Fluid adaptive dissipation method based on physical information graph neural network enhanced ROE format
By abstracting the computational grid into a graph structure and dynamically adjusting eigenvalues using GCN, the numerical dissipation control problem of the traditional Roe scheme under complex flow conditions is solved, achieving fluid simulation with higher accuracy and stability.
Patent Information
- Application Number
- CN202510874145.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-27
- Publication Date
- 2025-10-31
AI Technical Summary
The traditional Roe scheme performs well in capturing strong discontinuities such as shock waves, but the quality of the numerical solution depends on the precise control of numerical dissipation in the scheme. Traditional entropy correction methods lack universality and are difficult to achieve optimal results under complex flow conditions, resulting in insufficient accuracy and stability of the solution.
The computational grid of the finite volume method is abstracted into a graph structure. Graph convolutional neural networks (GCNs) are used to aggregate neighborhood information and dynamically adjust feature values to adaptively control entropy correction parameters. By introducing a loss function constrained by physical information to optimize the dissipation strategy, the stability and accuracy of the numerical solution are ensured.
It significantly improves shock wave capture capability, eliminates numerical instability, increases flow field resolution, maintains computational efficiency and numerical stability, and ensures that the calculation results conform to the basic laws of thermodynamics.
Smart Images
Figure CN120874656A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computational fluid dynamics and artificial intelligence, specifically to a fluid adaptive dissipation method based on the ROE format enhanced by a physical information graph neural network. Background Technology
[0002] Computational Fluid Dynamics (CFD), as an interdisciplinary field studying fluid flow phenomena, plays a crucial role in aerodynamics research. With the rapid development of computer hardware and the continuous advancement of numerical algorithms, CFD enables the detailed simulation and in-depth analysis of increasingly complex flow phenomena. In particular, its accurate predictions are of core value for engineering design and scientific exploration of complex flows characterized by shock waves, contact discontinuities, and multi-scale turbulent structures. Among numerous CFD numerical methods, the Finite Volume Method (FVM) is widely used due to its inherent conservation properties and good adaptability to complex geometries. Among these, the Godunov scheme, especially the Roe scheme, has become one of the standard tools for solving hyperbolic conservation law equations (such as the Euler equations) due to its superior ability to capture discontinuities, and has achieved great success in fields such as supersonic aerodynamics.
[0003] However, despite the excellent performance of the Roe scheme in capturing strong discontinuities such as shock waves, the quality of its numerical solutions largely depends on the precise control of numerical dissipation within the scheme. This is a long-standing and challenging problem. On the one hand, numerical dissipation is a necessary mechanism to suppress non-physical oscillations and ensure computational stability; on the other hand, excessive numerical dissipation can unnecessarily smooth out sharp physical features, such as reducing the steepness of shock waves, obscuring interfaces of contact discontinuities, and the fine vortex structure of dissipative turbulence, thus significantly reducing the accuracy of the solution. Traditional Roe schemes typically introduce entropy corrections to avoid generating non-physical expanding shock waves, such as the method proposed by Harten, which modifies eigenvalues to ensure the entropy condition is satisfied. While these entropy correction methods alleviate the problem to some extent, their core Harten entropy correction parameters are often based on empirical or semi-empirical formulas, lacking universality and failing to achieve optimal results under various complex flow conditions. These parameters are usually problem-dependent, and their adjustment often requires extensive trial and error and specialized experience, limiting the scheme's adaptability and reliability in unknown flow scenarios. Therefore, when faced with more challenging flow problems such as complex shock wave interactions, slowly moving weak shock waves, and high-precision turbulence simulations, the standard Roe scheme and its traditional entropy correction mechanism still fall short in balancing stability and accuracy.
[0004] To overcome these limitations, researchers have explored various adaptive dissipation control strategies. For example, Adaptive Mesh Refinement (AMR) can refine the mesh in high-gradient regions to improve local resolution, but it mainly focuses on the optimal allocation of computational resources and has limited ability to intelligently control the localized dissipation characteristics of the numerical scheme itself. Other methods attempt to dynamically adjust the size of the dissipation term or switch between different numerical schemes based on local flow field features (such as pressure gradients, density gradients, or specific shock wave sensors). For example, the ROE-SV scheme, by adding a shear-viscosity structure to the ROE scheme, alleviates the severity of instability to some extent, but instability still exists. While these strategies based on simple sensors improve the adaptability of the scheme to some extent, they often fail to fully capture the complex topology and multi-scale characteristics of the flow field, and the threshold settings of their criteria are often empirical. Therefore, how to design a numerical method that can more deeply understand the physical characteristics of the local flow field and accordingly perform refined and adaptive dissipation control is one of the key scientific problems that urgently need to be solved in the field of CFD.
[0005] In recent years, artificial intelligence technologies, represented by deep learning, especially graph neural networks (GNNs), have demonstrated enormous potential in processing non-Euclidean structured data, providing a novel perspective for solving the aforementioned challenges in CFD. Graph neural networks, particularly graph convolutional networks (GCNs), can directly operate on graph-structured data, effectively aggregating node neighborhood information to learn and identify complex spatial dependencies and patterns. Considering that the computational grid of FVMs inherently possesses a graph structure (cells as nodes, interfaces as edges), this lays the foundation for the application of GNNs in the field of CFD. The core motivation of this research is to explore how to leverage the powerful graph learning capabilities of GCNs to perceive and understand the local flow field topology features of each interface on the computational grid, and based on this understanding, adaptively adjust key parameters in the Roe scheme—specifically, by modulating eigenvalues to control numerical dissipation related to entropy conditions—thereby maximizing the accuracy and physical realism of the solution while ensuring computational stability. Summary of the Invention
[0006] This paper proposes a fluid adaptive dissipation method based on a physical information graph neural network-enhanced ROE scheme, aiming to solve the numerical dissipation control problem faced by the traditional ROE scheme in computational fluid dynamics (CFD).
[0007] The technical method proposed in this invention includes the following parts:
[0008] Step 1: Abstract the computational mesh of the Finite Volume Method (FVM) into a graph structure. The specific process is as follows:
[0009] (1) The abstract FVM mesh is a graph θ = (v, ε), where each node v in the set V is... i A computational unit c in the corresponding FVM i The set E is then composed of the edges e connecting adjacent nodes. ij Composition, representing the computational unit c i With c j The physical interface between f ij ;
[0010] (2) Define a feature vector x for each node. i First, there are the basic physical quantities, including the conserved variables within the unit (density, momentum component, total energy) and the original variables (density, velocity component, pressure). Second, there are the derived physical quantities, such as Mach number, speed of sound, key variable gradient (pressure / density gradient), velocity divergence, and vorticity.
[0011] (3) For each edge e ij Define eigenvectors Includes unit normal vector n ij Area A ij centroid vector r ij .
[0012] Step 2: Aggregate neighborhood information using the GCN model to predict the entropy correction parameter at the interface. The specific steps are as follows:
[0013] (1) Build a dedicated GCN network model;
[0014] (2) The mapping relationship between local flow field characteristics and optimal dissipation parameters is learned by aggregating neighborhood information;
[0015] Step 3: Predict the flow field parameters at the next moment based on the flow field characteristics at the current moment. Then, the interface f is calculated based on the Harten-type entropy correction function. ij Modified eigenvalue modulus of each feature field k Then assemble the GCN-modulated Roe stream.
[0016] Step 4: Construct a specialized loss function, including using the mean square error of the enhanced numerical flux versus the target numerical flux as a numerical loss term, and an entropy constraint loss term to ensure that the numerical solution conforms to the second theorem of thermodynamics.
[0017] The beneficial effects of this invention are as follows:
[0018] (1) The present invention improves the shock wave capture capability by dynamically adjusting the eigenvalue regularization parameter through GCN network, and effectively eliminates the numerical instability phenomenon that occurs in high-speed flow in traditional methods.
[0019] (2) The present invention significantly improves the flow field resolution through the neighborhood information aggregation mechanism of graph structure, and can more clearly capture fine flow structures such as contact discontinuities and eddies.
[0020] (3) While maintaining computational efficiency, the present invention enhances numerical stability and can operate reliably even under extreme conditions.
[0021] (4) This invention ensures that the calculation results conform to the basic laws of thermodynamics through a physical constraint mechanism. Attached Figure Description
[0022] Figure 1 This is a flowchart of a fluid adaptive dissipation method based on a physical information graph neural network-enhanced ROE format;
[0023] Figure 2 An explanatory diagram for abstracting the computational grid into a graph;
[0024] Figure 3 A comparison of the results of the three-dimensional hypersonic flow around a cylinder; Detailed Implementation
[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0026] Figure 1 The flowchart of the fluid adaptive dissipation method based on the enhanced ROE format of the present invention is presented. As shown in the figure, the present invention is implemented as follows: A fluid adaptive dissipation method based on the enhanced ROE format using a physical information graph neural network includes the following steps:
[0027] S101: Abstract the computational grid into a graph structure;
[0028] S102: Build GCN;
[0029] S103: Dynamically adjust the eigenvalue modulus;
[0030] S104: Introduce physical information constraints;
[0031] In step S101, the specific steps for abstracting the computational mesh into a graph structure are as follows:
[0032] The abstract FVM mesh is a graph θ = (v, ε), where each node v in the set V is... i A computational unit c in the corresponding FVM i The set E is then composed of the edges e connecting adjacent nodes. ij Composition, representing the computational unit c i With cj The physical interface between f ij .
