Simplified calculation of molten metal free surfaces in electromagnetic fields Part I: Mathematical model

This is the first of a two-part paper which presents a simple simulation algorithm for an approximated free surface calculation of steady, electromagnetically driven molten metal flows. Based on a simplified treatment of the momentum equations, a Poisson equation is established by which the pressure can be calculated only based on the force density field. The free surface is determined by applying a linear pressure-dependant approximation for the melt volume contained in thfi surface cells. At the free boundary, also the normal force density is considered within a proper computation of the electromagnetic field and pressure. Using an iterative inward gathering of the melt volume, the free surface is reconstructed under strictly volume conserving conditions, without the numerical creation of unphysical holes in the melt or of separated fluid droplets, respectively. Comparisons of computational and experimental results for the verification of model validity will be presented in the second part of the paper.