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Charge dynamics play essential role in many practical applications such assemiconductors, electrochemical devices and transmembrane ion channels. AMaxwell-Amp\`{e}re Nernst-Planck (MANP) model that describes charge dynamicsvia concentrations and the electric displacement is able to take effects beyondmean-field approximations into account. To obtain physically faithful numericalsolutions, we develop a structure-preserving numerical method for the MANPmodel whose solution has several physical properties of importance. By theSlotboom transform with entropic-mean approximations, a positivity preservingscheme with Scharfetter-Gummel fluxes is derived for the generalizedNernst-Planck equations. To deal with the curl-free constraint, the dielectricdisplacement from the Maxwell-Amp\`{e}re equation is further updated with alocal relaxation algorithm of linear computational complexity. We prove thatthe proposed numerical method unconditionally preserves the mass conservationand the solution positivity at the discrete level, and satisfies the discreteenergy dissipation law with a time-step restriction. Numerical experimentsverify that our numerical method has expected accuracy and structure-preservingproperties. Applications to ion transport with large convection, arising fromboundary-layer electric field and Born solvation interactions, furtherdemonstrate that the MANP formulation with the proposed numerical scheme hasattractive performance and can effectively describe charge dynamics with largeconvection of high numerical cell P\'{e}clet numbers.

Structure-preserving numerical method for Maxwell-Amp\`{e}re Nernst-Planck model