# The Refined Simulation Methods of Fluctuating Wind and Aerodynamic Forces Relative to Moving Trains
## 1 Introduction  
In recent years, high-speed trains have become more sensitive to wind loads with the continuously increasing operation speed of railway trains and the development of lighter car bodies. Aerodynamic forces are becoming the main factor restricting trains' rising speed and safe operation [1]. Newly built railways in China extend to the dangerous western mountainous areas, where the wind fields are influenced by complex factors such as atmospheric circulation, mountainous terrain, and local environment temperature. The prominent features of the wind environment in mountainous areas are that it is inhomogeneous and non-stationary, with high wind speed and large wind attack angles, which is significantly different from the homogeneous and stationary wind environment in flat areas [2]. As high-speed trains pass through an inhomogeneous and non-stationary wind environment, the wind environment around moving trains changes with space andtime. The wind loads acting on moving trains present time-varying characteristics, which induce complicated train responses. Simulating fluctuating wind and aerodynamic forces relative to moving trains is the precondition to investigating the operation safety of trains under complex wind environments. At present, the simulation methods of fluctuating wind relative to moving trains could be approximately summarized into two categories. One approach is discretizing the spatially continuous natural wind field into a correlated finite-point wind field. As the train passes through the simulation point of the wind field, the wind speed value at the corresponding time of the simulation point is selected by the 'interpolation' method to construct the wind field relative to the moving train. This method is inefficient because it simulates many unused fluctuating winds. The application of 'interpolation' easily leads to a sudden change in the wind speed [3]. Another method directly simulates the fluctuating wind speed with the wind spectrum relative to moving trains, effectively improving the simulation efficiency. The wind spectrum relative to the moving train differs from that relative to the static position in space, which involves the natural wind environment, train speed, wind direction, and other influencing factors. [PERSON] [4] investigates the wind speed spectrum characteristics of a moving vehicle under turbulent crosswinds and proposes the approximate analytical expressions of the wind speed spectrum of a moving vehicle, which are inapplicable to wind environments characterized by inhomogeneity and non-stationarity. [PERSON] [5] and [PERSON] [6] successively establish the wind spectrum function of moving trains through theoretical derivation, which is suitable for specified environmental wind spectrums such as the von Karman spectrum. Based on the wind spectrum function relative to the moving train established by [PERSON], an approximate analytical expression of the wind spectrum for a moving train is proposed by [PERSON] et al. [7] using numerical fitting, which is suitable for the environmental Kaimal wind spectrum. [PERSON] et al. [8] further derive the fluctuating wind spectrum function suitable for any wind spectrum based on [PERSON]'s frozen turbulence hypothesis, but without considering inhomogeneous and non-stationary wind environments. [PERSON] et al. [9,10] successively propose the approximate analytical expressions of wind spectrum relative to a moving train based on the Kaimal spectrum by the numerical fitting method, which applies to stationary and non-stationary crosswind environments. [PERSON] et al. [11] test the fluctuating wind parameters of moving points in a wind tunnel, and the results show that the parameters of fluctuating wind appear to have significant differences between the moving points and the stationary points. [PERSON] et al. [12] and [PERSON] et al.