A method for constructing interface conditions for compressible two-medium flow fields using neural network models
Patent Information
- Application Number
- CN202211111769.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-13
- Publication Date
- 2026-09-01
- Estimated Expiration
- 2042-09-13
AI Technical Summary
[0004]但是，气液界面附近状态方程及物性参数的多样性会导致两介质黎曼问题求解复杂
[0011]1)本发明旨在设计一种嵌入物理约束的两介质黎曼问题预测代理模型，将基于大数据的机器学习技术应用于可压缩两介质流场界面条件的构建。这种代理模型不同于传统的公式表达，包含了大数据中的丰富流场信息，同时避免了复杂的迭代求解过程。该项技术能够有效模拟包含强激波或强间断的挑战性难题，改进传统方法的计算效率和稳定性，可以应用于各类可压缩两介质流体界面演变问题的流场仿真；
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Figure CN115526097B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the technical field of fluid dynamics simulation, and in particular to a method for constructing interface conditions of a compressible two-medium flow field using a neural network model. Background Technology
[0002] The dynamic characteristics of the interface motion in compressible two-medium flow fields are of great significance for the study of high-speed flow fields containing droplets and bubbles. High-confidence numerical simulations are playing an increasingly important role.
[0003] Because the physical properties of the different fluids on either side of the interface differ significantly, directly applying numerical schemes for simulating single-medium fluids to multi-medium fluid problems can lead to numerical instability. This is especially true when highly nonlinear waves, such as shock waves, interact with the interface, easily causing non-physical oscillations near the interface and even making calculations difficult. Sharp interface methods, such as virtual fluid methods, treat the interface as a special type of boundary. They construct boundary conditions near the interface based on the virtual flow field derived from the solution to the two-medium Riemann problem, thus avoiding numerical instability near the interface and easily extending to multi-dimensional problems.
[0004] However, the diversity of the equations of state and physical properties near the gas-liquid interface complicates the solution of the two-medium Riemann problem. If factors such as viscosity, surface tension, phase transitions, and chemical reactions are considered, the iterative process for solving the interface problem may become even more cumbersome and complex, and computational efficiency and stability still require further improvement. Summary of the Invention
[0005] This application provides a method for constructing interface conditions for compressible two-medium flow fields using a neural network model. The aim is to accurately construct these interface conditions, ensuring computational stability during the solution process. This method is applicable to state equations describing different fluid thermodynamic properties, avoids iterative solutions, and increases the solution efficiency and success rate of the compressible two-medium flow field simulation model. The simulation results obtained through this model have high technical guidance value in practical applications.
[0006] Firstly, a modeling method is provided, which is applied to a compressible two-medium flow field model, including:
[0007] The first flow field state at the flow field interface at the first moment is input into the neural network model, which is used to output... and For the two-medium nonlinear equation f L +f R +Δu=0 in the function f L The predicted value, For function f R The predicted value, where the velocity difference Δu = uR -u L L represents the fluid on the first side, R represents the fluid on the second side, and u represents the fluid velocity;
[0008] Based on the output of the neural network model, a first interface condition is determined, which is used to indicate the interface conditions on both sides of the flow field interface at the first moment.
[0009] Based on the first interface conditions and the first flow field state, the second flow field state at the second moment of the flow field interface is determined.
[0010] Compared with the prior art, the solution provided in this application has at least the following beneficial technical effects:
[0011] 1) This invention aims to design a predictive surrogate model for two-medium Riemannian problems with embedded physical constraints, applying big data-based machine learning techniques to construct interface conditions for compressible two-medium flow fields. This surrogate model differs from traditional formulaic expressions, incorporating rich flow field information from big data while avoiding complex iterative solutions. This technique can effectively simulate challenging problems involving strong shock waves or strong discontinuities, improving the computational efficiency and stability of traditional methods, and can be applied to flow field simulation of various compressible two-medium fluid interface evolution problems.
