Four different approaches were considered for modelling the electromagneticfields of high-intensity electric arcs: i) the three-dimensional model, ii) the twodimensionalaxi-symmetric model, iii) the electric potential formulation, and iv) themagnetic field formulation. The underlying assumptions and the differences betweenthese models are described in detail. Models i) to iii) reduce to the same limit for anaxi-symmetric configuration with negligible radial current density, contrary to modeliv). Models i) to iii) were retained and implemented in the open source CFD softwareOpenFOAM. The simulation results were first validated against the analytic solutionof an infinite electric rod. Perfect agreement was obtained for all the models tested.The electromagnetic models i) to iii) were then coupled with thermal fluid mechanicsin OpenFOAM, and applied to the calculation of an axi-symmetric Gas Tungsten ArcWelding (GTAW) test case with short arc (2mm) and truncated conical electrode tip.Models i) and ii) lead to the same simulation results, but not model iii). Model iii)is suited in the specific limit of long axi-symmetric arc, with negligible electrode tipeffect. For short axi-symmetric arc, the more general axi-symmetric formulation ofmodel ii) should instead be used.