On a viscous-hydrodynamic model for semiconductors: numerical simulation and stability analysis

We deal with a hydrodynamic model for semiconductors with a physical viscosity in the momentum/energy equations. The discretization uses a first-order finite difference scheme with upwinding based on the characteristic variables. We perform a stability analysis of the numerical method applied to a linearized incompletely parabolic system assuming vanishing viscosity in one space dimension although the analysis can be extended to the two dimensional case. A thorough numerical parametric study as a function of the heat conductivity and of the momentum viscosity is carried out in order to investigate their effect on the development of shocks in both one and two space dimensions. Received: 30 January 2001 / Accepted: 30 May 2001