Abstract
In this paper, based on the reformulation of the Nernst–Planck equations, we construct an unconditionally stable semi-implicit linearized difference scheme for the time dependent Poisson–Nernst–Planck system. The method preserves several important physical laws at full discrete level without any constraints on the time step size, including: mass conservation, ion concentration positivity, free energy dissipation. The proposed method is a linearized method, which can be implemented efficiently. Furthermore, the method can be extended to the case of multi-ions without any difficulty. The paper ends with supporting numerical results which confirm well with theoretical findings.
Published Version
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