Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices (Q1316044)

The proposed method for solving the Boltzmann-Poisson system (modelling charge transport in semiconductor devices) is based on forward Euler time discretization and a general upwind scheme for dealing with the differential terms; the discretization is designed such that mass is conserved at each step. The method is closely related to the methods of \textit{A. J. Chorin} [Commun. Pure Appl. Math. 25, 171-186 (1972; Zbl 0226.65077)] and \textit{G. A. Sod} [Commun. Pure Appl. Math. 30, 391-419 (1977; Zbl 0336.65049)] for solving the Boltzmann equation for a steady shock wave. Numerical examples illustrate the reliability of the scheme.