Obtaining unsteady hydrodynamic performance is of great significance for seaplane design. Common methods for obtaining unsteady hydrodynamic performance data include tank test and Computational Fluid Dynamics (CFD) numerical simulation, which are costly and time-consuming. Therefore, it is necessary to obtain unsteady hydrodynamic performance in a low-cost and high-precision manner. Due to the strong nonlinearity, complex data distribution, and temporal characteristics of unsteady hydrodynamic performance, the prediction of it is challenging. This paper proposes a Temporal Convolutional Diffusion Model (TCDM) for predicting the unsteady hydrodynamic performance of seaplanes given design parameters. Under the framework of a classifier-free guided diffusion model, TCDM learns the distribution patterns of unsteady hydrodynamic performance data with the designed denoising module based on temporal convolutional network and captures the temporal features of unsteady hydrodynamic performance data. Using CFD simulation data, the proposed method is compared with the alternative methods to demonstrate its accuracy and generalization. This paper provides a method that enables the rapid and accurate prediction of unsteady hydrodynamic performance data, expecting to shorten the design cycle of seaplanes.

The shape of aircraft with ‌telescopic deformed structures‌ is complex, and the distribution of ‌aerothermal‌ data varies ‌significantly‌. Traditional surrogate models to capture the ‌aerothermal‌ heating distribution of ‌telescopic structures‌, hindering effective prediction struggle on structural surfaces. Based on ‌the conditional diffusion model, ‌the Heating-MLP Diffusion (HMD) method for deformable structures‌ was proposed, comprising two processes: forward diffusion and reverse denoising. In the forward diffusion process, the original ‌aerothermal‌ data is gradually ‌corrupted‌ until it becomes pure Gaussian noise. In the reverse denoising process, ‌using‌ the shape and operating conditions of the deformed structure as ‌conditional inputs‌, a fully connected neural network predicts the noise added at each diffusion step, thereby learning the implicit ‌distribution characteristics of aerothermal‌ heating data, thus enabling ‌the prediction of aerothermal heating‌ on the surface grid points of ‌aircraft telescopic deformed wings‌. Numerical simulation data validated the proposed model. Experimental results demonstrate that compared with Gaussian processes, neural processes, and neural networks, the ‌conditional diffusion model-based‌ aerothermal prediction method achieves higher accuracy, with a mean absolute percentage error of ～10%. This evidence proves its effectiveness in predicting ‌aerothermal heating‌ on ‌high-speed aircraft‌ wings with telescopic deformed structures providing an accurate prediction model for engineering applications.

Holographic hydrodynamic load distribution is of important significance in assessing the hydrodynamic performance of a seaplane, while model testing is a common method to obtain flow field data in the seaplane design. However, the hydrodynamic load test can only obtain a limited amount of sensor data with insufficient accuracy, thereby necessitating the holographic flow field reconstruction. Nevertheless, the hydrodynamic load data is highly nonlinear and sparse, resulting in difficult application of the traditional flow field reconstruction method. We use Temporal Convolutional Network（TCN）to model the time-sequential flow field reconstruction problem of the seaplane entering the water at the bottom of the ship, learn the flow field law through the excellent nonlinear fitting ability of deep learning, and propose the reconstruction loss of a fusion diffusion model for the sparsity of the samples on the basis of the traditional TCN to improve the prediction accuracy of the neural network. The training set is used to train the diffusion model, then the trained diffusion model is fused into the training process of the TCN, and connected to the output of theTCN, while the reconstruction error is calculated. The constraints are imposed on the training of the TCN to improve the reconstruction performance of the flow field. This paper first compares the three models of the traditional TCN, the Gated Recurrent Unit（GRU）and the fully connected network, and verifies the superiority of the TCN in modelling accuracy and generalization ability of non-constant water load reconstruction. The necessity of considering the timing factor in the hydrodynamic load reconstruction through the single-frame reconstruction experiments is illustrated, on the basis of which the validity of the TCN fused with the diffusion model for reconstructing the non-constant flow field is verified. This study provides an effective modelling method for reconstructing the non-constant flow field, acilitating comprehensive assessment of the mechanical properties of the vehicle using model tests.

