Hybrid Acceleration Method and Related Device for Computational Fluid Dynamics Simulation Based on Data Dimensionality Reduction and Multigrid Interpolation

Abstract

This application discloses a hybrid acceleration method and related apparatus for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, relating to the field of computational fluid dynamics technology. The method includes: calling a reduced-order prediction model based on the fine-grid physical field data of the current time step to generate a coarse-grid predicted physical field for the current time step; spatially interpolating the coarse-grid predicted physical field of the current time step and mapping it onto a fine-grid to generate initial fine-grid field data for the current time step; using the initial fine-grid field data of the current time step as initial conditions, continuing to perform computational fluid dynamics solutions for the next number of time steps on the fine-grid to generate updated fine-grid physical field data; using the updated fine-grid physical field data as the benchmark for the next iteration cycle until a preset total simulation time step is reached, and outputting the final simulation result of the target physical field. This application fundamentally reduces the dependence of high-fidelity simulation on fine-grid computational resources.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics technology, and in particular to a hybrid acceleration method and related apparatus for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation. Background Technology

[0002] Computational Fluid Dynamics (CFD), as a crucial tool for studying the laws governing fluid motion, has played a fundamental role in numerous scientific and engineering fields. As research objects become increasingly complex and sophisticated, engineering practice demands greater depth and breadth in its understanding of flow phenomena. High-fidelity numerical simulations typically require lengthy unsteady solutions on extremely fine computational grids, inevitably leading to significant computational resource consumption and time costs. This high computational cost has become a prominent bottleneck restricting the in-depth application of CFD in rapid design iterations, multi-scheme comparisons, and large-scale parameter spaces. Therefore, effectively improving the computational efficiency of high-fidelity flow simulations while ensuring the reliability of the solutions has become one of the key scientific problems urgently needing to be solved in the field of computational fluid dynamics.

[0003] To improve the efficiency of computational fluid dynamics (CFD) solutions, scholars both domestically and internationally have conducted extensive and fruitful research. Early research focused primarily on accelerating the numerical algorithms themselves. This involved improving linear system solvers, developing preconditioning techniques, and employing adaptive mesh refinement strategies to reduce the computational cost per iteration without altering the discrete form of the governing equations. While these methods achieved significant speedups in specific examples, their effectiveness often heavily depends on the mathematical characteristics and mesh topology of the problem. When the geometric configuration or physical boundary conditions of the computational model change, the acceleration strategies tailored to the original problem may struggle to maintain their efficiency advantage. Researchers need a solid foundation in numerical computation to re-adjust and validate these strategies, which to some extent limits their generalization ability and application value in complex engineering problems.

[0004] In recent years, the rapid development of data-driven technologies has provided new ideas for accelerating computational fluid dynamics. An important research direction is to utilize neural networks to construct surrogate models or reduced-order models. By learning flow patterns from high-fidelity sample data, these models establish a rapid mapping relationship between input parameters and key flow field outputs. Reduced-order models, in particular, project high-dimensional flow field information into a low-dimensional subspace, significantly reducing computational degrees of freedom while preserving the dominant flow structure. These methods have demonstrated a good balance between accuracy and efficiency in predicting various flow and heat transfer problems. However, most current surrogate and reduced-order models primarily serve as backend replacement tools independent of the solver's iterative process, focusing on reconstructing or predicting the final calculation results, with limited integration with the underlying numerical solution framework.

[0005] To overcome these limitations, researchers have begun exploring deeper integration of data-driven modules into the iterative solution process of computational fluid dynamics. A series of coupled frameworks have been proposed, such as using neural networks to predict intermediate variables during iteration to reduce the number of convergence steps, or alternating computations with reduced-order models and standard numerical solvers to improve efficiency. Some studies have attempted to integrate machine learning models into open-source computational frameworks to replace local computational steps such as turbulence models, or to reconstruct high-fidelity flow fields from coarse-grid solutions. These exploratory works have preliminarily verified the feasibility of data-driven modules and numerical solvers working together. Nevertheless, existing methods still have certain limitations in practical applications. Some strategies still rely on high-cost computations on fine-grid surfaces during training or deployment, making it difficult to fundamentally eliminate the resource burden of fine-grid solutions. Other methods aimed at reconstructing high-precision flow fields from low-resolution results are more often used as post-processing steps after the solution is completed, rather than directly affecting the solution process to reduce iterative computation. These factors collectively mean that current techniques still have room for improvement in balancing computational accuracy and acceleration stability. Summary of the Invention

[0006] The purpose of this application is to provide a hybrid acceleration method and related apparatus for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, which can fundamentally reduce the dependence of high-fidelity simulation on fine-grid computing resources.

[0007] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, including: The initial calculation parameters of the target physical field are obtained, and a computational fluid dynamics solution with a preset initial time step is performed on a fine mesh based on the initial calculation parameters to generate initial fine mesh physical field data. Based on the fine-grid physical field data of the current time step, a pre-built reduced-order prediction model is invoked to generate the coarse-grid predicted physical field of the current time step; the reduced-order prediction model is constructed based on the computational fluid dynamics simulation results on the coarse grid; in the first iteration cycle, the fine-grid physical field data of the current time step is the fine-grid physical field data of the last time step in the initial fine-grid physical field data; Spatial interpolation is performed on the coarse-grid predicted physical field at the current time step to generate the interpolated result at the current time step, and the interpolated result at the current time step is mapped onto the fine-grid to generate the fine-grid initial field data at the current time step. Using the initial field data of the fine mesh at the current time step as the initial conditions for the computational fluid dynamics solution, the computational fluid dynamics solution for the next preset time step is continued on the fine mesh to generate updated fine mesh physical field data; Determine whether the preset total simulation time step has been reached; If so, output the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data, and use the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data as the final simulation result of the target physical field; If not, the fine-grid physical field data of the last time step in the updated fine-grid physical field data will be used as the fine-grid physical field data of the current time step in the next iteration cycle, and the process will return to the step "Based on the fine-grid physical field data of the current time step, call the pre-built reduced-order prediction model to generate the coarse-grid prediction physical field of the current time step".

