A stable fixed point method for the numerical simulation of a kinetic collisional sheath

Abstract

This work introduces a numerical fixed point method to approximate the solutions of a Vlasov-Poisson-Boltzmann boundary value problem which arises when modeling a bi-species collisional sheath. Our method relies on the exact integration of the transport equations by means of the characteristic curves. A special care is given about the choice of a suitable phase space discretization together with the use of adequate quadrature formulas so as to ensure that the numerical fixed point method is stable. Numerical experiments are carried out in order to illustrate the effects of the various physical parameters that are in the scope of the analysis. Some results going beyond the scope of the analysis are also given.