## 1 Introduction
[PERSON] [22] presented a numerical model to analyze the propagation of a wavefront along tunnels. Evolution experiments of the compression wave was tested at Euerwang tunnel in Germany [23], and the wave steepening was measured. [PERSON] [24] carried out field measurements in Shinkansen; the results showed that the compression wave with a waveform of pressure that has shallow valleys steepen more easily. [PERSON] [25] investigated the influence of ballast on the pressure gradient of the compression wave in railway tunnels based on actual vehicle tests, indicating that it has a relieving effect on the steepness of the compressive wave front. [PERSON] [26] studied the wavefront propagation using FVM methods, and the simulation demonstrated the presence of the most unfavorable tunnel length. [PERSON] [27] proposed a one-dimensional model to investigate the propagation process of compressed waves in the tunnel, then the wall friction and heat transfer effects were analyzed. When the compression wave propagates to the end of the tunnel, a part is released outside in the form of a pulse wave, forming the MPW. [PERSON] [28] performed a model experiment to investigate the impacts of the environment around the tunnel exit on the MPW, and a modification of a prediction model for MPW amplitude was made based on the experimental results. [PERSON] [29] conducted a serious of filed measurements to study the MPW and the transient pressure, which obtained the variation of the MPW with the position and train's speed. The mitigation methods of the MPW can be divided into two types, active and passive. The passive means reduces the MPW using a hood with the inside partition at the tunnel exit portal [30], while the active methods of alleviation are intended to generate pressure disturbances equal and opposite to the MPW that would exist in their absence [31]. In engineering practice, several opening holes with small aera can be set on the exit portal to reduce the MPW emitting from the tunnel. The entrance hood is a main approach to mitigating the MPW by delaying the rising time of the pressure, which is effective when the train speed is less than 350 km/h. With the continuous progress of high-speed railways, train speeds increase continuously. The experimental speed has reached Mach 0.5 [32], and the maximum speed of a single train in the tunnel reaches 403 km/h. It is difficult to satisfy the MPW mitigation requirement at the speed of 400 km/h or above solely using the entrance hood. The tunnel hoods in existing research mostly have top openings, which can cause difficulties in operation and maintenance under the influence of falling rocks and other factors, and can easily lead to safety issues. In addition, a double-track railway is usually used in current designs, so the entrance hood is located at the tunnel's exit when the train runs in reverse directions, the effects of which on the MPW are rarely reported. In summary, scholars have conducted extensive research on hoods at the tunnel entrance. Establishing a tunnel hood at the tunnel entrance can effectively alleviate micro-pressure waves, but it is difficult for the current tunnel hoods to meet the demand for mitigation at higher speeds, and there are many parameters that affect the tunnel hood. The numerical method is used to study the effects of the hood located at the entrance or exit of a tunnel on the compression wave and the MPW. Then, the influences of the cross-section area, oblique slope, and opening number of the hood are analyzed, and the optimum configuration of the hood installed in both the entrance and exit of the tunnel is also studied. The purpose of this study is to reduce the micro-pressure wave generated by trains entering tunnels at higher speeds, and to provide reference for the construction of tunnel hoods at speeds of 400 km/h or above.