<p>A multiphysics numerical model was developed to simulate nitrogen alloying during a laboratory-scale pressurized electroslag remelting (PESR) of high-nitrogen stainless steel. The model couples magnetohydrodynamic (MHD) flow, heat transfer, solidification, and species transport, including nitrogen absorption from Si₃N₄ additives fed onto the slag-free surface. Two additive feeding strategies, namely continuous and interrupted, were examined to evaluate their influence on nitrogen distribution during ingot growth. The results indicate that nitrogen transport is governed by the interaction between interfacial nitrogen transfer rate and convective mixing within the slag and melt pool. Lorentz-force-driven recirculation enhances nitrogen dissolution and lateral transport in the slag, while buoyancy-driven convection in the molten metal controls redistribution prior to solidification. Continuous feeding increases overall nitrogen uptake by sustaining a concentration gradient at the slag–metal interface, whereas interrupted feeding promotes partial homogenization but limits final nitrogen absorption. In both cases, incomplete mixing before solidification leads to spatial variations in nitrogen concentration. Results are validated against an experiment.</p>