A Dynamic Mass Transport Method For Poisson-Nernst-Planck Equations

Author

Hailiang Liu
Wumaier Maimaitiyiming, Missouri University of Science and TechnologyFollow

Abstract

A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type variational formulation naturally enforces solution positivity and the energy law as for the continuous PNP system. The fully discrete scheme is further formulated as a constrained minimization problem, shown to be solvable, and satisfy all three solution properties (mass conservation, positivity and energy dissipation) independent of time step size or the spatial mesh size. Numerical experiments are conducted to validate convergence of the computed solutions and verify the structure preserving property of the proposed scheme.

Recommended Citation

H. Liu and W. Maimaitiyiming, "A Dynamic Mass Transport Method For Poisson-Nernst-Planck Equations," Journal of Computational Physics, vol. 473, article no. 111699, Elsevier, Jan 2023.

The definitive version is available at https://doi.org/10.1016/j.jcp.2022.111699

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS1812666

Keywords and Phrases

Energy dissipation; Optimal transport; PNP equations; Positivity; Wasserstein distance

International Standard Serial Number (ISSN)

1090-2716; 0021-9991

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

15 Jan 2023