients' treatment outcomes and quality of life. Therefore, the development of high-precision flow field blood flow velocity calculation methods is of great value in promoting medical progress and improving public health levels.

[0003] Computational fluid dynamics (CFD) technology is a classic fluid dynamics numerical simulation method that can simulate the flow of fluid in a pipe and calculate the local pressure and flow velocity in a three-dimensional (3D) flow field. Applying the CFD method to the study of human hemodynamics can non-invasively calculate blood pressure and blood flow velocity in blood vessels in vitro, providing technical means for the diagnosis and treatment of clinical cardiovascular diseases. However, the traditional CFD calculation method requires quantitative solution of the Navier-Stokes (NS) equation in the 3D flow field, as shown in the following formula:

[0004]

[0005] Where vi is the fluid velocity tensor, ρ is the fluid density, p is the pressure, μ is the fluid kinematic viscosity, and Xi is the volume force. This equation involves solving multiple partial differential equations of physical quantities, which is very complicated, resulting in high computational time cost and difficulty in real-time application in engineering and clinical practice.

[0006] At present, there are literature reports on the rapid solution of 3D CFD based on deep learning. Li et al. used a dual-channel neural network model to predict the 3D CFD flow field of the aorta and coronary artery, but used the same and fixed fluid boundary conditions for different models, and its essence was to predict the impact of different geometric information on the coronary artery flow field.

[0007] Raissi et al. developed a Physics-informed neural networks (PINN) model to predict the flow field details in intracranial aneurysms by encoding the NS equations into the loss function. However, the algorithm needs to be trained separately for each aneurysm model, which means that it cannot predict 3D flow fields of different geometric shapes and has no application value. The limitation of PINN is that the NS equations are too complex to be accurately fitted by the neural network model. Therefore, there is no research to achieve accurate and fast deep learning prediction methods for 3D flow fields with different geometric models and different boundary conditions. Summary of the invention

[0008] Based on this, in order to solve the above technical problems, a method and system for constructing a prediction model of fluid mechanics flow field velocity is provided to solve the problems of slow calculation speed of the existing technology for predicting flow field blood flow velocity, inability to use different boundary conditions or the same prediction model cannot cope with different geometric models.

[0009] In a first aspect, a method for constructing a prediction model of fluid mechanics flow field velocity, the method comprising:

[0010] Acquire a large number of coronary artery CTA images of patients with coronary heart disease, and construct 3D vascular geometric models according to the coronary artery CTA images;

[0011] Add blood and contrast agent to the 3D blood vessel geometry model to simulate the flow of contrast agent in the blood; set different inlet flow rates and physiological pressure boundary conditions in different 3D blood vessel geometry models, and perform CFD simulation to obtain simulation results, and construct training samples, test samples and test samples of the PDMNN neural network based on the obtained large number of simulation results; the simulation results include a 3D point cloud of contrast agent particle concentration in the flow field and an actual flow field velocity;

[0012] The 3D point cloud of contrast agent particle concentration in the flow field obtained based on coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions are input into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function, and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network calculation convergence to obtain a prediction model for fluid mechanics flow field velocity.

[0013] In the above scheme, optionally, the method further includes: encoding a penalty term of the prediction result at the boundary of the 3D blood vessel geometric model in the loss function.

[0014] In the above solution, further optionally, the penalty term of the prediction result at the boundary of the 3D blood vessel geometric model is:

[0015]

[0016] Among them, v i is the velocity tensor, P is the pressure, x is the 3D model point cloud coordinate, ρ is the density, μ is the viscosity, t is the time, C is the particle concentration in the fluid, is the fluid boundary domain, and n is the number of model outlets and inlets.

[0017] In the above scheme, optionally, the method also includes: introducing blood vessel radius information into the PDMNN neural network, so that the PDMNN neural network makes a preliminary prediction of the blood flow velocity and then corrects the preliminary predicted blood flow velocity according to the blood vessel radius information.

[0018] In the above scheme, optionally, the advection diffusion equation is

[0019]

[0020] Among them, v i is the velocity tensor, C is the particle concentration in the fluid, and t is the time.

