A Dynamic Mass Transport Method For Poisson-Nernst-Planck Equations
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.
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
Mathematics and Statistics
Keywords and Phrases
Energy dissipation; Optimal transport; PNP equations; Positivity; Wasserstein distance
International Standard Serial Number (ISSN)
Article - Journal
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15 Jan 2023