Unconditional positivity-preserving and energy stable schemes for a reduced poisson-nernst-planck system

Author

Hailiang Liu
Wumaier Maimaitiyiming, Missouri University of Science and TechnologyFollow

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.

Recommended Citation

H. Liu and W. Maimaitiyiming, "Unconditional positivity-preserving and energy stable schemes for a reduced poisson-nernst-planck system," Communications in Computational Physics, vol. 27, no. 5, pp. 1505 - 1529, Global Science Press, May 2020.

The definitive version is available at https://doi.org/10.4208/CICP.OA-2019-0063

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant 1107291

Keywords and Phrases

Biological channels; Diffusion models; Ion transport; Positivity

International Standard Serial Number (ISSN)

1991-7120; 1815-2406

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Global Science Press, All rights reserved.

Publication Date

01 May 2020