[0021] In the above solution, optionally, after acquiring a large number of coronary artery CTA images of patients with coronary heart disease, the method further includes: segmenting a target area of ​​the coronary artery CTA images.

[0022] In the above scheme, optionally, after obtaining the simulation results, a large number of simulation results are subjected to data cleaning, and training samples, test samples and verification samples of the PDMNN neural network are constructed according to the simulation results after data cleaning.

[0023] In a second aspect, a system for constructing a prediction model of fluid mechanics flow field velocity is provided, the system comprising:

[0024] 3D vascular geometry model building module: used to obtain a large number of coronary artery CTA images of patients with coronary heart disease, and to build 3D vascular geometry models according to the coronary artery CTA images;

[0025] CFD simulation module: used to add blood and contrast agent to the 3D vascular geometry model, simulate the flow of contrast agent in the blood, set different inlet flow rates and physiological pressure boundary conditions in different 3D vascular geometry models, and perform CFD simulation to obtain simulation results, and construct training samples, test samples and test samples of the PDMNN neural network based on the obtained large number of simulation results; the simulation results include 3D point cloud of contrast agent particle concentration in the flow field and actual flow field velocity;

[0026] Prediction model training module: used to input the 3D point cloud of contrast agent particle concentration in the flow field obtained based on the coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions into the PDMNN neural network for learning; encode the advection diffusion equation into the loss function and use the relationship between the contrast agent concentration and the fluid velocity to drive the PDMNN neural network to calculate and converge, so as to obtain a prediction model of the fluid mechanics flow field velocity.

[0027] In a third aspect, a computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of a method for constructing a prediction model of a fluid mechanics flow field velocity as described in the first aspect are implemented.

[0028] In a fourth aspect, a computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of a method for constructing a predictive model of fluid dynamics flow field velocity as described in the first aspect above.

[0029] This application has at least the following beneficial effects:

[0030] In constructing the prediction model, the present application sets two fluid materials, blood and contrast agent, in the constructed 3D vascular geometric model to simulate the flow of contrast agent in the blood, thereby providing particle concentration information. At the same time, a PDMNN network with dual-path input is developed, and the 3D point cloud of the coronary model, the actual flow field velocity, and the 3D point cloud of the contrast agent particle concentration in the flow field are input simultaneously, wherein the 3D point cloud of the coronary model can provide geometric information, and the 3D point cloud of the contrast agent particle concentration can provide physical information, so that the neural network can capture multi-dimensional features at the same time and accurately predict the flow field velocity; in the process of optimizing the prediction model, a simple advection diffusion equation is used as the driver of the neural network model, which can guide the neural network to achieve more accurate fitting and achieve a more accurate 3D flow field velocity prediction effect. Therefore, the prediction model constructed in the above manner can achieve the prediction effect more accurately and quickly, and can also face different geometric models and different boundary conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic flow chart of a method for constructing a prediction model of fluid mechanics flow field velocity is provided for one embodiment of the present application;

[0032] Figure 2 A neural network architecture diagram of a prediction model is provided for one embodiment of the present application;

[0033] Figure 3 A flow chart of the prediction model predicting 3D CFD flow field velocity in one embodiment of the present application;

[0034] Figure 4 The figure is a comparison chart of the prediction results using the prediction model of the present application and the calculation results using traditional CFD calculations. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0036] In one embodiment, Figure 1 As shown, a method for constructing a prediction model of fluid mechanics flow field velocity is provided, the method comprising:

[0037] Step S1: obtaining a large number of coronary artery CTA images of patients with coronary heart disease, and constructing 3D vascular geometric models according to the coronary artery CTA images;

[0038] Step S2: adding blood and contrast agent to the 3D blood vessel geometric model to simulate the flow of contrast agent in the blood; setting different inlet flow rates and physiological pressure boundary conditions in different 3D blood vessel geometric models, and performing CFD simulation to obtain simulation results, and constructing training samples, test samples and test samples of the PDMNN neural network based on the obtained large number of simulation results; the simulation results include a 3D point cloud of the contrast agent particle concentration in the flow field and the actual flow field velocity;

[0039] Step S3: Input the 3D point cloud of the contrast agent particle concentration in the flow field obtained based on the coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions into the PDMNN neural network for learning; encode the advection diffusion equation into the loss function and use the relationship between the contrast agent concentration and the fluid velocity to drive the PDMNN neural network to calculate and converge, so as to obtain a prediction model of the fluid mechanics flow field velocity.

