Numerical solutions of a viscous-hydrodynamic model for semiconductors: the supersonic case
In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we consider the simulation of a one-dimensional n(+)-n-n(+) diode, whose solution exhibits at low temperatures strong discontinuities, and investigate the effect of the momentum viscosity on the shock waves. Numerical experiments, performed also on a two-dimensional test case, demonstrate that the numerical scheme, working on non-uniform grids, is suitable to describe solutions with strong variations in time and space. Well-posedness for the boundary conditions is discussed, and a linear stability estimate is established for the one-dimensional n(+)-n-n(+) diode benchmark problem.
hydrodynamics semiconductors finite differences