This axisymmetric finite element model takes into account the several contributions involved: electromagnetic interactions (Lorentz force, Joule heating), heat transfer (diffusion, convection, radiation...) and fluid flow (in the plasma and weld pool). The mass, momentum and energy conservation equations are coupled with the quasi-static Maxwell equations for the electromagnetic contribution calculations. The nonlinear problem is discretized by employing a classical Galerkin formulation excepted for the magnetic field computation where the Least Square Finite Element Method (LSFEM) is utilized. It permits, unlike conventional methods, to efficiently solve first order differential equations like Ampere's law.

Computational results are presented for a stationary argon arc at atmospheric pressure for various current intensity values and sulfur concentrations in the stainless steel workpiece. The free surface is considered to be spatially not deformable. The weld pool profiles, the predicted temperatures in the arc, current density and heat flux distributions at the anode surface are in agreement with experiments and literature results. The calculated convective flow in the weld pool is mainly dominated by the arc/plasma drag force and the Marangoni force when comparing to other forces : buoyancy force and electromagnetic force. Also, it is found that heating of the workpiece by thermal conduction and thermionic heating are about equal.