Both drift diffusion (DD) and the hydrodynamic (HD) models can be derived from the moments of the Boltzmann transport equation (BTE) using simplified approximation valid for long channel devices. The DD scheme is the most classical approach and usually solves the Poisson equation and the continuity equations for carriers considering the drift and diffusion components. In this approach, the charge transit time is assumed to be very large in comparison to the energy relaxation time. On the other hand, the HD method solves the DD scheme with the energy balance equations obtained from the moments of BTE. Thus, one may capture and calculate physical details such as carrier heating and the velocity overshoot effect. Needless to say, an accurate discretization method is required in HD simulation, since the governing equations are strongly coupled and one has to deal with larger number of variables compared to the DD scheme.