A finite difference shock-capturing upwind discretization method in two dimensions is presented in detail for simulation of homogeneous and nonhomogeneous devices. The model is based on the solutions to the highly coupled nonlinear partial differential equations of the full hydrodynamic model. These solutions allow one to calculate the electron drift velocity and other device parameters as a function of the applied electric field. 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where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable.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 numerical simulations are shown for a two-dimensional SiC MESFET device, and are in fair agreement with other theoretical or experimental methods

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