Solution of Turbulent Flow and Solidification in Continuous Casting of Round Steel Billets with a Meshless Method

Continuous casting is the most widely used process in the steelmaking industry. Understanding the physical phenomena and modeling them is essential for mitigating casting defects. This study uses a mixture-continuum formulation in axisymmetry to model this process computationally. A physical model incorporating coupled mass, momentum, and energy equations for solidification with melt turbulence was employed, assuming Newtonian, incompressible behavior and the k-epsilon turbulence model. The model provides insights into the thermo-fluid dynamics during solidification. For the numerical simulation, the Local Radial Basis Function Collocation Method (LRBFCM), a meshless approach, is utilized and compared against the more traditional Finite Volume Method (FVM). The results demonstrate that the meshless LRBFCM offers comparable accuracy and convergence to the FVM while reducing the computational complexity associated with mesh generation. These findings suggest that LRBFCM is a viable alternative for simulating complex metallurgical processes, such as continuous casting, with competitive performance.