Solve SWE with the FV on Unstructured Grid

Solving Shallow Water Equation (SWE) with cell-centered Finite Volume Method on unstructured grid.

Shallow water equation:

$$\frac{\partial}{\partial t} \begin{bmatrix} h\\\ hv_x\\\ hv_y \end{bmatrix} + \frac{\partial}{\partial t} \begin{bmatrix} hv_x\\\ hv_x^2 + gh^2/2\\\ hv_xv_y \end{bmatrix} + \frac{\partial}{\partial t} \begin{bmatrix} hv_y\\\ hv_xv_y\\\ hv_y^2 + gh^2/2 \end{bmatrix} =0$$

Solving SWE using a FV method of Lax-Friedrichs type in 2D. Use perfect wall boundary condition.