Although the development time of cross-border e-commerce in China is very short, the scale of its transactions and the speed of development are amazing, and as a supporting foundation for promoting economic and trade globalization, cross-border e-commerce has an extremely important strategy for this guiding role. This not only brings new opportunities to cross-border e-commerce companies but also excavates a huge potential market for the logistics industry. Cross-border e-commerce not only breaks through the trade barriers between countries; it makes trade move towards borderlessness and at the same time triggers major changes in international trade. This paper introduces partial differential equations into the video surveillance image enhancement system of cross-border e-commerce logistics. Aiming at the shortcomings of the contrast enhancement method based on gradient field equalization, this paper proposes a partial differential enhancement method based on histogram equalization. By proposing a gradient transformation function, the edges and textures with relatively small gradient values are enhanced to make the original weaker texture details clearer. In order to better adjust the brightness and contrast of the image, combined with histogram equalization, we propose an inverse equalization transformation. When the histogram equalization and the inverse equalization transform are combined reasonably, the brightness and contrast of the image can be adjusted very well. In this paper, the finite difference method is used for discretization when solving partial differential equations, and Euler’s equation is obtained by applying the principle of least squares. By introducing the heat equation, the direct solution of Euler’s equation is converted into an iterative form, which greatly reduces the amount of calculation. This article uses statistical methods to obtain the empirical formula of the fractional differential order. This empirical formula makes the calculation of the order of the fractional derivative easy and can be extended to other fractional image enhancement models and overcomes the shortcomings of the traditional fractional derivative order obtained through experience or a large number of experiments. Experiments show that the proposed algorithm not only enhances detailed texture information but also improves image clarity, overall brightness, and contrast without color distortion. The objective evaluation indicators also show the superiority of the algorithm.

To analyze the dynamic characteristics of hammer shocks caused by engine surge, a serpentine inlet with a front fuselage is simulated under conditions of subsonic inflow and three flight angles based on the improved delayed detached eddy simulation method. An unsteady back pressure boundary condition in an aerodynamic interface plane is used to simulate the overpressure during engine surge. There is a certain angle between the normal line of the hammer shock and the centerline, which is approximately equal to the corresponding flight angle. The inlet wall pressures are above 2.3 times of the free-stream static pressure, and even local transient pressures reach more than 3 times. Complex flow field structures are generated behind the shock, which are affected by the centrifugal force and lateral pressure gradient. The velocities and intensities of the hammer shocks and the pressure distributions on the wall and the shapes of the flow field structures are greatly affected by the flight angle. In a large yaw angle, the hammer shock velocity is the fastest, and the internal airflow and load are the most severe. In particular, it is necessary to consider the influence of the ultra-high dynamic loads in the opposite direction at the two bends in a short period of time.

Aerodynamic shape refinement optimization for passenger aircraft is difficult and requires a significant workload. The adjoint-based gradient optimization method can quickly find local optimal solutions based on the initial shape in these types of problems. The optimization model of the common research model for the drag coefficient minimization and wing thickness constraints with a large-scale grid is established, and the drag coefficient is reduced by 10.2 counts while maintaining the lift coefficient. The stress-blended eddy simulation is used for unsteady simulations, and the optimized configuration can effectively eliminate oscillations in the middle of the upper wing surface. The spanwise flow is reduced and the pressure response on the wing surface is due primarily to shock chordal motion. For aerodynamic analyses with similar shapes, the dynamic mode decomposition (DMD) analysis shows that the upper wing surface mode amplitudes and spanwise instability modes of the optimized design are weaker, and the fluctuations of the pressure are more stable. Therefore, DMD is suitable for refined shape optimization analyses.

Fluid mechanics is an important area where deep learning produces excellent results and can bring about scientific innovation because of its high dimensionality, significant nonlinearity, and ability to process an enormous amount of data. Deep learning technology is currently being used to study fluid mechanics, and its application potential is gradually being demonstrated. We propose a novel multi-resolution convolutional interaction network (MCIN), a hierarchical forecast framework based on a convolutional neural network. This structure can capture temporal dependencies at multiple temporal resolutions to enhance the forecasting performance of the original time series. The high-dimensional data of the flow around a cylinder is projected into a low-dimensional subspace using a variational autoencoder (VAE) as a nonlinear order-reduction technique. Then the data of the subspace are used as the input to MCIN to forecast future velocity fields. The proposed MCIN is compared to non-intrusive reduced-order models based on dynamic mode decomposition and long short-term memory, combined with a VAE. The results demonstrate that MCIN has superior stability to other models in forecasting the evolution of complicated fluid flows and has the potential to forecast a greater number of future outcomes.

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