  A finite difference upwind discretization scheme in two dimensions is
presented in detail for the transient simulation of the highly coupled
non-linear partial differential equations of the full hydrodynamic model,
providing thereby a practical engineering tool for improved charge carrier
transport simulations at high electric fields and frequencies. The
discretization scheme preserves the conservation and transportive properties of
the equations. The hydrodynamic model is able to describe inertia effects which
play an increasing role in different fields of micro- and optoelectronics,
where simplified charge transport models like the drift-diffusion model and the
energy balance model are no longer applicable. Results of extensive numerical
simulations are shown for a two-dimensional MESFET device. A comparison of the
hydrodynamic model to the commonly used energy balance model is given and the
accuracy of the results is discussed.