[0012] 2) The neural network construction method with embedded physical constraints proposed in this invention does not directly output the fitting results of the four interface solutions of the Riemann problem, but instead outputs two function values representing the physical relationships. In this way, the discontinuities in the flow field can be expressed in the loss function as constraints on these two function values, which not only makes the results of the neural network surrogate model more in line with physical requirements, but also makes it very simple and convenient to apply;
[0013] 3) This invention uses deep neural networks to solve the compressible two-medium Riemann problem, which is different from the traditional formula expression. It is applicable to various types of state equations, avoids complex iterative solution processes, helps to improve the computational efficiency and stability of traditional methods, and has greater versatility.
[0014] 4) The present invention is based on the interface conditional neural network surrogate model constructed by the two-medium Riemann solution, which can realize modular programming, can be applied to various existing CFD solution programs, and is easy to maintain and expand.
[0015] In conjunction with the first aspect, in some implementations of the first aspect, the neural network model includes H hidden layers, and the neural network model satisfies:
[0016] X1 = σ(B1 + W1D)
[0017] X j+1 =σ(B j+1+W j+1 X j )
[0018]
[0019] Where X j W represents the neuron in the j-th hidden layer. j B represents the weight matrix corresponding to the j-th hidden layer. j Let σ(x) represent the bias vector corresponding to the j-th hidden layer, j = 1, ..., H-1, and σ(x) be the activation function, D = [p L ,p R ,ρ L ,ρ R ,Δu] T p L p R ρ represents the pressure on both sides of the flow field interface. L ρ R These represent the densities on both sides of the flow field interface.
[0020] Based on the simulation results provided in the embodiments of this application, the neural network model provided in the embodiments of this application can have relatively high accuracy in solving the stress and speed of the Riemann problem.
[0021] In conjunction with the first aspect, in some implementations of the first aspect, the activation function of the neural network is the ReLU function, denoted as σ(x) = max(0,x).
[0022] In conjunction with the first aspect, in some implementations of the first aspect, the loss function of the neural network model includes an error loss function and constraints corresponding to the nonlinear equations of the two media.
[0023] This application constructs the constraint conditions of the loss function based on the discontinuity relationship of the flow field, so that the output of the neural network model can conform to the solution law of the two-medium flow field.
[0024] In conjunction with the first aspect, in some implementations of the first aspect, the neural network model is trained by inputting N training samples.
[0025] f for the i-th sample L function value, f for the i-th sample R function value, f for the i-th sample L Function prediction value, f for the i-th sample R Function prediction value, Δu (i)Let λ represent the velocity difference of the i-th sample, N represent the number of samples, and λ represent the penalty factor.
[0026] By controlling the constraints constructed by the discontinuous relationship of the flow field through the penalty factor, the effect of the constraints on the neural network training model can be controlled, so that the output of the neural network model can closely reflect the actual situation of the two-medium flow field.
[0027] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:
[0028] Based on the output of the neural network model, the pressure solution p of the two-medium Riemann problem is obtained. I and density solution ρ IL ρ IR The two-medium Riemann problem satisfies:
[0029]
[0030] In conjunction with the first aspect, in some implementations of the first aspect, the flow field model is a one-dimensional model, and the first interface conditions include:
[0031] The interfacial conditions of the first-side fluid.
[0032] The interfacial conditions of the second-side fluid,
[0033] Where ρ * p represents the virtual fluid density. * Indicates virtual fluid pressure; u * p represents the virtual fluid velocity in a one-dimensional problem. L p R ρ represents the pressure on both sides of the flow field interface. L ρ R These represent the densities on both sides of the flow field interface.
[0034] In conjunction with the first aspect, in some implementations of the first aspect, the flow field model is a multidimensional model, and the first interface conditions include:
[0035] The interfacial conditions of the first-side fluid.
[0036] The interfacial conditions of the second-side fluid,
[0037] Where ρ * p represents the virtual fluid density. * Represents virtual fluid pressure, u * The virtual fluid velocity V represents a one-dimensional problem. * V represents the virtual fluid velocity vector for a multidimensional problem.L and V R Let n represent the velocity vectors on both sides of the flow field interface, and p represent the unit normal vector of the interface. L p R ρ represents the pressure on both sides of the flow field interface. L ρ R These represent the densities on both sides of the flow field interface.
