New approach for imposing the nonlinear floating potential boundary condition in the Poisson-continuity coupled system

Purpose The purpose of this study is to develop a new approach for simulating the ion flow field with the floating conductors based on the existing inversion method. Design/methodology/approach The space charge keeps charging the floating conductors until the dynamic balance is reached. The corresponding floating potential boundary condition is linearized as the combination of the equipotential constraints and natural boundary condition, which can be directly imposed in the inversion process. Findings The numerical results demonstrate that the modified inversion algorithm performs well in the ion flow field with the floating conductors and the floating potential converges within five steps' iterations. The proposed approach is applied to investigate the effect of the grounded line to the floating conductors in the practical high voltage direct current (HVDC) transmission lines. Originality/value The modified inverse algorithm provides a general way to deal with the Kapzov hypothesis and the floating boundary condition simultaneously within one loop, which can be applied to the multiphysics systems with different kinds of irregular boundary conditions.