[0008] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described above.

[0009] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described above.

[0010] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described above.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a hybrid acceleration method and related apparatus for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation. By calling a pre-built reduced-order prediction model based on the fine-grid physical field data of the current time step, a coarse-grid predicted physical field of the current time step is generated. This solves the problem that existing data-driven methods still rely on the high cost of fine-grid computation during the training or deployment phase, making it difficult to fundamentally get rid of the resource burden. It enables online rapid prediction of the flow field by building a reduced-order model based only on the coarse-grid simulation results, significantly reducing the dependence on fine-grid data.

[0012] By spatially interpolating the physical field predicted by the coarse grid at the current time step, the interpolated result at the current time step is generated. The interpolated result at the current time step is then mapped onto the fine grid to generate the initial field data of the fine grid at the current time step. This solves the interface problem that the coarse grid prediction result cannot be directly used as the input of the fine grid solver and requires cross-grid data transfer. It realizes the seamless connection between the coarse grid prediction field and the fine grid solution space, providing high-quality initial conditions for subsequent fine grid calculations.

[0013] By using the initial field data of the fine mesh at the current time step as the initial condition for the computational fluid dynamics solution, and continuing to perform the computational fluid dynamics solution for the next preset time step on the fine mesh, updated fine mesh physical field data is generated. This solves the problem that the reduced-order model as an independent post-processing tool cannot directly reduce the amount of iterative computation. It realizes the deep integration of data-driven prediction and numerical solver, and suppresses error accumulation through periodic fine mesh correction, so that the acceleration process and the solution process can be carried out in tandem.

[0014] By using the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data as the fine-mesh physical field data of the current time step in the next iteration cycle, and returning to the iteration until the preset total simulation time step is reached, the final simulation result of the target physical field is output. This solves the problem of stability degradation caused by error accumulation in existing acceleration methods during long-term simulations. It realizes continuous correction of prediction bias in an iterative closed-loop manner, and steadily advances to the preset simulation endpoint while ensuring computational accuracy, significantly improving the robustness and engineering applicability of the acceleration framework. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1This is an application environment diagram of a hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, as described in Embodiment 1 of this application. Figure 2 This is a flowchart illustrating a hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, as described in Embodiment 1 of this application. Figure 3 This is a schematic diagram of the hybrid acceleration framework process in Embodiment 2 of this application; Figure 4 This is a schematic diagram of the nearest neighbor interpolation method in Embodiment 2 of this application; Figure 5a This is a schematic diagram of the thermal conductivity model provided in Embodiment 3 of this application; Figure 5b This is a schematic diagram of the heated backward step flow model provided in Embodiment 3 of this application; Figure 6 A schematic diagram of the training results of the reduced-order prediction model in Example 1 provided in Embodiment 3 of this application; Figure 7 This is a schematic diagram showing the singular values ​​and cumulative energy percentages of each flow field variable under different modal orders in Example 2 provided in Embodiment 3 of this application; Figure 8 A schematic diagram illustrating the regression performance of the reduced-order prediction model provided in Embodiment 3 of this application for predicting the time modal coefficients in Example 2; Figure 9 This is a schematic diagram comparing the transient absolute error and mean absolute error of the hybrid CFD-ROM obtained by training with different coarse grid resolutions, as provided in Embodiment 3 of this application. Figure 10a The evolution diagram of the absolute temperature error over time obtained by hybrid CFD-ROM simulation under five coarse grid resolution training conditions provided in Example 2 of Embodiment 3 of this application; Figure 10b The diagram showing the evolution of the absolute pressure error over time obtained from hybrid CFD-ROM simulation under five coarse grid resolution training conditions, as provided in Example 2 of Embodiment 3 of this application; Figure 10c The following is a schematic diagram illustrating the evolution of the absolute velocity error over time obtained from hybrid CFD-ROM simulation under five coarse grid resolution training conditions, as provided in Example 2 of Embodiment 3 of this application. Figure 11a A schematic diagram comparing the results of hybrid CFD-ROM calculations with fine-grid CFD results trained at different coarse-grid resolutions for the temperature field provided in Embodiment 3 of this application at τ=49 s; Figure 11bA schematic diagram comparing the results of hybrid CFD-ROM calculations with fine-grid CFD results trained at different coarse-grid resolutions for the pressure field provided in Embodiment 3 of this application at τ=49 s; Figure 11c A schematic diagram comparing the results of hybrid CFD-ROM calculations with fine-grid CFD results trained at different coarse-grid resolutions for the velocity field provided in Embodiment 3 of this application at τ=49 s; Figure 12 A schematic diagram comparing the transient absolute error and mean absolute error of Example 1 under different CFD(i)–ROM(j) interpolation strategies provided in Embodiment 3 of this application; Figure 13a This is a schematic diagram comparing the transient absolute error and mean absolute error of temperature relative to fine-grid CFD in Example 2 under different interpolation strategies provided in Embodiment 3 of this application. Figure 13b This is a schematic diagram comparing the transient absolute error and mean absolute error of pressure relative to fine-grid CFD in Example 2 under different interpolation strategies provided in Embodiment 3 of this application. Figure 13c This is a schematic diagram comparing the transient absolute error and mean absolute error of the velocity relative to the fine-grid CFD in Example 2 under different interpolation strategies provided in Embodiment 3 of this application. Figure 14 A schematic diagram comparing the velocity field and error distribution of the hybrid CFD-ROM with the fine-grid CFD results for the three interpolation strategies provided in Embodiment 3 of this application; Figure 15 This is a schematic diagram of the structure of a computer device provided in Embodiment 4 of this application. Detailed Implementation

[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation provided in this application can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send the initial calculation parameters of the target physics field to server 104. Server 104 performs a computational fluid dynamics solution for a preset number of initial time steps on a fine mesh based on the initial calculation parameters, generating initial fine mesh physics field data. Based on the fine mesh physics field data of the current time step, it calls a reduced-order prediction model to generate a coarse mesh predicted physics field for the current time step. In the first iteration cycle, the fine mesh physics field data of the current time step is the fine mesh physics field data of the last time step in the initial fine mesh physics field data. Spatial interpolation is performed on the coarse mesh predicted physics field of the current time step and mapped onto the fine mesh to generate the initial fine mesh field data of the current time step. Using the initial fine mesh field data of the current time step as the initial condition, the computational fluid dynamics solution for the next number of time steps is performed on the fine mesh to generate updated fine mesh physics field data. The updated fine mesh physics field data is used as the benchmark for the next iteration cycle until the preset total simulation time step is reached, and the final simulation result of the target physics field is output. Server 104 can feed back the obtained final simulation result of the target physics field to terminal 102.