[0038] The neural network model provided in this application can be applied to solving one-dimensional and multi-dimensional interface conditions, as well as one-dimensional process models and multi-dimensional flow field models, and has a relatively wide range of applications.
[0039] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:
[0040] The second flow field state is input into the neural network model;
[0041] Based on the output of the neural network model, a second interface condition is determined, which is used to indicate the interface conditions on both sides of the flow field interface at the second time.
[0042] Based on the second interface conditions and the second flow field state, the third flow field state at the third time point is determined.
[0043] Interface conditions can be limited to a specific moment, which helps improve the accuracy of model calculations.
[0044] In conjunction with the first aspect, in some implementations of the first aspect, the first flow field state and the first interface condition both correspond to the first node of the flow field interface, and the method further includes:
[0045] The fourth flow field state of the second node of the flow field interface at the first moment is input into the neural network model;
[0046] Based on the output of the neural network model, a third interface condition is determined, which corresponds to the second node. The first interface condition and the third interface condition are used to indicate the interface conditions on both sides of the flow field interface at the first moment.
[0047] Determining the second flow field state at the second moment of the flow field interface based on the first interface conditions and the first flow field state includes:
[0048] The second flow field state is determined based on the first flow field state, the first interface condition, the third interface condition, and the fourth flow field state.
[0049] Interface conditions can be limited to a specific node, which helps improve the accuracy of model calculations.
[0050] In a second aspect, an electronic device is provided for performing the modeling method as described in any of the implementations of the first aspect above. Attached Figure Description
[0051] Figure 1 This is a schematic diagram of the initial value Riemann problem for the Euler equations of one-dimensional two-medium inviscid flow.
[0052] Figure 2 This is a schematic flowchart illustrating a modeling method provided in an embodiment of this application.
[0053] Figure 3 The neural network architecture for the two-medium Euler equation Riemann problem provided in this application embodiment.
[0054] Figure 4 A flowchart illustrating the method for constructing a neural network proxy model of compressible two-medium flow field interface conditions provided in this application embodiment.
[0055] Figure 5 A comparison between the calculation results of the surrogate model for the gas-water Riemann problem provided in the embodiments of this application and the exact solution. Detailed Implementation
[0056] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0057] Problems involving gas-liquid mixing in the combustion chamber of scramjet engines, underwater explosions, and underwater gas jets all involve the interaction of two compressible fluids. Accurately simulating the evolution of the two-medium flow field requires establishing interface condition models for different media. These models are then used to calculate the two-medium flow field, thereby obtaining simulations of interface evolution and instability processes. When defining the interface conditions for the compressible two-medium flow field, it is necessary to solve the initial value Riemann problem of the one-dimensional two-medium inviscid flow Euler equations along the interface normal.
[0058]
[0059] Here, U = [ρ, ρu, E] T F = [ρu, ρu 2 +p,(E+p)u] T Let ρ represent the conserved variables and flux along the interface normal direction, respectively. ρ is the fluid density, u is the fluid velocity, p is the fluid pressure, and E = ρe + ρu. 2 / 2 is the total energy of the fluid, and e is the internal energy per unit mass of the fluid. U L =[ρ L ,ρ L u L E L ] T and UR =[ρ R ,ρ R u R E R ] T It is determined by the position x of the flow field interface. I Two separate fluid constant states, where the subscript L indicates the left side of the flow field interface, R indicates the right side of the flow field interface, and I indicates the flow field interface itself. See [link / reference]. Figure 1 .
[0060] Initial pressure p on both sides of the flow field interface L p R Density ρ L ρ R The velocity difference Δu = u across the flow field interface R -u L Given uniform values within a specific range, the Riemann problem of the one-dimensional two-medium Euler equation can be transformed into the following nonlinear equation:
[0061] f L +f R +Δu=0
[0062] in, H = L or R
[0063] The pressure solution p of the two-medium Riemann problem can be obtained. I and density solution ρ IL ρ IR .
