Unconditional Positivity-Preserving and Energy Stable Schemes for a Reduced Poisson-Nernst-Planck System (Communications in Computational Physics, 2020)
The Poisson-Nernst-Planck (PNP) system is a widely accepted model forsimulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reducedPNP system, which can well approximate the three dimensional ion channel problem.Positivity of numerical solutions is proven to hold true independent of the size of timesteps and the choice of the Poisson solver. The scheme is easy to implement withoutresorting to any iteration method. Several numerical examples further confirm thepositivity-preserving property, and demonstrate the accuracy, efficiency, and robustness of the proposed scheme, as well as the fast approach to steady states.
Keywords: Biological channels; diffusion models; ion transport; positivity.