In a first step, we consider the delicate problem of the derivation of positive, entropy preserving and wellbalanced scheme for the shallowwater model. Several schemes were recently proposed in the literature but, in general, the wellbalanced property just concerns the steady states at rest. Here, we derive a fully wellbalanced method able to exactly restore all the steady states (at rest or moving). In addition, the scheme is proved to be positive preserving and entropy stable. Next, we extend the wellbalanced schemes to approximate the weak solutions of more sophisticated models. In this talk, we will consider the Ripa model and the Euler equations with gravity potential. Now, the main difficulty stays in the formulation of the steady states of interest since they are governed by nonlinear PDE and explicit formulation cannot be reached. A suitable numerical scheme is thus derived, which is able to correctly approximate the steady states.
