In this study, we introduce a method that combines the characteristic method with the finite volume approach, termed the FVC scheme. Originally developed in its multidimensional form during the doctoral research of Ziggaf et al. \cite{Ziggaf}, our aim here is to adapt this scheme to unstructured hybrid meshes, focusing on the numerical simulation of the movement and dispersion of passive substances in natural aquatic environments, such as tracking the concentration of a pollutant in the sea (see, e.g.,\cite{Benkhaldoun,Vanzo}). This involves employing a coupled model that integrates shallow water equations (\ref{TrnsP1}) with a depth-averaged movement-dispersion equation (\ref{Diffusion}). Additionally, we have conducted a simulation in the Strait of Gibraltar to examine the dynamics and pathway of a solute introduced at the entrance of the strait\\[-0.3em] \begin{equation}\label{TrnsP1} \left\{ \begin{array}{ll} \displaystyle \partial_{t} h + \nabla \cdot (h\textbf{u}) = 0, \\[.11em] \displaystyle \partial_{t} h\textbf{u} + \nabla \cdot (h\textbf{u} \otimes\textbf{u}) + \frac{1}{2}\grad{(gh^2)} = -gh\grad{Z} - f_c \times h\textbf{u}^{\perp} - r(h,\textbf{u}) + \tau (h,\breve{\textbf{u}}). \end{array} \right. \end{equation} The unknowns are the water height $h(t,x,y) \geqslant 0$ and the average horizontal velocity $\textbf{u}(t, x, y)$. The pollutant transport and diffusion equation (\ref{TrnsP1}) is: \begin{equation}\label{Diffusion} \partial_{t} hC + \nabla \cdot (h\textbf{u}C) -\nabla\cdot (hD\nabla C) = hQ, \end{equation} where $C$ is the average concentration of the pollutant and $D$ is the diffusion coefficient. $Q$ represents the source of pollution, and the friction terms are $r(h,\textbf{u})$ and $\tau(h,\breve{\textbf{u}})$.