Numerical results provided by simulating a fluid-flow equation with a discontinuous initial condition are reported within 1D geometry. Three different equations have been used: the linear advection equation, the nonlinear Burgers equation and the adiabatic Navier-Stokes 3 equation system. The numerical results are compared to analytical results got from the equivalent partial differential equation associated with the numerical method used. By doing so, the shape of the numerical result, diffusive or oscillating, the oscillation wavelength, the over/undershoot amplitude and damping of the parasitic oscillations are explained qualitatively and quantitatively. This allows to highlight the differences between the various numerical methods.