[0020] The terminal 102 can be, but is not limited to, various desktop computers, laptops, and IoT devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers, or it can be a cloud server.

[0021] In one exemplary embodiment, such as Figure 2 As shown, a hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 205. Wherein: Step 201: Obtain the initial calculation parameters of the target physical field, and perform computational fluid dynamics solution on the fine mesh with a preset initial time step based on the initial calculation parameters to generate initial fine mesh physical field data.

[0022] Step 202: Based on the fine-grid physical field data of the current time step, call the pre-built reduced-order prediction model to generate the coarse-grid prediction physical field of the current time step; the reduced-order prediction model is built based on the computational fluid dynamics simulation results on the coarse grid; in the first iteration cycle, the fine-grid physical field data of the current time step is the fine-grid physical field data of the last time step in the initial fine-grid physical field data.

[0023] Step 203: Spatial interpolation is performed on the coarse-grid predicted physical field of the current time step to generate the interpolated result of the current time step, and the interpolated result of the current time step is mapped onto the fine-grid to generate the fine-grid initial field data of the current time step.

[0024] Step 204: Using the initial field data of the fine mesh at the current time step as the initial condition for the computational fluid dynamics solution, continue to perform the computational fluid dynamics solution for the next preset time step on the fine mesh to generate updated fine mesh physical field data.

[0025] Step 205: Determine whether the preset total simulation time step has been reached; if yes, output the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data, and use the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data as the final simulation result of the target physical field; if no, use the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data as the fine-mesh physical field data of the current time step in the next iteration cycle, and return to step "Based on the fine-mesh physical field data of the current time step, call the pre-built reduced-order prediction model to generate the coarse-mesh prediction physical field of the current time step".

[0026] Implementing steps 201 to 205 above has the following beneficial effects: (1) By calling the pre-built reduced-order prediction model based on the fine-grid physical field data of the current time step, the coarse-grid predicted physical field of the current time step is generated. This solves the problem that existing data-driven methods still rely on the high cost of fine-grid computation during the training or deployment phase and are difficult to fundamentally get rid of the resource burden. It realizes that the flow field can be predicted online quickly by building a reduced-order model based only on the coarse-grid simulation results, which significantly reduces the dependence on fine-grid data.

[0027] (2) By performing spatial interpolation on the physical field predicted by the coarse grid at the current time step, the interpolated result at the current time step is generated, and the interpolated result at the current time step is mapped onto the fine grid to generate the initial field data of the fine grid at the current time step. This solves the interface problem that the coarse grid prediction result cannot be directly used as the input of the fine grid solver and requires cross-grid data transfer, and realizes the seamless connection between the coarse grid prediction field and the fine grid solution space, providing high-quality initial conditions for subsequent fine grid calculations.

[0028] (3) By using the initial field data of the fine mesh at the current time step as the initial condition for computational fluid dynamics solution, the computational fluid dynamics solution of the next time step is continued on the fine mesh to generate updated fine mesh physical field data. This solves the problem that the reduced-order model as an independent post-processing tool cannot directly reduce the amount of iterative computation. It realizes the deep integration of data-driven prediction and numerical solver. The periodic fine mesh correction suppresses error accumulation, so that the acceleration process and the solution process are carried out in tandem.

[0029] (4) By using the fine-grid physical field data of the last time step in the updated fine-grid physical field data as the fine-grid physical field data of the current time step in the next iteration cycle, and returning to the iteration until the preset total simulation time step is reached, the final simulation result of the target physical field is output. This solves the problem of stability decline caused by error accumulation in the existing acceleration method during long-term simulation. It realizes continuous correction of prediction deviation in an iterative closed-loop manner, and steadily advances to the preset simulation endpoint while ensuring computational accuracy, which significantly improves the robustness and engineering applicability of the acceleration framework.

[0030] In summary, this application constructs a hybrid iterative framework that alternates between order-reduced prediction models and fine-mesh solving. In the offline stage, it relies solely on low-cost coarse-mesh data for model training, while in the online stage, it alternates between periodic fine-mesh correction and coarse-mesh prediction. This fundamentally reduces the dependence of high-fidelity simulation on fine-mesh computing resources and effectively suppresses the accumulation of errors in data-driven prediction. While balancing computational accuracy and acceleration, it improves the stability and versatility of the method, providing a practical and feasible technical path for efficient and high-fidelity numerical simulation of complex flow and heat transfer problems.

[0031] Further, step 202, based on the fine-grid physical field data of the current time step, calls the pre-built reduced-order prediction model to generate the coarse-grid predicted physical field of the current time step, specifically including: Step 2021: Input the fine-grid physical field data of the current time step into the pre-built reduced-order prediction model to predict the corresponding prediction mode coefficient vector.

[0032] Step 2022: Linearly combine the predicted mode coefficient vector with the pre-stored dominant mode matrix and truncated singular value matrix in the reduced-order prediction model to reconstruct the coarse-grid predicted physics field at the current time step.

[0033] Furthermore, the construction process of the reduced-order prediction model in step 202 specifically includes: Step a1: Select multiple training conditions and corresponding operating parameters within the preset parameter space, and perform computational fluid dynamics simulation on the corresponding training conditions based on the operating parameters on a coarse grid to obtain the target physics snapshot dataset; the target physics snapshot dataset includes target physics snapshots under multiple conditions and multiple time steps.

