A Vector Hamilton-Jacobi formulation of the Euler equations for fluids is studied numerically. The objective is to find the sentivity of a flow with respect to a parameter, which is solution of the linearized Euler equations with Dirac singularities in the initial conditions. A Hamilton-Jacobi formulation uses integral of the primitive variable so that Dirac singularities become shocks. It is shown here that there are vector Hamilton-Jacobi formulations for any vector conservation laws and that they can be simulated numerically. We discuss some links from a discrete point of view and show numerical results. Joint work with O. Pironneau