Numerical solutions of Euler–Poisson systems for potential flows

Steady-state Euler–Poisson systems for potential flows are studied here from a numerical point of view. The main idea is to use iterative schemes to solve a system of linear partial differential equations together with nonlinear algebraic equations instead of solving a fully nonlinear system of partial differential equations. We present two numerical schemes of finite volume type to compute approximate solutions of the systems for semiconductors in unipolar and bipolar cases. The numerical simulations are carried out in two space dimensions, in which some smallness conditions on given data and parameters in the proof of existence of solutions to the systems are clearly illustrated.