[0034] Step a2 involves orthogonally decomposing the target physical field snapshot dataset to extract the dominant mode matrix, the truncated singular value matrix, and the mode coefficient vector corresponding to each target physical field snapshot, which characterize the main features of the target physical field.

[0035] Step a3: Construct the training dataset; the training dataset includes multiple sample data, each of which includes the running parameters and modal coefficient vectors corresponding to each target physical field snapshot.

[0036] Step a4: Based on the training dataset, the pre-constructed artificial neural network model is trained to obtain the trained artificial neural network model. Then, based on the dominant mode matrix, the truncated singular value matrix, and the trained artificial neural network model, a reduced-order prediction model is constructed. The artificial neural network model is a multilayer perceptron neural network, which includes an input layer, multiple hidden layers, and an output layer. The input layer corresponds to the operating parameters corresponding to each target physical field snapshot, the output layer corresponds to the mode coefficients corresponding to each target physical field snapshot, and each hidden layer uses the ReLU activation function.

[0037] Further, in step a2, orthogonal decomposition is performed on each target physics snapshot in the target physics snapshot dataset to extract the dominant mode matrix, the truncated singular value matrix, and the mode coefficient vector corresponding to each target physics snapshot, which characterize the main features of the target physics. Specifically, this includes: Step a21: Combine all target physical field snapshots in the target physical field snapshot dataset into a dataset matrix, and perform singular value decomposition on the dataset matrix to obtain the spatial basis vector matrix, singular value matrix, and right singular vector matrix.

[0038] Step a22: Sort the singular value matrix in descending order, and determine the truncation order based on the cumulative energy ratio of the singular values ​​in the sorted singular value matrix.

[0039] Step a23: Extract the first few truncation order spatial basis vectors from the spatial basis vector matrix as the dominant mode matrix, extract the first few truncation order singular values ​​from the singular value matrix to form the truncated singular value matrix, and extract the first few truncation order column vectors from the right singular vector matrix as the mode coefficient vectors corresponding to each target physical field snapshot.

[0040] Further, in step 203, spatial interpolation is performed on the coarse-grid predicted physical field at the current time step to generate the interpolated result for the current time step. This interpolated result is then mapped onto the fine-grid to generate the fine-grid initial field data for the current time step. Specifically, this includes: Step 2031: Using the nearest neighbor interpolation method, find the current coarse grid node that is closest to the current fine grid node in the coarse grid predicted physics field at the current time step, and determine the physical quantity value corresponding to the current coarse grid node as the result after interpolation at the current time step; the current fine grid node is any node on the fine grid.

[0041] Step 2032: Assign the interpolated results of the current time step to the corresponding nodes on the fine grid to generate the initial field data of the fine grid for the current time step.

[0042] Example 2 In another exemplary embodiment of this application, in order to accurately describe the specific implementation process of the proposed hybrid acceleration framework consisting of an offline training phase and an online solving phase, and by combining Proper Orthogonal Decomposition (POD) and artificial neural network technology, an offline reduced-order model is constructed and alternately coupled with a fine-mesh computational fluid dynamics solver in the online solving phase, thereby achieving simulation acceleration.

[0043] Hybrid acceleration framework description: such as Figure 3 As shown, the hybrid acceleration framework consists of two parts: an offline training phase and an online solution phase.

[0044] In the offline training phase, a representative set of training conditions is first selected within a predefined parameter space, and CFD numerical simulations are performed on a relatively coarse computational grid (i.e., a coarse grid). Snapshot data of the target physical field (such as temperature, pressure, and velocity) are collected under multiple training conditions and at multiple time steps. Subsequently, these coarse grid solutions are expanded spatially to form a dataset matrix, and orthogonal decomposition is used to extract the dominant modes characterizing the main flow and heat transfer features and their corresponding modal coefficients. Further, an artificial neural network model is trained to establish a nonlinear mapping relationship between operating parameters and time information to modal coefficients, thereby constructing a reduced-order prediction model (ROM) capable of rapidly reconstructing the coarse grid flow field under any given input conditions.

[0045] Building upon this foundation, the online solution phase couples the ROM with high-fidelity fine-mesh CFD computation through a time-stepping approach. For a given target training condition, the CFD solver first runs several initial steps on the fine mesh to obtain a sufficiently analytical early transient solution. In subsequent iterations, the trained ROM is invoked, and the coarse-mesh flow field is directly predicted based on the fine-mesh physics data of the current time step. Subsequently, this coarse-mesh prediction result is mapped to the fine mesh using an interpolation method and used as the initial field input solver for the next stage of CFD computation. By alternating between the ROM prediction field and the short-time CFD propagation phases on the fine mesh, this framework can significantly reduce the overall computational cost while maintaining high accuracy.

[0046] Orthogonal decomposition: To achieve a low-dimensional representation of the flow field data, a series of snapshot data of the target physical field obtained from numerical simulation (corresponding to solutions at different times and under different operating conditions) are first organized into a dataset matrix. ,in, This represents the total number of spatial grid nodes (i.e., the dimension of each snapshot). The number of snapshots is equal to the number of time steps. Number of training conditions The product of, i.e. Subsequently, Singular Value Decomposition (SVD) is performed on the dataset matrix to extract the dominant modes characterizing the main flow and heat transfer features. This decomposition can be expressed as: (1); in, The dataset matrix; The column vectors are orthogonal spatial basis vectors, i.e., POD modes; For a singular value matrix, its diagonal elements Characterize the energy intensity corresponding to each mode and arrange them in descending order; It is a right singular vector matrix, and its column vectors correspond to the time coefficients of each mode.