[0064] Figure 2 This is a schematic structural diagram of a modeling method provided in an embodiment of this application. Figure 2 The modeling method shown can be applied to, for example, Figure 1 The compressible two-medium flow field model is shown.
[0065] 110. The first flow field state of the flow field interface at the first moment is input into the neural network model, and the neural network model is used to output... and For the two-medium nonlinear equation f L +f R +Δu=0 in the function f L The predicted value, For function f R The predicted value, where the velocity difference Δu = u R -u L L represents the fluid on the first side, R represents the fluid on the second side, and u represents the fluid velocity.
[0066] Neural network models can be like Figure 3As shown. The neural network model provided in this application embodiment can be a neural network with embedded physical constraints, used to realize the regression prediction of the Riemann solution of two media, and then apply the obtained prediction results to the construction of the flow field interface conditions of different media in the flow field solution program.
[0067] In some embodiments, the neural network model includes H hidden layers, and the neural network model satisfies:
[0068] X1 = σ(B1 + W1D)
[0069] X j+1 =σ(B j+1 +W j+1 X j ),
[0070]
[0071] Where X j W represents the neuron in the j-th hidden layer. j B represents the weight matrix corresponding to the j-th hidden layer. j Let σ(x) represent the bias vector corresponding to the j-th hidden layer, j = 1, ..., H-1, where σ(x) is the activation function, and D = [p L ,p R ,ρ L ,ρ R ,Δu] T p L p R ρ represents the pressure on both sides of the flow field interface. L ρ R These represent the densities on both sides of the flow field interface.
[0072] The input data for the first hidden layer X1 of the neural network model includes the neural network's input data D = [p L ,p R ,ρ L ,ρ R ,Δu] T The output of the first hidden layer X1 can be used as the input data for the second hidden layer X2, which also includes the weight matrix W1 and bias vector B1 corresponding to the second hidden layer X2. Similarly, the (j+1)th hidden layer X... j+1 The input data includes the j-th hidden layer X j The output data, and the data of the (j+1)th hidden layer X j+1 The corresponding weight matrix W j+1 and bias vector B j+1 The last hidden layer X HThe output data can be input to the output layer of the neural network. Output layer The input data also includes the output layer The corresponding weight matrix W H+1 and bias vector B H+1 .
[0073] In some embodiments, σ can be a ReLU activation function, represented as σ(x) = max(0,x).
[0074] The training process of the neural network provided in the embodiments of this application is described below.
[0075] First, obtain N training samples, where any training sample can include p. L p R ρ L ρ R Δu and its corresponding function f L and f R N training samples are obtained, for example, through random output. Let D = [p] L ,p R ,ρ L ,ρ R ,Δu] T As input data to the neural network, the corresponding output data As [f L ,f R ] T The predicted value. Based on the loss function of the neural network model, hyperparameters such as the number of hidden layers H, the number of neurons M in each hidden layer, the batch size S, and the learning rate η can be adjusted as adjustable parameters.
[0076] In some embodiments, the loss function of the neural network model may include an error loss function and constraints corresponding to the nonlinear equations of the two media. For example, the loss function may be defined as the mean squared error loss function L. mse With the constraint L embedded in physical information pc sum:
[0077]
[0078] Here, N represents the number of samples. f for the i-th sample L function value, f for the i-th sample R function value, f for the i-th sample L Function prediction value, f for the i-th sample R Function prediction value, Δu (i)Let λ represent the velocity difference of the i-th sample, N represent the number of samples, and λ represent the penalty factor, which is generally taken in the range of [0.0001, 0.1].
[0079] Based on the neural network model and loss function, the hyperparameters in the neural network are optimized through data training, including the number of hidden layers H, the number of neurons M in each hidden layer, the batch size S, and the learning rate η, until... The training results meet the requirements.
[0080] 120. Based on the output of the neural network model, determine the first interface condition. The first interface condition is used to indicate the interface conditions on both sides of the flow field interface at the first moment.
[0081] For a one-dimensional problem, define the interface conditions for the flow field on the left side of the interface.
