High-order Scharfetter-Gummel-based schemes and applications to gas discharge modeling

A generalized Scharfetter-Gummel method is proposed to construct the numerical flux for one-dimensional drift-diffusion equations. Instead of taking a constant approximation as Scharfetter and Gummel did in [1], we consider p-degree polynomial with p≥1. The high order moments approximating function serve intermediaries bring correction flux, that other end turns out be solution derivatives. Therefore, local reconstructions are required. resulting schemes discretize at same time convective diffusive fluxes without having employ separately different methods do so. new p=1 p=2 employed simulate atmospheric pressure discharge where they applied continuity equations electrons ions, solved simultaneously Poisson's equation. Numerical results indicate our robust highly accurate.