[0033] Define a feature vector x for each node i First, there are the basic physical quantities, including the conserved variables within the unit (density, momentum component, total energy) and the original variables (density, velocity component, pressure). Second, there are the derived physical quantities, such as Mach number, speed of sound, key variable gradient (pressure / density gradient), velocity divergence, and vorticity.
[0034] For each edge e ij Define eigenvectors Includes unit normal vector n ij Area A ij centroid vector r ij .
[0035] In step S102, a GCN with an L layer is constructed.
[0036] The information transmission between nodes is as follows: node v at level l+1 i Hidden representation It is achieved by aggregating its own representation at layer l. and all its neighboring nodes v j Representation of ∈N(i) at level l This is used for calculation. This process can usually be formalized as... Where H (0) It is the initial node feature matrix X. It is an adjacency matrix with self-connections added. It is its angle matrix, σ is the trainable weight matrix of the l-th layer, and σ is the nonlinear activation function. From a message-passing perspective, in each layer, each node sends a "message" to its neighbors and receives messages from them, then combines this information with its own data for aggregation and nonlinear transformation to form a new, higher-level feature representation. As the number of GCN layers increases, the receptive field of the nodes expands, enabling the final node embedding to capture information from multi-hop neighbors, thus understanding a larger range of flow field structures.
[0037] After L graph convolutional layers, GCN provides each unit v. i Generate node embedding vectors To predict interface-specific parameters Embedding vectors of two units sharing the interface and They are combined (e.g., splicing, averaging, or differencing operations) and then passed through one or more fully connected layers of an MLP. edge :
[0038]
[0039] Where M is the number of characteristic fields (e.g., M = 3 for the one-dimensional Euler equation and M = 4 for the two-dimensional Euler equation). Each The output activation function must be positive to maintain the physical relevance of the Harten-type correction.
[0040] In step S103, the flow field parameters for the next time step are predicted using the GCN based on the flow field characteristics at the current time step. Then, the interface f is calculated based on the Harten-type entropy correction function. ij Modified eigenvalue modulus of each feature field k
[0041]
[0042] Then, the GCN-modulated Roe stream Assemble as follows:
[0043]
[0044] in diagonal elements are The diagonal matrix. This flux is then used in the update step of the FVM.
[0045] In step S104, to train a graph convolutional neural network (GCN) to optimize adaptive dissipation in the Roe format, the present invention obtains the GCN-enhanced numerical flux F through supervision. j GCN , and the corresponding target numerical flux The difference between them is measured as a data loss function. Mean Squared Error (MSE), which is the square of the L2 norm, is typically used to quantify this difference.
[0046]
[0047] Where N samples It represents the total number of flow field grids participating in the training in the current training batch, and ||·|| represents the Euclidean norm of the vector difference.
[0048] To ensure that the numerical format enhanced by the graph neural network (GNN) adheres to fundamental thermodynamic principles, particularly the second law of thermodynamics, this invention introduces a physical information loss term L. entropy .
[0049] The core of this method lies in establishing a rigorous mathematical entropy constraint mechanism. For the Euler equations, we select a convex entropy function with a clear physical meaning. Where p is pressure and is the specific heat ratio. This entropy function is inversely proportional to the physical entropy; its increase corresponds to a decrease in physical entropy. Based on this, we further define entropy flux. and entropy variables Together, they form the mathematical foundation of entropy analysis.
[0050] In the specific implementation, we define the numerical entropy generation rate D at each computation interface j. S ,j(U L U R ,F j GCN )=(V(U R )-V(U L )) T F j GCN (U L U R )-(Q(U R )-Q(U L According to the entropy stability theory, to ensure that the numerical solution conforms to the second law of thermodynamics, D must be satisfied. S,j ≤0. Therefore, we designed a special entropy-constrained loss function L. entropy The ReLU function penalizes any situation that leads to a decrease in entropy. The small parameter ε0 introduced here can flexibly adjust the minimum allowable dissipation, ensuring stability while avoiding excessive dissipation.