[0082]
[0083] Define the interface conditions for the flow field on the right side of the interface.
[0084]
[0085] For multidimensional problems, define the interface conditions for the flow field on the left side of the interface.
[0086]
[0087] Define the interface conditions for the flow field on the right side of the interface.
[0088]
[0089] Here, the superscript * indicates a virtual fluid near the interface between the two media. ρ * p represents the virtual fluid density. * Indicates virtual fluid pressure; u * The virtual fluid velocity Δu represents a one-dimensional problem. n V represents the velocity difference between the left and right sides of the flow field interface. * V represents the virtual fluid velocity vector for a multidimensional problem. L and V R Let represent the velocity vectors on both sides of the flow field interface in a multidimensional problem. Let n represent the unit normal vector of the interface. Initially, n and V... L and V R This can be specified by the user. In non-initial states, n and V... L and V R It can be obtained through simulation or other methods.
[0090] In some embodiments, n, V L and V R The solution can be combined with and Irrelevant, n and V in the first interface conditions L and V R It can belong to the first time step or the second time step; in other embodiments, n, V L and V R The solution can be combined with and Related to n and V in the first interface conditions L and V R It can belong to the first moment.
[0091] 130. Based on the first interface conditions and the first flow field state, determine the second flow field state at the second moment of the flow field interface.
[0092] The second moment can be the moment following the first moment. In other words, the flow field state of the next calculation step can be calculated from the interface conditions of the previous calculation step.
[0093] Optionally, the modeling method further includes: inputting the second flow field state into the neural network model; determining the second interface condition based on the output of the neural network model, the second interface condition being used to indicate the interface conditions on both sides of the flow field interface at the second time; and determining the third flow field state at the third time based on the second interface condition and the second flow field state.
[0094] In other words, by using steps 110 to 130 above, the flow field state at the second time step can be calculated from the interface conditions at the first time step. This allows for the selection of a suitable single-medium scheme to calculate each flow field state, pushing the solutions of all flow fields to the new time step, and obtaining the flow field of the entire computational domain based on the interface position at the new time step. By iteratively executing steps 110 to 130 above, the flow field states at multiple time steps can be obtained sequentially, ultimately yielding the simulation results of the flow field changing over time.
[0095] Optionally, the first flow field state and the first interface condition both correspond to the first node of the flow field interface. The modeling method further includes: inputting the fourth flow field state of the second node of the flow field interface at the first moment into the neural network model; determining the third interface condition based on the output of the neural network model, wherein the third interface condition corresponds to the second node, and the first interface condition and the third interface condition are used to indicate the interface conditions on both sides of the flow field interface at the first moment; and determining the second flow field state of the flow field interface at the second moment based on the first interface condition and the first flow field state, including: determining the second flow field state based on the first flow field state, the first interface condition, the third interface condition, and the fourth flow field state.
[0096] In other words, by executing steps 110-120 above, the interface conditions of a node in the flow field model at a certain moment can be obtained. By iteratively executing steps 110-120 above, the interface conditions of all nodes in the flow field model at that moment can be obtained, that is, the interface conditions of nodes in all virtual fluid regions near each fluid interface can be obtained. Then, based on the interface conditions of all nodes, the flow field state of the flow field model can be solved.
[0097] This application will be further described in detail below.
[0098] Example 1
[0099] Figure 4 The process of solving the pressure and velocity of the gas-water Riemann problem using the technique of this invention is presented. Figure 5 A comparison is presented between the calculated pressure and velocity results and the exact solution of the gas-water Riemann problem solved using the technique of this invention. The rigid gas equation of state p = (N-1)ρe-NB is used to describe air and water. Here, the left side of the interface is air, with N = 1.4, B = 0, and p... L =1.0, ρ L =0.01, u L =0.0, the right side of the interface is water, N=7.15, B=3309.0, p R =100.0, ρ R =1.0, u R =0.0. In the neural network architecture, the number of hidden layers H=2, the number of neurons in the first hidden layer M=200, the number of neurons in the second hidden layer M=80, the batch size S=1024, the learning rate η=0.01, and the penalty factor λ=0.0001. It can be seen that the calculation results of the surrogate model agree well with the exact solution.
