## 2 Numerical Methods  
### Numerical Methods and Conditions  
We used the FLACS code ver. 20.2 of Gexcon [25]. We applied an unsteady, Reynolds-averaged Navier-Stokes (RANS) approach to the analysis of turbulent flow in a large space. The governing equations were the Favre-averaged mass conservation, momentum, energy, and species equations. The governing equations are solved with a finite volume method (FVM). The pressure and velocity are corrected by the SIMPLE method, and this can be applicable for compressible flows. The FLACS adopts the standard k-\(\varepsilon\) turbulence model for the simulation of turbulent flows and the EDC model for the combustion, respectively; the details have been published [25]. The simulated conditions were the same as those of the experimental TEST 1 and TEST 3 in terms of liquid hydrogen leakage, evaporation, and dispersion in the FFI report [17]. Liquid hydrogen was released vertically onto the ground at a height of 0.5 m with mass flow rates of 0.225 and 0.73 kg/s for 13 and 15 min, respectively, from a 1-inch-diameter pipe of a liquid hydrogen storage tank. Table 1 shows the release and weather conditions for each leakage case in the experiments. The computations were conducted using identical release and weather conditions to simulate the leakage of liquid hydrogen.  
Figure 1 shows a schematic of the computational domain, the location of leakage source, and the surroundings. The wind direction was defined by an angle \(\theta\) measured counterclockwise from the east. In Figure 1, \"\(\times\)\" sign indicates the location of hydrogen leakage; an ISO container of dimensions 13 \(\times\) 2.5 \(\times\) 5.2-m\({}^{3}\) served as an obstacle. The atmospheric pressures, ambient temperatures, and dry air consists of 21% oxygen and 79% nitrogen by volume were preset for the entire solution domain and Boundaries A to D. The wind speed and direction shown in Table 1 were also imposed to the Boundaries A to D. The temperature of ground surface was set to be the same as the ambient temperature. Apart from the initial state, there was no change in hydrogen concentration and vapor cloud temperature in the computational results as time progressed, and the computations were carried out up to 800 s for each leakage case.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Case**} & **Leaked Outflow** & **Tank Pressure** & **Wind Speed** & **Wind Direction,** & **Ambient** & **Weather Conditions** \\  & **Rate (kg/s)** & **(bary)** & **(m/s)** & **(dog)** & **Temperature (‘C)** & **Weather Conditions** \\ \hline
1 & 0.225 & 2 & 3.2 & 246 & 1.0 & overcast, rain prior to test \\ \hline
2 & 0.730 & 10 & 5.8 & 259 & 2.9 & overcast, rain prior to test \\ \hline \end{tabular}
\end{table}
Table 1: Conditions for liquid hydrogen release and weather [17].  
Figure 1: Schematic of the computational domain showing the geometries of the leak source, obstacle, and the surrounding environment.  
Liquid hydrogen was tank-stored at approximately 20 K; after leakage, it rapidly vaporized and dispersed. Thus, the phases of leaked hydrogen can be gas and liquid. The FLACS code simulates gaseous flow and liquid pool with pseudo-source model and liquid pool model, separately when hydrogen is released [25]. After the release of liquid hydrogen, a portion rapidly vaporizes, and the remaining liquid hydrogen forms a pool from which vapor emanates. To date, the physical models for gaseous release and liquid pool formation used in FLACS have not been rigorously validated for liquid hydrogen. Even models that can consider two-phase behavior, such as HEM, have been tested for liquid hydrogen leakage [22; 23], but they have not been implemented in FLACS. Thus, we utilized two distinct models: the pseudo-source model and the liquid pool model, as well as a hybrid model that considers both simultaneously, to simulate liquid hydrogen leaks. When using the pure pseudo-source model, all leaked hydrogen was assumed to be in a gaseous state.