The accuracy of numerical computation heavily relies on appropriate meshing, which serves as the foundation for numerical computation. Although adaptive refinement methods are available, an adaptive numerical solution is likely to be ineffective if it originates from a poorly initial mesh. Therefore, it is crucial to generate meshes that accurately capture the geometric features. As an indispensable input in meshing methods, the Mesh Size Function (MSF) determines the quality of the generated mesh. However, the current generation of MSF involves human participation to specify numerous parameters, leading to difficulties in practical usage. Considering the capacity of machine learning to reveal the latent relationships within data, this paper proposes a novel machine learning method, Implicit Geometry Neural Network (IGNN), for automatic prediction of appropriate MSFs based on the existing mesh data, enabling the generation of unstructured meshes that align precisely with geometric features. IGNN employs the generative adversarial theory to learn the mapping between the implicit representation of the geometry (Signed Distance Function, SDF) and the corresponding MSF. Experimental results show that the proposed method is capable of automatically generating appropriate meshes and achieving comparable meshing results compared to traditional methods. This paper demonstrates the possibility of significantly decreasing the workload of mesh generation using machine learning techniques, and it is expected to increase the automation level of mesh generation.

With the availability of high-performance computing technology and the development of advanced numerical simulation methods, Computational Fluid Dynamics (CFD) is becoming more and more practical and efficient in engineering. As one of the high-precision representative algorithms, the high-order Discontinuous Galerkin Method (DGM) has not only attracted widespread attention from scholars in the CFD research community, but also received strong development. However, when DGM is extended to high-speed aerodynamic flow field calculations, non-physical numerical Gibbs oscillations near shock waves often significantly affect the numerical accuracy and even cause calculation failure. Data driven approaches based on machine learning techniques can be used to learn the characteristics of Gibbs noise, which motivates us to use it in high-speed DG applications. To achieve this goal, labeled data need to be generated in order to train the machine learning models. This paper proposes a new method for denoising modeling of Gibbs phenomenon using a machine learning technique, the zero-shot learning strategy, to eliminate acquiring large amounts of CFD data. The model adopts a graph convolutional network combined with graph attention mechanism to learn the denoising paradigm from synthetic Gibbs noise data and generalize to DGM numerical simulation data. Numerical simulation results show that the Gibbs denoising model proposed in this paper can suppress the numerical oscillation near shock waves in the high-order DGM. Our work automates the extension of DGM to high-speed aerodynamic flow field calculations with higher generalization and lower cost.

The high-order discontinuous Galerkin (DG) method for the high-speed compressible flow field calculations will cause non-physical numerical oscillation near the shock wave, affecting numerical accuracy and even leading to calculation failure, similar to the accumulation of Gibbs noise in the image processing field. In the high-order DG methods, restraining shock oscillation or eliminating the Gibbs phenomenon to ensure the stability of the calculation process has become a challenge. A Gibbs phenomenon intelligent denoising model composed of graph attention mechanism and graph convolutional network is proposed by using machine learning technology. This model can restrain the oscillation near the shock wave in DG calculation, while ensuring the convergence of DG calculation and improving the effectiveness of shock wave capturing. After constructing a training dataset from Gibbs noise data generated by DG calculation, this model trains the graph neural network under the guidance of graph convolutional filters. In the numerical simulation experiment of NACA0012 airfoil under transonic and supersonic inflow conditions, the Gibbs phenomenon intelligent denoising model is embedded in the DG calculation. The experimental results show that the Gibbs phenomenon has been eliminated and shock oscillation has been effectively restrained .

