## 3 Numerical Modelling Approach
### Detonation and Near-Field Blast Propagation (Stage 1)  
Cubic 3D domains were used to model detonation and subsequent blast wave propagation in the air. The simulations were conducted up to a distance of R \(<\) 0.15 m in the 75% scale setup and R \(<\) 0.2 m in the 100% scale setup. These distances corresponded to the blast wave propagation reaching the nearest reflective surface, which in this case was the corner side wall (Figure 4).  
\begin{table}
\begin{tabular}{l l l l l} \hline
**Sensor Model** & **Maximum Operating Pressure** & **Sensitivity** & **Allocated Gauge** \\ \hline PCB 113B28 [28] & 50 psi & 344 kPa & 100 mV/psi & B3 \\ \hline PCB 113B27 [29] & 100 psi & 689 kPa & 50 mV/psi & B1, B2 \\ \hline PCB 113B21 [30] & 200 psi & 1378 kPa & 25 mV/psi & A \\ \hline \end{tabular}
\end{table}
Table 1: Pressure instrumentation properties and experiment allocation.  
PE-4 material was specified at the centre of the domain containing elements of atmospheric air, such that the explosion and resulting shockwave propagated outwards from the centre. Cuboid charge geometries were specified to have an aspect ratio of 1:1:2, consistent with the experiments. For a specified density of 1601 kg/m\({}^{3}\) for PE-4, the 9 g charge had dimensions 14.1 \(\times\) 14.1 \(\times\) 28.2 mm, and the 21.3 g charge had dimensions 18.8 \(\times\) 18.8 \(\times\) 37.6 mm. Transmissive boundary conditions were assigned to all domain faces to allow air to exit after being accelerated by the shock wave. Default values for the PE-4 and air equations of state (EOS) were used in the computations and retrieved from the Viper::Blast library (Table 2). The Jones-Wilkins-Lee (JWL) EOS [34,35] was used to model the PE-4 material (Equation (3))  
\[p=a\bigg{(}1-\frac{\omega}{R_{1}V}\bigg{)}e^{-R_{1}V}+B\bigg{(}1-\frac{\omega} {R_{2}V}\bigg{)}e^{-R_{2}V}+\frac{\omega}{V}e \tag{3}\]  
In Equation (3), p denotes pressure, and V and e are the specific volume and specific internal energy of the explosive, respectively. Parameters A, B, R1, R2, and \(\omega\) are constants evaluated through experiments for any high-explosive material. For the PE-4 material, values for these parameters were taken from the Viper::Blast built-in material library is listed in Table 2.  
The air was modelled as an ideal gas EOS with an ambient pressure of 101.3 kPa by specifying the adiabatic constant, \(\gamma\) = 1.4, the air density, \(\rho\) = 1.225 kg/m\({}^{3}\), and the initial internal energy, e = 2.068 \(\times\) 10\({}^{5}\) kJ/kg (Table 2).  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Air** & **PE-4** \\ \hline Equation of State (EOS) & Ideal gas & JWL \\ \hline \multirow{4}{*}{Initial Conditions} & \(\gamma\) = 1.4 & A = 9.593 \(\times\) 10\({}^{5}\) MPa \\  & e = 2.068 \(\times\) 10\({}^{5}\) kJ/kg & B = 4.914 GPa \\ \cline{1-1}  & \(\rho\) = 2.068 \(\times\) 10\({}^{5}\) kJ/kg & R1 = 5.616 \\ \cline{1-1}  & \(\rho\) = 1.225 kg/m\({}^{3}\) & R2 = 1.804 \\ \cline{1-1}  & \(\omega\) = 0.136 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters used for modelling air and PE-4.  
Figure 4: A total of a 100% scale CFD model set up in Viper::Blast after remapping the initial 3D analysis in plain view (**left**) and elevation view (**right**).  
A JWL + afterburn solver modelled both the detonation of explosive material and subsequent shock wave propagation through the air. It includes a programmed burn model and a Jones-Wilkins-Lee (JWL) equation of state to enable modelling detonation of the charge and detonation products, along with an additional afterburn component. A cell size of 0.75 mm was specified as it was found to maximise the accuracy of the charge detonation and early blast wave propagation.  
CFD analyses for each cuboid charge mass (9 g and 21.3 g PE-4) were performed until the shock front propagated to the domain boundary, then saved as a 3D remap file for the initial conditions for subsequent 3D analyses.