Nonoscillatory streamline upwind formulations for drift-diffusion equation

Several representative discretization schemes for the drift-diffusion (or convection-diffusion) equation are reviewed. After the discussion of the drawbacks being inherent in the previous approaches, a discretization method named NOSU (nonoscillatory streamline upwind) for the convection-diffusion equation is developed. The NOSU approach substantially eliminates the interior and boundary layer oscillations and efficiently reduces the crosswind effect. A popular discriminating test problem is analyzed with the present method and some previous approaches. The numerical results demonstrate the superiority of the present method over the previous approaches in accurately solving the convection-diffusion equation