[0047] To achieve effective order reduction while preserving key feature information, the SVD results are truncated, retaining only the first few features. The dominant singular values ​​and their corresponding The first mode is used to construct a low-dimensional approximate model. After truncation, the matrix... It can be approximated as: (2); in, This is the matrix of dominant modes retained after truncation, containing the retained dominant modes; The truncated singular value matrix, This is the corresponding reserved modal coefficient matrix. Any snapshot of the target's physical field can be obtained from this. The linear combination of modes is approximately represented by the combination coefficients, which are given by the mode coefficient vector. Given, and It can be obtained through the following formula: (3); in, Let be the modal coefficient vector, and the subscript indicates the first... First mode, To preserve the total number of modes.

[0048] Truncate the mode to the front The error introduced by the first step can usually be measured by the energy percentage. The cumulative energy ratio of a singular value to the total energy is defined as: (4); in, For the front The cumulative energy percentage of the singularity of order 1. This represents singular values. In practical applications, the cutoff order can be determined based on a preset energy threshold (such as 99.9%). .

[0049] Offline Reconstruction Based on Neural Networks: To efficiently predict the physical field distribution under new operating conditions or time steps, this application introduces a feedforward neural network to establish a nonlinear mapping relationship between input parameters and POD mode coefficients. This network takes a vector consisting of operating parameters (such as boundary condition parameters) corresponding to the training conditions and time as input, and outputs a vector with a dimension of [missing information - likely a specific dimension]. The modality coefficient vector. The network structure uses a multilayer perceptron (MLP), with each hidden layer using the ReLU activation function, and the output layer corresponding to... One modal coefficient.

[0050] Offline simulation data is used for neural network training. The training dataset consists of input parameters and their corresponding POD mode coefficients, and regularization (such as L2 regularization) is introduced to reduce the risk of overfitting. After training, the neural network can quickly predict mode coefficients under any given input conditions. Subsequently, the predicted mode coefficients are combined with the pre-calculated dominant mode matrix and the truncated singular value matrix to reconstruct an approximate coarse-grid predicted physics field, expressed as: (5); in, To predict the physical field obtained from the reconstruction; The dominant mode matrix retained after truncation; The truncated singular value matrix; This is the predicted modal coefficient vector.

[0051] Iterative Interpolation Strategy: This application employs an iterative interpolation strategy for coupled computation, that is, in a step-by-step manner... Interpolation iterations are performed with each time step constituting one cycle. In the initial stage, a fine-mesh CFD method is first used to calculate the initial values. The physical field distribution within the nth time step. For the nth time step... At each time step, instead of directly performing CFD advancement on the fine mesh, a pre-trained ROM model is invoked to quickly predict the coarse mesh solution corresponding to that time step. Subsequently, the coarse mesh prediction result is mapped back to the fine mesh and used as the initial field for subsequent advancement calculations of the fine mesh CFD solver.

[0052] The mapping process uses the nearest-neighbor interpolation method, such as... Figure 4 As shown: For each node on the fine mesh, find the node in the coarse mesh that is closest to it, and assign the physical quantity at that coarse mesh node to the fine mesh node. For example... Figure 2 As shown, this interpolation method can be expressed as: (6); in, Represents the physical quantity to be interpolated; These are the coordinates of the fine-grid nodes; Coarse grid node coordinates; subscript and These represent fine and coarse meshes, respectively. This is the output result of the ROM; For index number.

[0053] The above iterative process continues as time progresses: the fine-mesh CFD solver continues to calculate the next... The proposed method performs a first time step; at the subsequent target time step, the ROM is called again for prediction, and the prediction is mapped to a fine mesh through interpolation, serving as the initial condition for the next CFD advancement. By comparing the accelerated calculation results with the pure fine-mesh CFD benchmark solution, and selecting several characteristic quantities (such as temperature, pressure, velocity, etc.) as evaluation indicators, the computational accuracy and acceleration effect of the proposed method can be assessed.

[0054] Example 3 This embodiment, based on Embodiments 1 and 2, and in conjunction with a specific physical model, further illustrates the implementation process and effects of the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation. Those skilled in the art will understand that the specific parameters below are merely examples and do not constitute a limitation of this application.

[0055] 3.1. Two typical two-dimensional (2D) transient problems are selected as verification examples: Specifically, two physical problems of different complexities are selected to comprehensively evaluate the performance of the proposed method. For example... Figure 5a As shown, the first example is a two-dimensional transient solid-state heat conduction model consisting of an aluminum material region. The left boundary is set as a type II boundary condition (constant heat flux density boundary), the right boundary is a type III boundary condition (convective heat transfer), and both the upper and lower boundaries are adiabatic. This example involves only a single physical process and has a relatively simple governing equation, making it suitable for basic verification.

[0056] The second example is as follows Figure 5b The diagram shows a heated airflow model along a stepped platform. The computational domain consists of an inlet section with a height of 4 m and a subsequent abrupt expansion section. The step height is 1 m, forming an upstream channel of 3.8 m in length and a downstream channel of 30 m in length. Air enters from the left, with the upper wall being an adiabatic boundary. The lower wall upstream of the step is also an adiabatic boundary. A constant heat flux density boundary is applied to the lower wall downstream of the step to achieve heating. The outlet is located at the far right of the computational domain. This configuration incorporates coupled processes such as flow separation, convective heat transfer, and heat transfer, exhibiting more complex flow and heat transfer characteristics, making it suitable for evaluating the processing capability of the method under complex physical conditions.

[0057] The computational domains of both examples were discretized using a fully structured uniform mesh generated by ANSYS ICEM. Given the relatively simple geometry, a uniformly distributed structured mesh was used throughout the computational domain to ensure mesh quality and facilitate interpolation during the numerical solution process. The mesh resolution settings are shown in Table 1, where fine meshes are used to generate high-fidelity benchmark solutions, and coarse meshes are used to train reduced-order prediction models. For Example 1, the fine mesh has 22,500 nodes, and the five sets of coarse meshes have the following node counts: 18,225, 14,400, 11,025, 8,100, and 5,625, respectively. For Example 2, the fine mesh has 148,680 nodes, and the five sets of coarse meshes have the following node counts: 103,250, 66,090, 37,170, 16,520, and 4,130, respectively. Table 1. Coarse-fine mesh schemes for Example 1 and Example 2

[0058] 3.2. Control equations: This embodiment considers two different physical processes: the pure heat conduction process of the two-dimensional aluminum block and the flow and heat transfer process of two-dimensional incompressible air onto the step after heating.

