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.

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