Dear FreeFem++ users,
Solving hyperbolic problem with FreeFem++ using finite volume method is still an open problem.
Recently, I find an approach in order to solve this problem on structured mesh. More precisely, we can define in FreeFem++ the quantity types of finite volume such as up-wind scheme, HLL flux, well balanced scheme with hydrostatic reconstruction that are used in the numerical resolution of the variational problem.
I applied this technic to the Shallow Water 2D equations as you can see in the following link: