The behaviour of liquid slag in the mould is one of the key research areas of the continuous steel casting process. Numerical simulations of steel casting in the mould equipped with submerged entry nozzle, intended for slab casting, have been carried out within the study. For modelling the behaviour of the interfaces of the liquid steel - liquid slag - air system, the VOF method was employed. In the conducted simulations, seven different procedures for the discretization of the interface of individual phases were tested. The computation results have revealed that the “entrapment” of fine slag portions into liquid steel occurs in the system under investigation; the cause of this phenomenon is explicated by the Kelvin-Helmholtz theory.
 L.C. Hibbler, R. Liu, B.G. Thomas, Review of Mould Flux Entrainment Mechanisms and Model Investigation of Entrainment by Shear-Layer Instability, Proceedings 7th ECCC Conference, Dusseldorf (2011).
 M. Iguchi, J. Yoshida, T. Shimizu, Y. Mizuno, Model Study on the Entrapment of Mold Powder into Molten Steel, ISIJ International 40, 685-691 (2000).
 N. Kasai, M.Iguchi, Water-model Experiment on Melting Powder Trapping by Vortex in the Continuous Casting Mold 47, 982-987 (2007).
 A. Vakhrushev, M. Wu, A. Ludwig, G. Nitzl, Y. Tang, Gernot Hackl, Experimental Verification of a 3-Phase Continuous Casting Simulation Using a W ater Model, Proceedings 8th ECCC Conference, Graz (2014).
 K. Tsutsumi, K. Watanabe, M. Suzuki, M. Nakada, Effect of properties of mold powder entrapped in molten steel in a continuous casting process, The South African Institute of Mining and Metallurgy, 803-806 (2004).
 Y.S. Gutierrez-Montiel, R.D.Morales, Control of Meniscus Stability in Medium Thickness-straight Walls Slab Mould, ISIJ International 53, 230-239 (2013).
 P. Mishra, S.K. Ajmani, A. Kumar, K.K. Shrivastava, Review article on physical and numerical modelling of SEN and mould for continuous slab casting, International Journal of Engineering Science and Technology (IJEST) 4, 2234-2243 (2012).
 Z. Liu, M. Jiang, F. Tsukihashi, Euler-Euler-Lagrangian Modeling for Two-Phase Flow and Particle Transport in Continuous Casting Mold, ISIJ International 54, 1314-1323 (2014).
 GB.G. Thomas, Q. Yuan, S. Mahmood, R. Liu, R. Chaudhary, Transport and Entrapment of Particles in Steel Continuous Casting, Metallurgical and Materials Transactions B 45B, 22-35 (2014).
 Z. Liu, L. Li, F. Qi, B. Li, M. Jiang, F. Tsukihashi: Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach, Metallurgical and Materials Transactions B 46B, 406-420 (2014).
 P.E. Ramirez-Lopez, P.D. Lee, K.C. Mills, Explicit Modelling of Slag Infiltration and Shell Formation during Mould Oscillation in Continuous Casting, ISIJ International 50, 425-434 (2010).
 I.C. Ramos, R.D. Morales, S. Garcia-Hernandez, Effects of Immersion Depth on Flow Turbulence of Liquid Steel in Slab Mold Using a Nozzle with Upward Angle Rectangular Ports, ISIJ International 54, 1797-1806 (2014).
 A. Jonayat, B.G. Thomas, Transient Thermo-fluid Model of Meniscus Behavior and Slag Consumption in Steel Continuous Casting, Metallurgical and Materials Transactions B 45B, 1842-1864 (2014).
 M. Bielnicki, J. Jowsa, A. Cwudziński, Multiphase numerical model of molten steel and slag behavior in the continuous casting mould, Archives of Metallurgy and Materials 60, 257-262 (2015).
 C.W. Hirt, B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, Journal of Computational Physics 39, 201-225 (1981).
 V.V. Ranad,: Computational Flow Modeling for Chemical Reactor Engineering, Academic Press, New York (2002).
 W.F. Noh, P.R. Woodward, SLICK (Simple Line Interface Calculation, Lecture Notes in Physics 59, 330-360, (1976).
 D.L. Youngs, Time-dependent multi-material flow with large fluid distortion, Numerical Methods for Fluid Dynamics 273-285 (1982).
 O. Ubbink, R.I. Issa, Method for capturing sharp fluid interfaces on arbitrary meshes, J. Comput. Phys. 153, 26-50 (1999).
 S. Muzaferija, M. Peric, P. Sames, T. Schelin, A two-fluid Navier-Stokes solver to simulate water entry, Proc. Twenty- Second Symposium on Naval Hydrodynamics (1988).
 E. Olsson, G. Kreiss, A conservative Level Set method for two phase flow, J. Comput. Phys. 210, 225-246 (2005).
 O. Ubbink, Numerical prediction of two fluid systems with sharp interfaces, Thesis Ph.D., Imperial College London (1997).