[0051] experiment:
[0052] To verify the effectiveness of the method proposed in this invention, we conducted comparative experiments with other Roe schemes using a three-dimensional hypersonic flow around a cylinder problem. The schemes compared included the Roe scheme, the Roe-SV scheme, and the GCN-Roe scheme of this invention.
[0053] In our experiments, we set the number of layers in the GCN model to L=3. The first graph convolutional layer maps the input feature dimension to 128 dimensions; the subsequent two hidden graph convolutional layers each maintain a 256-dimensional feature representation. A rectified linear unit (ReLU) is used as the activation function after each graph convolutional layer. To stabilize the training process, layer normalization is applied after the activation function of each GCN layer. The label values are calculated using a third-order WENO format, ensuring the accuracy and reliability of the data labels. The model is trained using the Adam optimizer with an initial learning rate of 5×10⁻⁶. -4A learning rate decay strategy was applied during training: the learning rate was multiplied by 0.5 if the total loss on the validation set did not decrease for 10 consecutive epochs. The batch size was set to 64. Training lasted for 200 epochs, and early stopping was enabled.
[0054] This paper presents a three-dimensional hypersonic flow around a cylinder, simulating the flow field structure formed by a hypersonic flow at Mach number 20 passing through a cylinder. A 40×16×20 hexahedral body-fitted mesh is used in the calculation. The initial flow field for the entire region is (p, u, v, w) = (1.4, 20, 0, 1). The time step selected during training is Δt = 1 × 10⁻⁶. -2 The training time steps were 380, and the time steps from 380 to 400 were used for testing. Figure 3 As can be seen, the ROE scheme produces obvious numerical oscillations and Carbuncle phenomena near the shock wavefront. Although the numerical results of the Roe-SV scheme do not show non-physical Carbuncle phenomena, they do show slight numerical oscillations. The Roe scheme based on GCN dissipation has good numerical stability and yields a stable bow shock structure.
[0055] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A fluid adaptive dissipation method based on a physical information graph neural network-enhanced ROE format, characterized in that, Includes the following steps: Step 1: Abstract the computational grid of the Finite Volume Method (FVM) into a graph structure; Step 2: Construct a dedicated GCN network model; Step 3: Combine Harten-type entropy correction function to dynamically adjust eigenvalue modulus and generate high-fidelity numerical flux; Step 4: Introduce physical information constraints based on entropy to ensure that the numerical solution conforms to the second law of thermodynamics.
2. The fluid adaptive dissipation method based on the physical information graph neural network-enhanced ROE format according to claim 1, characterized in that, Step one, which abstracts the computational mesh of the finite volume method into a graph structure, includes: Step 1: Abstract the FVM mesh as a graph θ = (v, ε), where each node v in the set V i A computational unit c in the corresponding FVM i The set E is then composed of the edges e connecting adjacent nodes. ij Composition, representing the computational unit c i With c j The physical interface between f ij . Step 2: Define a feature vector x for each node. i First, there are the basic physical quantities, including the conserved variables within the unit (density, momentum component, total energy) and the original variables (density, velocity component, pressure). Second, there are the derived physical quantities, such as Mach number, speed of sound, key variable gradient (pressure / density gradient), velocity divergence, and vorticity. Step 3: For each edge e ij Define eigenvectors Includes unit normal vector n ij Area A ij centroid vector r ij .
3. The fluid adaptive dissipation method based on the physical information graph neural network-enhanced ROE format according to claim 1, characterized in that, Step two involves aggregating neighborhood information using the GCN model to predict entropy correction parameters at the interface, including: Step 1: Construct a dedicated GCN network model; Step 2: Learn the mapping relationship between local flow field characteristics and optimal dissipation parameters by aggregating neighborhood information.
4. The fluid adaptive dissipation method based on the physical information graph neural network-enhanced ROE format according to claim 1, characterized in that, Step three, which combines the Harten-type entropy correction function to dynamically adjust the eigenvalue modulus and generate a high-fidelity numerical flux, includes: Step 1: Correct parameters by predicting entropy using the model. Step 2: Calculation interface for Harten-type entropy correction function f ij Modified eigenvalue modulus of each feature field k Step 3, Roe Flow Assembly.
5. The fluid adaptive dissipation method based on the physical information graph neural network-enhanced Roe format according to claim , characterized in that, Step four introduces physical information constraints based on entropy generation to ensure that the numerical solution conforms to the second law of thermodynamics, including: Step 1: Use relative error as the numerical term of the loss function; Step 2: Add physical constraint information based on entropy as a physical term in the loss function to ensure that the numerical solution conforms to the second law of thermodynamics.