Existing grid adaptation methods for numerical simulation of unsteady flow fields usually perform grid adjustment every time step, which increases the computational complexity and the possibility of accuracy loss. In view of this, based on the DG finite element method, an MMPDE mesh adaptation method combined with BPNN is proposed for intelligent mesh optimization of unsteady flow fields. The method first uses the DG finite element method to solve the unsteady N-S equation and obtain the statistical grid discontinuity. Using the initial grid and grid discontinuity to train the BPNN regression model, the discontinuity value of any node at any position can be predicted. The variational method, MMPDE, is selected to move grid nodes to conform to the distribution of discontinuities. Finally, the Laplacian grid smoothing method improves the grid quality. The feasibility of the method is verified by cases of unsteady flow fields around cylinders. The calculation results show that the method can complete the one-time adaptive adjustment of the grid without changing the grid topology and the number of nodes, which can significantly improve the accuracy and efficiency of numerical simulations for unsteady flow fields.

As a numerical method, the high-order discontinuous Galerkin (DG) method has the characteristics of high precision and is suitable for complex geometries. Meanwhile, due to its good dispersion and dissipation properties, the high-order DG method is well suited for implicit large eddy simulations. However, it usually takes a long time for solving unsteady flow fields, and how to reduce the computation cost is still a challenge. To tackle this issue, a deep neural network consisted with the three-dimensional convolution, the two-dimensional residual network and the attention mechanism has been proposed, which can extract the implied spatio-temporal characteristics of the flow field from the data. The numerical simulation for flow around a cylinder at different Reynolds numbers is carried out to obtain the data set for training, which is then used to predict the flow field for the future period. The results show that the deep neural network has a satisfactory ability of modeling the flow around a cylinder. The flow fields predicted by the deep neural network is in good agreement with those directly calculated by the CFD solver.

Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation. In light of the introduced large amount of computational costs for many adaptive mesh methods, moving mesh methods keep the number of nodes and topology of a mesh unchanged and do not increase CFD computational expense. As the state-of-the-art moving mesh method, the variational mesh adaptation approach has been introduced to CFD calculation. However, quickly estimating the flow field on the updated meshes during the iterative algorithm is challenging. A mesh optimization method, which embeds a machine learning regression model into the variational mesh adaptation, is proposed. The regression model captures the mapping between the initial mesh nodes and the flow field, so that the variational method could move mesh nodes iteratively by solving the mesh functional which is built from the estimated flow field on the updated mesh via the regression model. After the optimization, the density of the nodes in the high gradient area increases while the density in the low gradient area decreases. Benchmark examples are first used to verify the feasibility and effectiveness of the proposed method. And then we use the steady subsonic and transonic flows over cylinder and NACA0012 airfoil on unstructured triangular meshes to test our method. Results show that the proposed method significantly improves the accuracy of the local flow features on the adaptive meshes. Our work indicates that the proposed mesh optimization approach is promising for improving the accuracy and efficiency of CFD computation.

Deep learning has been probed for the airfoil performance prediction in recent years. Compared with the expensive CFD simulations and wind tunnel experiments, deep learning models can be leveraged to somewhat mitigate such expenses with proper means. Nevertheless, effective training of the data-driven models in deep learning severely hinges on the data in diversity and quantity. In this paper, we present a novel data augmented Generative Adversarial Network (GAN), daGAN, for rapid and accurate flow filed prediction, allowing the adaption to the task with sparse data. The presented approach consists of two modules, pre-training module and fine-tuning module. The pre-training module utilizes a conditional GAN (cGAN) to preliminarily estimate the distribution of the training data. In the fine-tuning module, we propose a novel adversarial architecture with two generators one of which fulfils a promising data augmentation operation, so that the complement data is adequately incorporated to boost the generalization of the model. We use numerical simulation data to verify the generalization of daGAN on airfoils and flow conditions with sparse training data. The results show that daGAN is a promising tool for rapid and accurate evaluation of detailed flow field without the requirement for big training data.