The Multicell Volume of Fluid (MC-VOF) Method for the Free Surface Simulation of MFD Flows. Part I: Mathematical Model

This paper is the first part of a two-part paper which presents a simulation algorithm of unsteady, electromagnetically driven molten metal flows with free surfaces. At the free boundary, the variable space-distribution of the normal Lorentz forces is taken into account by proper computation of the electromagnetic field and pressure. For each calculation time step, a transport equation of the melt's volume is solved for multicell blocks and subsequently, the free surface is reconstructed by an inward gathering of the melt volume. Therefore, the free surface can be more accurately simulated with the following improvements: (1) Consideration of the normal electromagnetic force densities exerted on the melt surface. (2) Strictly volume conserving displacement of the free surface. (3) Absence of numerically created holes in the melt or of separated fluid droplets, respectively. Comparisons between computational and experimental results to verify the validity of the mathematical model will be presented in the second part of the paper.