[0059] For Example 1 (pure thermal conductivity of aluminum block), the governing equations are derived based on the general thermal conductivity equations for two-dimensional solids. Under the assumption of constant material properties and neglecting internal heat sources, the temperature field satisfies the two-dimensional thermal conductivity equations: (7); in, For time, , and These represent the density, specific heat capacity at constant pressure, and thermal conductivity of aluminum, respectively.

[0060] For Example 2, the medium in the computational domain is air, and the flow is assumed to be turbulent, incompressible, Newtonian, and two-dimensional. RNG is used. k - ε The turbulence model describes turbulent transport, taking constant air properties and neglecting radiative heat transfer and buoyancy effects. The governing equations include the Reynolds-averaged continuity equation, momentum equation, and energy equation, coupled with turbulent kinetic energy... k and its dissipation rate ε Transport equations: Reynolds-averaged continuity equation: (8); in, and These are the velocity components in the x and y directions, respectively.

[0061] Momentum equation: (9); (10); Among them, turbulent viscosity By RNG k - ε The model provides: (11).

[0062] Energy equation: (12); in, For turbulent Prandtl number.

[0063] RNG k - ε Turbulence model equations: (13); (14); in, For turbulence generation; This is a correction for RNG.

[0064] RNG k - ε Model constants are taken =0.0845, =1.42, =1.68, =1.0, =1.3.

[0065] This embodiment uses ANSYS Fluent 2022R1 to solve the above Reynolds-averaged governing equations. The transient pressure-velocity coupling in the momentum equations uses the SIMPLE algorithm, and pressure discretization uses the PRESTO! format. Momentum, energy, k and ε All equations are discretized using a second-order upwind scheme, and the convergence residuals of all equations are set to 10. -6 .

[0066] 3.3. Boundary Conditions and Operating Conditions: To construct a controllable parameter space for ROM development, this embodiment sets the operating condition ranges for the two examples. As shown in Table 2, for example one, the heat flux density range at the left boundary is 5000–10000 W / m². 2 The convective heat transfer coefficient on the right side ranges from 500 to 1000 W / (m²). 2 The ambient temperature range is 300–350 K. For example two, the inlet velocity ranges from 1.0 to 3.0 m / s, the inlet temperature ranges from 273 to 303 K, and the heat flux density of the heated wall ranges from 1000 to 3000 W / m². 2 .

[0067] Latin Hypercube Sampling (LHS) was used to generate 15 training cases for each of the two examples within the aforementioned multidimensional parameter space to ensure uniform coverage of the case space. Furthermore, independent validation cases were selected for each example, as shown in Table 3: the validation case for example one was a heat flux density of 7500 W / m³. 2 convective heat transfer coefficient 750 W / (m²) 2 • K), ambient temperature 325 K; the verification conditions for example two are an inlet velocity of 2.0 m / s, an inlet temperature of 288 K, and a wall heat flux density of 2000 W / m. 2 . Table 2. Sampling parameter space table for Example 1 and Example 2 Table 3 Verification Operating Condition Parameters

[0068] 3.4. Results and Discussion: (1) Offline ROM Construction: Following the aforementioned orthogonal decomposition method, intrinsic orthogonal decomposition was performed on the training datasets of Example 1 and Example 2, respectively. Table 4 shows the singular values ​​and cumulative energy percentages corresponding to the first 10 POD modes of the temperature field in Example 1. The singular value of the first mode is 1.89 × 10⁻⁶. 6 The accumulated energy accounts for 99.999%, indicating that the temperature field energy is highly concentrated in the first mode. Introducing the second mode increases the accumulated energy to 99.9999%, while higher-order modes contribute very little. Therefore, this embodiment selects the first three POD modes for subsequent neural network regression modeling. Table 4. Singular values ​​and cumulative energy percentages of the temperature field in Example 1.

[0069] Figure 6 The performance of the artificial neural network regression model used to predict the modal coefficients of Example 1 is demonstrated. The network's input layer contains four features (corresponding to operating parameters), the two hidden layers have 20 and 10 neurons respectively, and the output layer has three nodes (corresponding to the first three modal coefficients). The predicted values ​​agree well with the reference values ​​obtained by projecting high-fidelity computational fluid dynamics data onto a POD, and the coefficient of determination R0 is [value missing]. 2 =0.9969, indicating that the neural network can accurately capture the mapping relationship between the operating parameters and the dominant mode coefficients.

[0070] For example two, Figure 7 The singular values ​​and modal energy distributions of (a) pressure, (b) temperature, (c) velocity component u, (d) velocity component v, (e) turbulent kinetic energy k, and (f) turbulent dissipation rate ε are presented respectively. (Pressure, temperature, and flow velocity components are also shown.) u The accumulated energy of the first 6 modes accounts for more than 99.999%; the normal velocity component v and turbulent variables k , ε Approximately 10–15 modes are required to reach the same energy threshold, reflecting the more dispersed energy distribution caused by the complex vortex structure in backward step flow. Considering both physical rationality and computational efficiency, this embodiment retains the first 6 POD modes for each physical field for neural network training, achieving a good balance between physical rationality and computational efficiency.

[0071] Figure 8The neural network regression results for each modal coefficient variable in Example 2 are presented. Compared to Example 1, the network structure in Example 2 consists of an input layer with four parameters, two hidden layers (60 and 40 neurons respectively), and an output layer with three nodes. The predicted coefficients for (a) pressure, (b) temperature, (c) velocity component u, (d) velocity component v, and (e) turbulent kinetic energy k and (f) turbulent dissipation rate ε are highly consistent with the reference values, and the coefficients of determination are respectively... R 2 =0.9925, 0.9991, 0.9981, 0.9952 and 0.9942; the regression accuracy of the normal velocity component v is relatively low ( R 2 (i = 0.8321), but it can still capture the dominant changing trend. Overall, the trained neural network can provide reliable modal coefficient predictions for subsequent flow field reconstruction.

