An Implicit-Explicit Runge-Kutta scheme for an extended hydrodynamic model describing charge transport in silicon semiconductors.

Abstract

Many applications involve hyperbolic systems of conservation laws with source terms. Solving numerically such systems is often challenging expecially when the source terms are stiff. We present here implicit-explicit (IMEX) Runge-Kutta schemes which are widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized partial differential equations (PDEs) of diffusion-convection type. The explicit part is treated by a strong-stability preserving (SSP) scheme, the implicit part is treated with a diagonally implicit Runge-Kutta (DIRK). These schemes avoid the onset of spuri- ous numerical oscillations arising near discontinuities of the solution. Here, an extended hydrodynamic model describing charge transport in semiconductors is considered, and applications to bulk silicon are presented.