## 2 Simulation Model  
### Model Design  
When the explosive detonates in the center of the cabin, an arbitrary surface is chosen through the location of the explosion point to intersect, giving the 2D rectangular cross-sectional diagram shown in Figure 1. The dual study of the spread of shock waves on the cross-section and the convergence effect at the corners simplifies the calculation and has a general character. Another study [20] adopted the same method in determining the influential factors for implosion loads.  
Figure 2 shows the 2D schematic diagram used in the simulation model. Set wall A as the long side and wall B as the short side. The convergence phenomenon at the corners is studied on half of the cross-section, where a and b are halves of the long and short sides, respectively. The red line area in Figure 2 is the corner area, a square with side length b, and the angle between the shock front and the wall surface is \(\Phi\). Each side of the corner area is equally divided into 10 parts, and pressure measurement points are set at the intersections, giving a total of 121 side points arranged as shown in Figure 3.  
The simulation model was run using AUTODYN-2D. The eulerian unit was used for air and the explosives were packed into the air unit. The initial rigid boundary conditions in AUTODYN are adopted for the air boundary to establish a 2D symmetrical model, as shown in Figure 4. The finite element model uses 0.5 mm \(\times\) 0.5 mm mesh. Simulations were carried out using 0.5 mm, 1 mm, 2 mm, and 4 mm meshes for the shock wave of a  
Figure 1: Cross-section through the center of the cabin.  
Figure 3: Coordinate distribution of measurement points.  
Figure 2: Two-dimensional schematic diagram of the calculation model.  
100 g charge at 1 m, indicating that the simulation results converged when the mesh size was 0.5 mm, as shown in Figure 5. The ideal gas equation of state is used for air:  
\[P=(\gamma-1)\rho e \tag{1}\]  
where \(\gamma\), \(\rho\), and \(e\) are the specific heat capacity, density, and internal energy of the air, respectively, and the values used for the simulation are \(\gamma=1.4\), \(\rho=1.225\times 10^{-3}\) g/cm\({}^{3}\), and \(e=2.068\times 10^{5}\) J.  
The Jones-Wilkins-Lee (JWL) equation of state is used for the explosive:  
\[P_{T}=C_{1}\bigg{(}1-\frac{\omega}{r_{1}v}\bigg{)}e^{-r_{1}v}+C_{2}\bigg{(}1- \frac{\omega}{r_{2}v}\bigg{)}e^{-r_{2}v}+\frac{\omega e}{v} \tag{2}\]  
where \(C_{1}\), \(C_{2}\), \(r_{1}\), \(r_{2}\), and \(\omega\) are constants, \(P_{T}\), \(v\), and \(e\) are the pressure, relative volume, and initial energy, respectively. The specific parameters of trinitrotoluene (TNT) are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Density, \(\rho\) (kg/m\({}^{3}\))** & **Detonation Velocity, \(D\) (m/s)** & **C-J Pressure (Pa)** & \(C_{1}\) (Pa)** \\ \hline
1630 & 6800 & \(2.10\times 10^{10}\) & \(3.74\times 10^{11}\) \\ \hline \(C_{2}\) & \(r_{1}\) & \(r_{2}\) & \(\omega\) \\ \hline \(3.75\times 10^{9}\) & 4.15 & 0.9 & 0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of TNT in the JWL equation of state.  
Figure 4: Finite element simulation model diagram.  
Figure 5: Grid convergence checking.