## 2 Materials and Methods
### Fluid-Structure Coupling Construction Method
#### 2.1.2 Fluid Model  
In this study, fluid models were utilized to simulate the behavior of liquids or gases in an air spring system. The fluid models can be broadly classified into hydraulic and pneumatic fluid models. Hydraulic fluid models were used to simulate the behavior of almost incompressible fluids, while introducing compressibility by assuming a linear relationship between pressure and volume. The required parameters for this model include the bulk modulus and reference density. Furthermore, the relationship between density and temperature can be simulated through the thermal expansion of the fluid. The reference density of the fluid \(\rho_{R}\) is obtained by considering the fluid density at zero pressure and the initial temperature \(\theta_{I}\). \[\rho_{R}=\rho(0,\theta_{I}) \tag{1}\]  
The compressibility of a fluid is described by a fluid volume model, which characterizes the relationship between the pressure and volume of the fluid, taking into account its thermodynamic properties and behavior under various conditions. The model considers the linear relationship between pressure and volume, and includes parameters such as bulk modulus and reference density, which are used to simulate the incompressible behavior of the fluid. Additionally, the thermal expansion of the fluid is also taken into account, and the relationship between density and temperature is established based on the fluid's initial temperature and pressure conditions. \[P=-K\bigg{(}\frac{V(P,\theta)-V_{0}(\theta)}{V_{0}(\theta_{I})}\bigg{)}\rho(0,\theta_{I})=-K\rho_{R}\Big{(}\rho^{-1}(P,\theta)-\rho_{0}^{-1}(\theta)\Big{)} \tag{2}\]  
where \(P\) represents the current pressure, \(\theta\) represents the current temperature, \(K\) represents the fluid bulk modulus, \(V=(P,\theta)\) represents the current volume, \(\rho(P,\theta)\) represents the density at pressure \(P\) and temperature \(\theta\), \(V_{0}(\theta)\) represents the volume under 0 pressure and temperature \(\theta\), \(V_{0}(\theta)\) represents the Volume at 0 pressure and initial temperature \(\theta\), and \(\rho_{0}(\theta)\) represents the density at 0 pressure and temperature \(\theta\). The coefficient of thermal expansion is a measure of the fractional change in fluid volume with respect to temperature. It is defined as the derivative of fluid volume with respect to temperature at a reference temperature, and is expressed as a function of temperature. This coefficient accounts for the change in fluid volume due to thermal expansion and is used to capture the temperature-dependent behavior of the fluid. The fluid volume change due to thermal expansion can be described by the coefficient of thermal expansion, which is defined as a function of temperature. The reference temperature, \(\theta_{0}\), is used to determine the average coefficient of thermal expansion, \(\alpha(\theta)\), which represents the total coefficient of expansion at the reference temperature. \[V_{0}(\theta)=V_{0}(\theta_{I})[1+3\alpha(\theta)(\theta-\theta_{0})-3\alpha (\theta_{I})(\theta_{I}-\theta_{0})] \tag{3}\]  
Figure 1: The flow cavity structure diagram. where \(\theta_{0}\) is the reference temperature of the coefficient of thermal expansion and \(\alpha(\theta)\) is the average coefficient of thermal expansion. When the coefficient of thermal expansion is constant, it is expressed as a function of fluid density alone, without the need for a reference temperature \(\theta_{0}\). In this case, the change in fluid volume due to thermal expansion can be described as a linear relationship between fluid density and temperature. \[\rho_{0}(\theta)=\rho_{R}/[1+3\alpha(\theta)(\theta-\theta_{0})-3\alpha(\theta _{I}-\theta_{0})] \tag{4}\]  
The compressible aerodynamic fluid model is based on an ideal gas, and the ideal gas equation is defined below.