[0072] (2) Impact of training mesh resolution: To evaluate the impact of the coarse mesh resolution used in ROM training on the accuracy of the hybrid framework, five sets of coarse meshes listed in Table 1 were used to construct ROMs for Example 1 and Example 2, respectively, and hybrid accelerated simulations were performed under verification conditions. The difference between the hybrid results and the pure fine-mesh CFD benchmark solution was quantitatively evaluated using absolute error (AE) and mean absolute error (MAE), defined as follows: (16); (17); in, This indicates the target physical quantity of interest in this application, including temperature, pressure, velocity, and turbulent flow rate, etc. This is the time step index, where k is the total number of time steps; subscript and The results represent the fine-grid CFD solution and the hybrid CFD-ROM prediction, respectively.

[0073] Figure 9 The results show the temperature AE and MAE of the hybrid frame over time under different coarse mesh training conditions in Example 1. As the training mesh becomes coarser, the peak absolute error increases and the fluctuation range widens. When using a finer training mesh (such as Coarse1, with a mesh size of about 80% of the fine mesh), the MAE is only 0.010 K. Even when using the coarsest mesh (Coarse 5, with a mesh size of about 25% of the fine mesh), the MAE is still controlled within 0.049 K, indicating that the method has good tolerance to mesh coarsening.

[0074] Figures 10a-10cTable 5 shows the (a) temperature, (b) pressure, and (c) velocity AE and MAE for Example 2 under different training grids. The model trained with the finest coarse grid (Coarse 1) obtained the lowest MAE (temperature 0.045 K, pressure 0.0041 Pa, velocity 4.21 × 10⁻⁶). -5 m / s); the MAE corresponding to the coarsest grid (Coarse 5, with approximately 97% reduction in grid size) are 0.454 K, 0.0189 Pa, and 1.17 × 10⁻⁶ Pa, respectively. -3 m / s, which is still within the acceptable range for engineering. Figures 11a-11c The spatial error distribution of each variable (temperature field, pressure field, and velocity field) at the transient time τ=49 s is further shown, which intuitively reflects the influence of the training grid resolution on the ability to capture flow structures. Table 5 shows the mean absolute errors of instantaneous average temperature, pressure, and velocity obtained from the hybrid frame simulation under five coarse mesh resolution training conditions in Example 2.

[0075] 3.5. Impact of interpolation strategies: This embodiment also examines the impact of different CFD and ROM alternating step allocation strategies (denoted as CFD(i)-ROM(j)) on simulation accuracy. The strategy settings are shown in Table 6. Figure 12 The temperature AE and MAE under different interpolation strategies are given in Example 1. The strategy with more consecutive CFD steps (such as CFD(3)-ROM(1) and CFD(2)-ROM(1)) has the highest accuracy, with MAE of 0.0041K and 0.0042K respectively, which can achieve 25%–33% computational savings. When CFD(1)-ROM(1) is used, the MAE increases to 0.010K, but the computational cost is reduced by about 50%. If the number of consecutive ROM steps is further increased (such as CFD(1)-ROM(3)), the MAE increases significantly to 0.587K, indicating that the cumulative effect of error cannot be ignored when the CFD correction is insufficient. Table 6 Interpolation strategy settings for Example 1 and Example 2

[0076] For example two, such as Figures 13a-13c As shown in Table 7, the CFD(1)-ROM(1) strategy (alternating at each step) achieved the optimal overall accuracy (temperature MAE = 0.043 K, pressure MAE = 0.0061 Pa, velocity MAE = 5.84 × 10⁻⁶). -5 The error fluctuation is relatively small (m / s). In contrast, the errors of both CFD(3)-ROM(1) and CFD(1)-ROM(3) strategies are significantly increased. Figure 14By selecting four consecutive time points from τ=45–48 s, the velocity field prediction results of three typical strategies were compared, further confirming the key role of frequent fine-grid correction in suppressing error accumulation and ensuring prediction stability. Table 7. Mean Absolute Errors of Instantaneous Average Temperature, Pressure, and Velocity under Different Interpolation Strategies in Example 2

[0077] 3.6. Conclusion: This embodiment verifies the effectiveness of the proposed hybrid acceleration framework through two typical computational examples. The results show that: (1) The resolution of the training mesh in ROM directly affects the accuracy of the hybrid frame, but the frame has a strong tolerance for mesh coarsening. For complex flow problems, even if the number of training mesh elements is reduced by about 97%, acceptable engineering accuracy can still be obtained (temperature MAE < 0.5 K, pressure MAE < 0.1 Pa, velocity MAE < 0.002 m / s).

[0078] (2) For weak transient problems, appropriately increasing the proportion of CFD steps can achieve significant acceleration (up to about 75%) with almost no loss of accuracy; for strong transient complex flows, the CFD(1)-ROM(1) strategy with each step alternating can most effectively suppress error accumulation and achieve the best balance between accuracy and efficiency.

[0079] (3) The framework can be started at any time without special initialization, and the continuous correction effect of CFD can suppress the error accumulation problem in the long-term evolution of independent ROM, thus improving the accuracy and stability of long-term simulation.

[0080] In summary, the hybrid acceleration method provided in this application offers a flexible, efficient, and reliable technical approach for high-fidelity transient CFD simulation.

[0081] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 15As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores and processes data. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network. When the computer program is executed by the processor, it implements a hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation.

[0082] Those skilled in the art will understand that Figure 15 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0083] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0084] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0085] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Moreover, the collection, use and processing of the relevant data are carried out in compliance with the relevant data protection laws and policies of the country where the location is located, and with the authorization granted by the owner of the corresponding device.

