## 1 Introduction
[16] implemented a discontinuous Galerkin (DG) method for the solution of the one-dimensional equations of variable area flow to simulate the pressure wave generated by a train travelling through a tunnel. [PERSON] and [PERSON] [17] applied an approximate compact Green's function to calculate the compression wave from a train entering a tunnel. In addition, they proposed a new method that couples the Kirchhoff formulation with the Euler equation to solve the generation and propagation of the compression wave. Through the analogy of the pipeline flow model, [PERSON] and [PERSON] [18] established a calculation model for vehicle interior pressure by using pressure and time to reflect vehicle airtightness parameters, referred to as the flow model. [PERSON] et al. [19; 20] investigated the effect of pressure variation on discomfort for high-speed train passengers and acquired the continuous assessments of pressure events using sliders and retrospective assessments. [PERSON] and [PERSON] [21] presented a simple analytical model for the train-induced flow and its effects on pedestrians. The expressions developed for the induced air velocity and pressure on the pedestrian surface, as well as their dependence with time, were obtained from the unsteady potential theory. Moreover, aiming at the horizontal wind effect on the aerodynamic performance of coaxial tri-rotor vehicle, [PERSON] et al. [22] obtained the streamline distribution, pressure distribution, velocity contour and vortex distribution with different horizontal wind conditions throughout the numerical simulations. The change in the aerodynamic performance can be used for reference by the high-speed elevator car air pressure compensation research. The severe air pressure fluctuation in enclosed passenger compartments is prone to cause the issue of passenger discomfort, such as ear pressing. The air pressure compensation and control is significant to improve passenger comfort. Aimed at the problem of human ear discomfort caused by air pressure changes in elevator cars, [PERSON] [23] proposed a method to reduce the lifting speed as the lifting distance becomes longer to slow down the air pressure change. Hitachi Elevator Company invented an elevator car air pressure control device [24], which used a fan to fill or extract air into the car to control the pressure in the car to change according to the set air pressure curve. [PERSON] et al. [25] developed an air pressure control system to control air pressure inside elevator cars to a steady rate of change. Based on the Internet of Things (IoTs) big data, [PERSON] et al. [26] proposed an adaptive iterative learning control algorithm to restrain the pressure fluctuation in the train according to the quasi-periodicity and repeatability of mass data in the process of train running in tunnels. [PERSON] et al. [27] proposed a kind of digital pressure control project to solve the problem of pressure fluctuation inside the high-speed train carriage. [PERSON] and [PERSON] [28] established a fuzzy-PID controller to adjust the gain parameters of the Proportion Integral Differential (PID) by using the fuzzy algorithm, so as to better adjust the working frequency of the air-conditioning fan, and to restrain, in real-time, the transmission of pressure from the outside to the inside of the train. While the existing research on the law of change, adjustment, compensation and control of the air pressure of the high-speed elevator car has been scarce, the relative research methods of the high-speed train can be as references due to the similarity of operating status. When a high-speed elevator runs quickly in a narrow and long shaft, it will cause strong airflow disturbances and drastic air pressure changes, which will have a great impact on the stability and the ride comfort of the elevator.