[0100] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.
Claims
1. A modeling method, characterized in that, The modeling method is applied to a compressible two-medium flow field model, including: The first flow field state at the flow field interface at the first moment is input into the neural network model, which is used to output... and , Two-medium nonlinear equations Middle function The predicted value, For function The predicted value, in which the speed difference L represents the fluid on the first side, R represents the fluid on the second side, and u represents the fluid velocity; Based on the output of the neural network model, a first interface condition is determined, which is used to indicate the interface conditions on both sides of the flow field interface at the first moment. Based on the first interface conditions and the first flow field state, determine the second flow field state at the second moment of the flow field interface; The method further includes: Based on the output of the neural network model, the pressure solution of the two-medium Riemann problem is obtained. and density solution , The two-medium Riemann problem satisfies: 。 2. The modeling method according to claim 1, characterized in that, The neural network model includes H hidden layers, and the neural network model satisfies: ， Where X j W represents the neuron in the j-th hidden layer. j B represents the weight matrix corresponding to the j-th hidden layer. j This represents the bias vector corresponding to the j-th hidden layer, j=1,…,H-1. For activation function, , , These represent the pressures on both sides of the flow field interface. , These represent the densities on both sides of the flow field interface.
3. The modeling method according to claim 2, characterized in that, The activation function of the neural network is the ReLU function, expressed as: .
4. The modeling method according to claim 1, characterized in that, The loss function of the neural network model includes an error loss function and constraints corresponding to the nonlinear equations of the two media.
5. The modeling method according to claim 4, characterized in that, The neural network model is obtained by training N training samples. , For the i-th sample function value, For the i-th sample function value, For the i-th sample Function prediction value, For the i-th sample Function prediction value, Let λ represent the velocity difference of the i-th sample, N represent the number of samples, and λ represent the penalty factor.
6. The modeling method according to claim 1, characterized in that, The flow field model is a one-dimensional model, and the first interface conditions include: The interfacial conditions of the first-side fluid. ; The interfacial conditions of the second-side fluid, ; in Represents virtual fluid density, Represents virtual fluid pressure; Virtual fluid velocity representing a one-dimensional problem, , These represent the pressures on both sides of the flow field interface. , These represent the densities on both sides of the flow field interface.
7. The modeling method according to claim 1, characterized in that, The flow field model is a multidimensional model, and the first interface conditions include: The interfacial conditions of the first-side fluid. ; The interfacial conditions of the second-side fluid, ; in Represents virtual fluid density, Represents virtual fluid pressure. Virtual fluid velocity representing a one-dimensional problem, The virtual fluid velocity vector represents a multidimensional problem. and Let represent the velocity vectors on both sides of the flow field interface, respectively. Represents the unit normal vector of the interface. , These represent the pressures on both sides of the flow field interface. , These represent the densities on both sides of the flow field interface.
8. The modeling method according to claim 1, characterized in that, The method further includes: The second flow field state is input into the neural network model; Based on the output of the neural network model, a second interface condition is determined, which is used to indicate the interface conditions on both sides of the flow field interface at the second time. Based on the second interface conditions and the second flow field state, the third flow field state at the third time point is determined.
9. The modeling method according to claim 1, characterized in that, The first flow field state and the first interface condition both correspond to the first node of the flow field interface, and the method further includes: The fourth flow field state of the second node of the flow field interface at the first moment is input into the neural network model; Based on the output of the neural network model, a third interface condition is determined, which corresponds to the second node. The first interface condition and the third interface condition are used to indicate the interface conditions on both sides of the flow field interface at the first moment. Determining the second flow field state at the second moment of the flow field interface based on the first interface conditions and the first flow field state includes: The second flow field state is determined based on the first flow field state, the first interface condition, the third interface condition, and the fourth flow field state.
10. An electronic device, characterized in that, The electronic device is used to perform the modeling method as described in any one of claims 1 to 9.