Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. Firstly, this work proposes a Maxwell--Ampère Nernst--Planck (MANP) framework for the description of charge dynamics via concentrations and the electric displacement. We analysis the properties of the MANP formulation from several aspects. To deal with the curl-free constraint of electric field, the field (or displacement) from the Maxwell-Ampère equation is further updated with a local relaxation algorithm of linear computational complexity. Secondly, to obtain physically faithful numerical solutions, we develop a structure-preserving numerical method for the MANP model whose solution has several physical properties of importance.