[0040] In this embodiment, in order to solve the problem that the complex NS equations in PINN are difficult to be accurately fitted by the neural network model, the present invention uses simple velocity-related physical equations to drive the neural network model to capture the local characteristics of the 3D flow field and improve the model performance. According to the advection diffusion equation, the velocity tensor vi and the particle concentration C in the fluid satisfy:

[0041]

[0042] Where t is time. Therefore, the flow velocity can be calculated based on the spatial concentration of particles in the fluid and the gradient of the concentration changing with time. The present invention extracts the particle concentration and flow velocity field in the fluid, improves the PINN algorithm, incorporates the advection diffusion equation into the loss function, and takes the advection diffusion equation as the leading factor, combines the data-driven method to drive the convergence of the neural network model, and forms a physics-data multi-derived neural network (PDMNN) network driven by both data and physics. According to the advection transport equation, there is a close connection between the two single variables of flow field velocity and particle concentration, and they are not affected by other physical factors. Therefore, the prediction of fluid velocity using fluid particle concentration can achieve very high accuracy. Compared with the existing PINN neural network, PDMNN adds a simpler physical equation to the loss function as a penalty term for the prediction result, which can obtain better prediction results and improve the generalization performance and physical interpretability of the neural network model.

[0043] This application collected coronary artery CTA images of 205 patients with coronary heart disease in the clinic and reconstructed their 3D vascular geometry model; set two fluid materials, blood and contrast agent, in the flow field to simulate the flow of contrast agent in the blood and provide particle concentration information; applied 11 different inlet flow rates and physiological pressure boundary conditions to different models, and performed a total of 2255 CFD simulations as deep learning model training and test samples; Figure 2 As shown in the figure, a dual-path input PDMNN neural network is designed. The dual paths of the network input the 3D point cloud of the coronary artery model and the 3D point cloud of the contrast agent particle concentration in the flow field respectively; the advection diffusion equation is encoded in the loss function of the network, and the relationship between the contrast agent concentration and the fluid velocity is used to drive the neural network calculation convergence.

[0044] Therefore, if Figure 3 As shown, through the prediction model, the 3D blood vessel point cloud and the contrast agent particle concentration point cloud are input, so that features can be extracted from the two types of data and integrated to predict the blood flow velocity. In the actual process, the contrast agent particle concentration point cloud extracts concentration information from the image through image processing methods.

[0045] In the above-mentioned method for constructing a prediction model of fluid mechanics flow field velocity, in constructing the prediction model, two fluid materials, blood and contrast agent, are set in the constructed 3D vascular geometry model to simulate the flow of contrast agent in the blood, thereby providing particle concentration information. At the same time, a PDMNN network with dual-path input is developed, and the 3D point cloud of the coronary model, the actual flow field velocity, and the 3D point cloud of the contrast agent particle concentration in the flow field are input simultaneously, wherein the 3D point cloud of the coronary model can provide geometric information, and the 3D point cloud of the contrast agent particle concentration can provide physical information, so that the neural network can capture multi-dimensional features at the same time and accurately predict the flow field velocity; in the process of optimizing the prediction model, a simple advection diffusion equation is used as the driver of the neural network model, which can guide the neural network to achieve more accurate fitting and achieve a more accurate 3D flow field velocity prediction effect. Therefore, the prediction model constructed in the above manner can achieve the prediction effect more accurately and quickly, and can also face different geometric models and different boundary conditions.

