Unconditional Positivity-Preserving and Energy Stable Schemes for a Reduced Poisson-Nernst-Planck System
Year: 2020
Author: Hailiang Liu, Wumaier Maimaitiyiming
Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1505–1529
Abstract
The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reduced PNP 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 time steps and the choice of the Poisson solver. The scheme is easy to implement without resorting to any iteration method. Several numerical examples further confirm the positivity-preserving property, and demonstrate the accuracy, efficiency, and robustness of the proposed scheme, as well as the fast approach to steady states.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0063
Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1505–1529
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Biological channels diffusion models ion transport positivity.