[0086] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, 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 can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0087] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0088] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0089] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation, characterized in that, include: The initial calculation parameters of the target physical field are obtained, and a computational fluid dynamics solution with a preset initial time step is performed on a fine mesh based on the initial calculation parameters to generate initial fine mesh physical field data. Based on the fine-grid physical field data of the current time step, a pre-built reduced-order prediction model is invoked to generate the coarse-grid predicted physical field of the current time step; the reduced-order prediction model is constructed based on the computational fluid dynamics simulation results on the coarse grid; in the first iteration cycle, the fine-grid physical field data of the current time step is the fine-grid physical field data of the last time step in the initial fine-grid physical field data; Spatial interpolation is performed on the coarse-grid predicted physical field at the current time step to generate the interpolated result at the current time step, and the interpolated result at the current time step is mapped onto the fine-grid to generate the fine-grid initial field data at the current time step. Using the initial field data of the fine mesh at the current time step as the initial conditions for the computational fluid dynamics solution, the computational fluid dynamics solution for the next preset time step is continued on the fine mesh to generate updated fine mesh physical field data; Determine whether the preset total simulation time step has been reached; If so, output the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data, and use the fine-mesh physical field data of the last time step in the updated fine-mesh physical field data as the final simulation result of the target physical field; If not, the fine-grid physical field data of the last time step in the updated fine-grid physical field data will be used as the fine-grid physical field data of the current time step in the next iteration cycle, and the process will return to the step "Based on the fine-grid physical field data of the current time step, call the pre-built reduced-order prediction model to generate the coarse-grid prediction physical field of the current time step".

2. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 1, characterized in that, The construction process of the reduced-order prediction model specifically includes: Multiple training conditions and corresponding operating parameters are selected within a preset parameter space. Computational fluid dynamics simulations are then performed on the corresponding training conditions on a coarse grid based on the operating parameters to obtain a target physics snapshot dataset. The target physics snapshot dataset includes target physics snapshots under multiple conditions and multiple time steps. The target physical field snapshot dataset is orthogonally decomposed to extract the dominant mode matrix, the truncated singular value matrix, and the mode coefficient vector corresponding to each target physical field snapshot, which characterize the main features of the target physical field. Construct a training dataset; the training dataset includes multiple sample data, each sample data includes the running parameters and modal coefficient vectors corresponding to each target physical field snapshot; Based on the training dataset, the pre-constructed artificial neural network model is trained to obtain the trained artificial neural network model. Based on the dominant mode matrix, the truncated singular value matrix, and the trained artificial neural network model, a reduced-order prediction model is constructed.

3. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 2, characterized in that, Orthogonal decomposition is performed on each target physics snapshot in the target physics snapshot dataset to extract the dominant mode matrix, the truncated singular value matrix, and the mode coefficient vector corresponding to each target physics snapshot, which characterize the main features of the target physics. Specifically, this includes: All target physics snapshots in the target physics snapshot dataset are combined into a dataset matrix. Singular value decomposition is performed on the dataset matrix to obtain the spatial basis vector matrix, the singular value matrix, and the right singular vector matrix. The singular value matrix is ​​sorted in descending order, and the truncation order is determined based on the cumulative energy ratio of the singular values ​​in the sorted singular value matrix. The dominant mode matrix is ​​obtained by truncating the spatial basis vector matrix with the order of the truncated spatial basis vectors, and the truncated singular values ​​are obtained from the singular value matrix with the order of the truncated singular values ​​to form the truncated singular value matrix. The column vectors with the order of the truncated singular values ​​are extracted from the right singular vector matrix as the mode coefficient vectors corresponding to each target physical field snapshot.

4. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 2, characterized in that, The artificial neural network model is a feedforward neural network, and the network structure of the feedforward neural network is a multilayer perceptron. The feedforward neural network includes an input layer, multiple hidden layers, and an output layer. The input layer corresponds to the operating parameters corresponding to each target physical field snapshot, and the output layer corresponds to the modal coefficients corresponding to each target physical field snapshot. Each hidden layer uses the ReLU activation function.

5. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 1, characterized in that, Spatial interpolation is performed on the coarse-grid predicted physics field at the current time step to generate the interpolated result for the current time step. This interpolated result is then mapped onto the fine-grid to generate the initial fine-grid field data for the current time step, specifically including: Using the nearest neighbor interpolation method, the coarse grid node that is closest to the current fine grid node is found in the coarse grid predicted physics field at the current time step, and the physical quantity value corresponding to the current coarse grid node is determined as the interpolated result at the current time step; the current fine grid node is any node on the fine grid. The interpolated results at the current time step are assigned to the corresponding nodes on the fine mesh to generate the initial field data of the fine mesh at the current time step.

6. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 5, characterized in that, The calculation formula for the nearest neighbor interpolation method is as follows: ； in, Represents the physical quantity to be interpolated; For fine grid node coordinates; Coarse grid node coordinates; subscript and These represent fine and coarse meshes, respectively. For index number.

7. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 1, characterized in that, Based on the fine-grid physics data at the current time step, a pre-built reduced-order prediction model is invoked to generate the coarse-grid predicted physics field for the current time step, specifically including: The fine-grid physical field data of the current time step is input into the pre-built reduced-order prediction model to predict the corresponding prediction mode coefficient vector. The predicted mode coefficient vector is linearly combined with the pre-stored dominant mode matrix and truncated singular value matrix in the reduced-order prediction model to reconstruct the coarse-grid predicted physics field at the current time step.

8. The hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in claim 7, characterized in that, The predicted mode coefficient vector is linearly combined with the pre-stored dominant mode matrix and truncated singular value matrix in the reduced-order prediction model to reconstruct the coarse-grid predicted physics field at the current time step, specifically as follows: ； in, Predict the physical field for the coarse grid at the current time step; The dominant mode matrix retained after truncation. The truncated singular value matrix; This is the vector for predicting mode coefficients.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the hybrid acceleration method for computational fluid dynamics simulation based on data dimensionality reduction and multigrid interpolation as described in any one of claims 1-8.

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