**3. Numerical methods**

At each time step, the calculation involves separate calculations in the arc region and the metal region, the coupling of the two regions through the interface boundary conditions described in Sections 2.4 and 2.5, and updating the arc and metal regions after obtaining the new free surface using the VOF method, Eq. (12), in the metal region.

The arc plasma region uses a fully implicit formulation and an upwind scheme for the combined convection/diffusion coefficients, and the SIMPLE algorithm [65] for the velocity and temperature fields. The metal region uses the method developed by Torrey et al. [59] to calculate the velocity and temperature fields.

The computational domain is 5 cm in radius and 3.04 cm in length. A nonuniform grid sys‐ tem is used with finer meshes near the electrode tip, in the arc column and the weld pool, where a fine mesh of 0.01 cm is used. Time step size is set as 5 × 10−6 s for a stable numerical solution.
