# The Refined Simulation Methods of Fluctuating Wind and Aerodynamic Forces Relative to Moving Trains
## 1 Introduction
[13] simulate the flow features of a high-speed train in crosswinds using the CFD method, which is time-consuming compared with the simulation of fluctuating wind relative to a moving train by a theoretical method. The existing research mainly focuses on the conventional homogeneous and stationary wind environment, while the wind spectrum of moving trains in special wind environments has seldom been investigated. The wind loads on trains consist of lateral forces, lift forces, and torques according to the type of load, as the cross-section of the car body is like a rectangle. The torque caused by the wind is small and can usually be ignored [14]. The wind loads on trains can also be divided into static and fluctuating ones according to the action mechanism. Simulating the static wind loads of the moving train is relatively simple. In contrast, the simulation of the fluctuating wind loads is relatively complex, which should consider the aerodynamic coefficients and admittance functions of trains under different wind directions and attack angles [8]. For the convenience of engineering applications, only along-wind fluctuating winds have been considered in most of the previous research [15], which simplifies the mathematical expression of the fluctuating wind loads of the moving trains. However, only considering the along-wind fluctuating winds, the simulated fluctuating wind loads of trains are too great at high speed, which is inconsistent with the actual situations [8]. [PERSON] et al. [16] studied the unsteady crosswind forces of a moving train subjected to a three-dimensional stochastic wind field with longitudinal, lateral, and vertical turbulences, and then established a prediction model for train force coefficients using CFD simulated data. In the analysis of wind-vehicle-bridge system coupling vibration, [PERSON] et al. [17] investigate the effects of both along-wind and vertical fluctuating winds on the unsteady aerodynamic forces of trains. [PERSON] et al. [18] analyze the overturning risk of a moving train under lateral winds, accounting for the influence of both the along-wind and across-wind fluctuating winds. The unsteady aerodynamic force expressions of a moving train were derived by [PERSON] et al. [8] regarding all the along-wind, across-wind, and vertical fluctuating winds. The admittance function is a key parameter in the simulation of the unsteady aerodynamic force, which is related to the shape of the train and is impossible to obtain by theoretical derivation directly. Generally, it is obtained by methods such as wind tunnel tests. [PERSON] et al. [8]. tested the admittance function of a CRH train on a high embankment, and the results show that the amplitude of the admittance function is not equal to the theoretical value of 1.0 in the low-frequency range. In addition, it decays rapidly in the high-frequency segment. Therefore, taking the admittance function as 1.0 in traditional research is inappropriate. [PERSON] [15] presented a method to transform the amplitude of the simplified admittance function from the frequency domain into the time domain by the weighting function, and the phase characteristics of the admittance function are ignored. The admittance function is a complex function, meaning a phase difference exists between the lateral and lift forces. If the phase difference of the admittance function is ignored, the simulated wind loads of trains are entirely synchronized with the fluctuating wind, i.e., the lateral and lift forces reach the maximum value simultaneously. In that case, the resultant force acting on the train is overestimated, which causes a larger result in the calculation responses of trains. The situation is more evident for complex wind environments such as dangerous mountainous areas, as the aerodynamic phase difference of trains may be of great variance. Accurate simulation of fluctuating winds and aerodynamic forces on a moving train is the precondition for conducting research, such as evaluating the overturning risk of trains and wind-vehicle-bridge coupling vibration.