A coupled electrode-plasma-workpiece mathematical model was proposed to study the development of arc plasma channels and the formation of discharge craters. In order to avoid deviations caused by heat source empirical equations and discrepancies in energy distribution type, a reliable simulation based on equilibrium discharge conditions was utilized to reveal the arc discharging process. To better describe this coupled model, the basic theoretical analysis of arc discharging was first introduced, after which the multi-field coupling and governing equations of arc discharging model were studied. Based on the simulation results, researchers investigated the heat transferred from the arc plasma channel to the workpiece and electrode and obtained the arc plasma shape. The discharge crater on the workpiece and the electrode erosion process were also analyzed. Additionally, a single arc discharging experiment was conducted in order to verify the simulation results. The experiment results reflect that the arc plasma shape and discharge crater morphology fits with the simulation results. The comparison indicates that the coupled electrode-plasma-workpiece model was effective in analyzing the arc discharging process. (C) 2019 Published by Elsevier Ltd.