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.

Conjugate heat transfer problems are widespread in practical engineering. Traditional methods such as the Finite Difference Method (FDM) and the Finite Volume Method (FVM) have been widely applied to solve these problems. The Smoothed Particle Hydrodynamics (SPH) method, a meshless particle method, offers advantages such as strong adaptability, suitability for analyzing complex structures, and high flexibility. Therefore, this method has seen extensive application and rapid development in fields such as ship design and geological disaster simulation. However, although there have been some applications of the SPH method in conjugate heat transfer problems, there is currently limited research on simulating heat transfer in actual engineering scenarios involving different functional materials, such as the simulation of heat transfer and heat-generating components. In view of this, we conduct numerical simulations of fluid-solid conjugate heat transfer using the SPH method. First, traditional test cases of natural convection in a closed square cavity and horizontal annular convection are simulated. Then, the focus shifts to simulating natural convection cases involving heat transfer blocks and heat-generating blocks. The results show a high degree of agreement with traditional methods, demonstrating the adaptability and accuracy of the SPH algorithm in simulating conjugate heat transfer problems involving different functional materials. Finally, the simulation of a heat sink with fin structures is carried out, analyzing the impact of parameters such as the heat transfer ratio and heat generation ratio on the cooling performance. These results verify the significant adaptability and flexibility of the SPH method in handling complex cases, providing theoretical support and practical guidance for solving complex engineering problems in the future.

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.

To decrease the difficulty of generating body-fitted meshes for complex geometries, the immersed boundary (IB) method based on Cartesian mesh has gradually become a popular numerical method for studying such problems in recent years. However, accuracy and efficiency of this method still need to be improved. Compared with the traditional finite volume scheme with second-order spatial accuracy, third-order or higher-order numerical methods have the advantages of high spatial accuracy, high numerical resolution and low numerical dissipation. However, the discontinuous Galerkin (DG) method, as one of the high-precision numerical methods, is still rarely applied with the immersed boundary. This paper proposes a high-order discontinuous Galerkin method for compressible flows by combining the advantage of the high-order discontinuous Galerkin method and the immersed boundary method. The boundary conditions in this paper are realized by the volume penalization method. Newton’s method iteration and MPI are used to improve computational efficiency. The inverse distance weight at interpolation point (IDW-IP) instead of the high-order polynomial defined in each element to perform high-order data reconstruction at the object surface. Based on the Cartesian grids, numerical tests are performed for two-dimensional steady and unsteady flows, and comparisons with those on traditional body-fitted grids are given.

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.