[0046] In one embodiment, the method further comprises: encoding a penalty term for prediction results at the boundary of the 3D blood vessel geometric model in the loss function.

[0047] In one embodiment, the penalty term for the prediction result at the boundary of the 3D blood vessel geometric model is:

[0048]

[0049] Among them, v i is the velocity tensor, P is the pressure, x is the 3D model point cloud coordinate, ρ is the density, μ is the viscosity, t is the time, C is the particle concentration in the fluid, is the fluid boundary domain, and n is the number of model outlets and inlets.

[0050] In this embodiment, a penalty for the prediction results at the boundary of the 3D model is applied separately to form a neural network model driven by both physics and data. Ensure that the model can provide more accurate prediction results at the boundary of the 3D blood vessel model, that is, the area where the blood vessel contacts the surrounding tissue. Because in actual fluid dynamics, the flow characteristics at the boundary are often more complex, such as changes in flow velocity, pressure distribution, etc., accurate prediction of these areas is crucial. By adding a penalty term to the loss function, the model will pay more attention to the prediction errors in these boundary areas during training, thereby optimizing the performance of the model in these key areas.

[0051] In one embodiment, the method further includes: introducing blood vessel radius information into the PDMNN neural network so that the PDMNN neural network makes a preliminary prediction of the blood flow velocity and then corrects the preliminary predicted blood flow velocity according to the blood vessel radius information.

[0052] In this embodiment, the vessel radius information is introduced before the network output to further correct the prediction results. The radius of the vessel is an important factor affecting the hemodynamic characteristics, especially when calculating the blood flow velocity and pressure distribution. Before the model outputs the prediction results, by introducing the vessel radius information, the prediction results can be further corrected and optimized. This correction takes into account the geometric characteristics of the blood vessels, making the prediction results more consistent with the actual physical conditions, and improving the accuracy and reliability of the prediction.

[0053] In one embodiment, after acquiring a large number of coronary artery CTA images of patients with coronary heart disease, the method further includes: segmenting a target area of ​​the coronary artery CTA images.

[0054] In one embodiment, after obtaining the simulation results, a large number of simulation results are subjected to data cleaning, and training samples, test samples and verification samples of the PDMNN neural network are constructed according to the simulation results after data cleaning.

[0055] In this embodiment, erroneous data in the simulation results are deleted and replaced to ensure the accuracy of the data.

[0056] like Figure 4 As shown, it is a comparison chart of the prediction results of 3D smooth speed using the traditional CFD calculation process speed and the prediction model of the present application. In the test set of 100 cases, the normalized mean square error between the flow velocity of each node in the flow field predicted by the PDMNN of the present application and the actual CFD calculation result is 0.0309, indicating a small error between the two.

[0057] In one embodiment, a system for constructing a prediction model of fluid mechanics flow field velocity is provided, the system comprising:

[0058] 3D vascular geometry model building module: used to obtain a large number of coronary artery CTA images of patients with coronary heart disease, and to build 3D vascular geometry models according to the coronary artery CTA images;

[0059] CFD simulation module: used to add blood and contrast agent to the 3D vascular geometry model to simulate the flow of contrast agent in the blood; set different inlet flow rates and physiological pressure boundary conditions in different 3D vascular geometry models, and perform CFD simulation to obtain simulation results, and construct training samples, test samples and test samples of the PDMNN neural network based on a large number of simulation results; the simulation results include 3D point cloud of contrast agent particle concentration in the flow field and actual flow field velocity;

[0060] Prediction model training module: used to input the 3D point cloud of contrast agent particle concentration in the flow field obtained based on the coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions into the PDMNN neural network for learning; encode the advection diffusion equation into the loss function and use the relationship between the contrast agent concentration and the fluid velocity to drive the PDMNN neural network to calculate and converge, so as to obtain a prediction model of the fluid mechanics flow field velocity.

