A dynamic mass transport method for Poisson-Nernst-Planck equations
arXiv:2205.01589 · doi:10.1016/j.jcp.2022.111699
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.
References in corpus (4)
- Ionic channels in biological membranes. Electrostatic analysis of a natural nanotube
- Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
- Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations
- An inverse averaging finite element method for solving the size-modified Poisson-Nernst-Planck equations in ion channel simulations