## 4 Numerical Results
### Pollutant Transport in the Strait of Gibraltar  
The Strait of Gibraltar, located between Spain (north) and Morocco (south), links the Mediterranean Sea and the Atlantic Ocean. It has an approximate length of 60 km between its western section, Barbate-Tangier and its eastern section, Gibraltar-Sebta. Its width varies from a minimum of about 14 km in the section Tarifa-Punta Cires to a maximum of 44 km in the section Barbate-Tangier. The Strait of Gibraltar contains two large bays, the Bay of Algeciras, which is located in the east of the strait, and the Bay of Tangier, located in the west (see Figure 6).  
The Strait of Gibraltar is one of the most used maritime ways in the world. More than 100,000 merchant vessels transit the strait every year [34]. In particular, oil vessels pose a threat to the ecological safety of the strait due to the serious consequences of oil spills. Indeed, historically, the Strait of Gibraltar has witnessed several oil spill accidents, for example, the accident of the Sea Spirit on the western side of the Strait of Gibraltar in 1990, and the accident of the Fedra-Tawe in Algeciras Bay in 2008 [34]. This is all the more concerning since the Strait of Gibraltar serves as the conduit through which surface water flows from the Atlantic to the Mediterranean sea [35]. With this in mind, it is clear that protecting the environment of the strait is crucial. An understanding of the hydrodynamics and pollutant transport in the Strait of Gibraltar is essential for the construction of intervention strategies.  
In this study, the dynamics and transport of a pollutant plume in the Strait of Gibraltar are simulated numerically. The main objective is to test the ability of the LRBF method to handle the complexities of the Strait of Gibraltar, including geometric and topographic complexity.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**6 s**} & \multicolumn{2}{c}{**12 s**} & \multicolumn{2}{c}{**20 s**} \\  & \(\boldsymbol{L^{1}}\)**-Error** & **RMS Error** & \(\boldsymbol{L^{1}}\)**-Error** & **RMS Error** & \(\boldsymbol{L^{1}}\)**-Error** & **RMS Error** \\ \hline Roe-MUSCL & \(0.249\times 10^{-1}\) & \(0.546\times 10^{-2}\) & \(0.383\times 10^{-1}\) & \(0.800\times 10^{-1}\) & \(0.501\times 10^{-1}\) & \(0.101\times 10^{-1}\) \\ LRBF & \(0.385\times 10^{-2}\) & \(0.97\times 10^{-3}\) & \(0.746\times 10^{-2}\) & \(0.149\times 10^{-2}\) & \(0.126\times 10^{-1}\) & \(0.233\times 10^{-2}\) \\ \hline \end{tabular}
\end{table}
Table 1: Results for the accuracy of the pollutant advection example using the LRBF and finite volume methods.  
Figure 4: Pollutant concentration distribution in the channel at times \(t=0\) s, 6 s, 12 s, and 20 s.  
The bathymetry used in this simulation is shown in Figure 6. The Strait of Gibraltar has an irregular bathymetry, exceeding a depth of 800 m on the eastern coast. The hydrodynamics of the strait are generated through the open boundaries by a difference in water height, producing the main component of the \(M2\) tide [36]. The Spanish and Moroccan coasts are assumed to be impermeable; hence, a no-slip condition is used for the velocity field. The present study examines the effects of releasing a non-active pollutant at the inlet  
Figure 5: Cross-section of the pollutant concentration in the straits at times \(t=6\) s, 12 s, and 20 s at \(y=5\) m.  
Figure 6: Location (**left**) and bathymetry (**right**) of the Strait of Gibraltar with details showing the initial location of oil spills from the Sea Spirit, Fedra, and Tawe accidents (red circles).  
In Figure 10, we show a comparison of the evolution of the maximum concentration calculated by the LRBF method and the finite volume method featuring the Roe-MUSCL scheme. Under the conditions used, the meshless method clearly minimizes numerical dissipation, even over long periods.  
Figure 8: Velocity field of the flow in the Strait of Gibraltar.  
Figure 9: Position and concentration of the pollutant released in the Strait of Gibraltar at different times.