  We consider in this work the numerical resolution of a 2D shallow water
system with a Coriolis effect and bottom friction stresses on unstructured
meshes by a new Finite Volume Characteristics (FVC) scheme, which has been
introduced in the preliminary works that will be cited below. Our main goal is
to extend this approach to 2D unstructured formalism while preserving the
physical and mathematical properties of the system, including the C-property.
First, we present our extension by preserving the advantages of the finite
volume discretization such as conservation property and the method of
characteristics such as elimination of Riemann solvers. Afterward, an approach
was applied to the topography source term that leads to a well-balanced scheme
satisfying the steady-state condition of still water. A semi-implicit treatment
will also be presented in this study to avoid stability problems for the other
source terms. Finally, the proposed finite volume method is verified on several
benchmark tests and shows good agreement with analytical solutions and
experimental results; moreover, it gives a noticeable accuracy and rapidity
improvement compared to the original approaches.
