Abstract: To develop a real-time mathematical model which can be valid ever at a transient state for simulating full continuous casting processes,a real-time simulation mathematical model of heat transfer and fluid flow was constructed considering turbulent flow on the basis of the arbitrary Lagrangian-Eulerian(ALE) algorithm and the Lam-Bremhorst low-Reynolds number k-ε formulation. By using this model,dynamic grids expansion under moving computational domains could be realized and the temperature field and fluid flow field could be simulated for the full process of steel continuous casting. As an example,the simulation results of X70 steel are in accordance with experimental measurements.