Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model

Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst-Planck (MANP) model that describes charge via concentrations the electric displacement is able to take effects beyond mean-field approximations into account. To obtain physically faithful numerical solutions, we develop a structure-preserving method for MANP whose solution has several physical properties of importance. By Slotboom transform with entropic-mean approximations, positivity preserving scheme Scharfetter-Gummel fluxes derived generalized equations. deal curl-free constraint, dielectric from equation further updated local relaxation algorithm linear computational complexity. We prove proposed unconditionally preserves mass conservation at discrete level, satisfies energy dissipation law time-step restriction. Numerical experiments verify our expected accuracy properties. Applications transport large convection, arising boundary-layer field Born solvation interactions, demonstrate formulation attractive performance can effectively describe convection high cell Péclet numbers.