[0061] For the specific definition of a system for constructing a prediction model of a fluid mechanics flow field velocity, please refer to the definition of a method for constructing a prediction model of a fluid mechanics flow field velocity in the above text, which will not be repeated here. Each module in the above-mentioned system for constructing a prediction model of a fluid mechanics flow field velocity can be implemented in whole or in part through software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0062] In one embodiment, a computer device is provided, which may be a server. The computer device includes a processor, a memory, and a network interface connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, the above-mentioned method for constructing a prediction model of fluid mechanics flow field velocity is implemented.

[0063] In one embodiment, a computer program product is also provided, including a computer program / instruction, which, when executed by a processor, involves all or part of the process in the above-mentioned embodiment method.

[0064] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, etc. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0065] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0066] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A method for constructing a prediction model for fluid mechanics flow field velocity, characterized in that: The method comprises: Acquire a large number of coronary artery CTA images of patients with coronary heart disease, and construct 3D vascular geometric models according to the coronary artery CTA images; Add blood and contrast agent to the 3D blood vessel geometry model to simulate the flow of contrast agent in the blood; set different inlet flow rates and physiological pressure boundary conditions in different 3D blood vessel geometry models, and perform CFD simulation to obtain simulation results, and construct training samples, test samples and test samples of the PDMNN neural network based on the obtained large number of simulation results; the simulation results include a 3D point cloud of contrast agent particle concentration in the flow field and an actual flow field velocity; The 3D point cloud of contrast agent particle concentration in the flow field obtained based on coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions are input into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function, and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network calculation convergence to obtain a prediction model for fluid mechanics flow field velocity.

2. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 1, characterized in that: The method further includes encoding a penalty term for prediction results at the boundary of the 3D blood vessel geometric model in the loss function.

3. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 2, characterized in that: The penalty term for the prediction result at the boundary of the 3D blood vessel geometric model is: Among them, v i is the velocity tensor, P is the pressure, x is the 3D model point cloud coordinate, ρ is the density, μ is the viscosity, t is the time, C is the particle concentration in the fluid, is the fluid boundary domain, and n is the number of model outlets and inlets.

4. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 1, characterized in that: The method also includes: introducing blood vessel radius information into the PDMNN neural network, so that after the PDMNN neural network makes a preliminary prediction of the blood flow velocity, the preliminary predicted blood flow velocity is corrected according to the blood vessel radius information.

5. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 1, characterized in that: The advection-diffusion equation is Among them, v i is the velocity tensor, C is the particle concentration in the fluid, and t is the time.

6. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 1, characterized in that: After acquiring a large number of coronary artery CTA images of patients with coronary heart disease, the method further includes: segmenting the target area of ​​the coronary artery CTA images.

7. The method for constructing a prediction model of fluid mechanics flow field velocity according to claim 1, characterized in that: After the simulation results are obtained, data cleaning is performed on the large number of simulation results obtained, and training samples, test samples and verification samples of the PDMNN neural network are constructed according to the simulation results after data cleaning.

8. A prediction model building system for fluid mechanics flow field velocity, characterized in that: The system comprises: 3D vascular geometry model building module: used to obtain a large number of coronary artery CTA images of patients with coronary heart disease, and build 3D vascular geometry models based on the coronary artery CTA images CFD simulation module: used to add blood and contrast agent to the 3D vascular geometry model to simulate the flow of contrast agent in the blood; set different inlet flow rates and physiological pressure boundary conditions in different 3D vascular geometry models, and perform CFD simulation to obtain simulation results, and construct training samples, test samples and test samples of the PDMNN neural network based on a large number of simulation results; the simulation results include 3D point cloud of contrast agent particle concentration in the flow field and actual flow field velocity; Prediction model training module: used to input the 3D point cloud of contrast agent particle concentration in the flow field obtained based on the coronary artery CTA images of a large number of coronary heart disease patients, the actual flow field velocity, the 3D point cloud of the 3D blood vessel geometry model and the corresponding inlet flow velocity boundary conditions into the PDMNN neural network for learning; encode the advection diffusion equation into the loss function and use the relationship between the contrast agent concentration and the fluid velocity to drive the PDMNN neural network to calculate and converge, so as to obtain a prediction model of the fluid mechanics flow field velocity.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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